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Masked smoothing using separable kernels for CT perfusion images

Masked smoothing using separable kernels for CT perfusion images Background: CT perfusion images have a high contrast ratio between voxels representing different anatomy, such as tissue or vessels, which makes image segmentation of tissue and vascular regions relatively easy. However, grey and white matter tissue regions have relatively low values and can suffer from poor signal to noise ratios. While smoothing can improve the image quality of the tissue regions, the inclusion of much higher valued vascular voxels can skew the tissue values. It is thus desirable to smooth tissue voxels separately from other voxel types, as has been previously implemented using mean filter kernels. We created a novel Masked Smoothing method that performs Gaussian smoothing restricted to tissue voxels. Unlike previous methods, it is implemented as a combination of separable kernels and is therefore fast enough to consider for clinical work, even for large kernel sizes. Methods: We compare our Masked Smoothing method to alternatives using Gaussian smoothing on an unaltered image volume and Gaussian smoothing on an image volume with vascular voxels set to zero. Each method was tested on simulation data, collected phantom data, and CT perfusion data sets. We then examined tissue voxels for bias and noise reduction. Results: Simulation and phantom experiments demonstrate that Masked Smoothing does not bias the underlying tissue value, whereas the other smoothing methods create significant bias. Furthermore, using actual CT perfusion data, we demonstrate significant differences in the calculated CBF and CBV values dependent on the smoothing method used. Conclusion: The Masked Smoothing is fast enough to allow eventual clinical usage and can remove the bias of tissue voxel values that neighbor blood vessels. Conversely, the other Gaussian smoothing methods introduced significant bias to the tissue voxels. Background SNR within tissue regions is relatively low. Spatial CT perfusion imaging uses many high resolution scans smoothing is often applied to trade high spatial reso- in a dynamic series to determine parametric image maps lution for improved SNR characteristics. However, regu- of Cerebral Blood Flow (CBF), Cerebral Blood Volume lar smoothing overestimates many tissue voxels due to (CBV), and Time to Peak (TTP), among other data nearby, high-valued vascular voxels. types. A characteristic of CT image volumes is the high While the importance of smoothing has been noted in contrast ratio of voxel intensity values located in skull the literature, it usually receives little discussion [2-4]. (or calcified regions) versus tissue regions, which can ex- Klotz and König gave a brief but important description ceed 15:1. Furthermore, with the injection of a tracer, of their smoothing method as a “running mean smooth- voxels representing vascular regions may have intensity ing procedure that operates separately on brain and vas- values greater than four times higher than neighboring cular pixels” [5] (pg 173). As such, their approach tissue regions. Kudo et al. demonstrated that the inclu- operated in 2D and avoided blurring from smoothing sion of vascular voxels could overestimate CBF [1]. The high valued vascular pixels into tissue regions. Our method also operates separately on brain and vascular pixels, however we use a Gaussian kernel. Furthermore, * Correspondence: dswack@buffalo.edu Dept. of Nuclear Medicine and Center for Positron Emission Tomography, our Masked Smoothing method can execute quickly, The University at Buffalo, State University of New York, Buffalo, NY, USA even when applied as 3D, by utilizing a combination of Full list of author information is available at the end of the article © 2014 Wack et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Wack et al. BMC Medical Imaging 2014, 14:28 Page 2 of 11 http://www.biomedcentral.com/1471-2342/14/28 separable kernels. This offers an improvement in execu- high valued vessel voxel. This inclusion will have a ten- tion time of a few orders of magnitude relative to what dency to artificially increase the smoothed value found could be achieved otherwise. at V from the true underlying tissue value. Our goal is A “separable” 3D smoothing kernel can be expressed to apply smoothing by only using voxels of like classes. as the outer product of three vectors, and 3D smoothing Excluding voxels of a different class could be achieved can be applied as three successive 1D smoothings in the by setting their weight values to zero, while rescaling the x, y, and z directions. While Gaussian kernels and mean weights of same class voxels so they sum to one. kernels are separable, they do not remain separable if We define sum of weights (SW) for V as the sum of they must exclude vascular voxels. Our method over- all weights of voxels that are both within the area of the comes this hurdle. smoothing kernel and the mask of the same tissue re- gion (without rescaling). SW will equal one if the all the Related methods voxels within the smoothing neighborhood of V are all Many smoothing methods are “adaptive” [6] and arrive of the same class as V . Otherwise SW will be less than at an optimal solution through the progressive refine- one. The reciprocal of SW (1/SW) can be used to rescale ment of an initial solution. Some methods preserve the weights so that they sum to one. edges [7,8], similar to our desire to separate vessel and Setting some weights to zero and rescaling the tissue voxels. Other methods consider the first or second remaining weights associated with each voxel within the spatial derivatives [9-12] or use the Discreet Cosine smoothing neighborhood of Vx is computationally cum- Transform [13]. A strength is these methods do not bersome. We can simplify the computation by making need a priori knowledge, such as voxel classifications [8]. two changes: 1) Rather than resetting the smoothing A 4D extension of bilateral filters varies the weight of kernel weight values of voxels outside of our tissue mask neighboring voxels according to distance and intensity, to zero, we instead set voxel values outside of our tissue or “similarity” differences [14,15], and has been applied mask to zero. 2) Rather than rescaling the individual to CT perfusion scans [16]. The TIPS (Time Intensity weights within our mask by 1/SW, we rescale the Profile Similarity) bilateral filter method [17] calculates weighted sum of voxel values by (1/SW), employing the the similarity of neighboring pixels across all image distributive property. That is, if SW is known for each frames. While this reduces processing time to some de- voxel, then smoothing the image with non-tissue voxels gree, the TIPS bilateral smoothing kernel is not strictly set to zero and dividing voxel by voxel by SW will result separable. While TIPS offers great flexibility in express- in the desired with-in class masked smoothing. Post- ing the smoothing formulation, its execution time [17], smoothing, non-tissue voxels can be set to zero, replaced even applied as a 2D filter, is much slower than what by their original values, or smoothed separately. can be achieved using separable 3D kernels. Fortunately, calculating SW for each tissue voxel is There are two advantages of CT perfusion imaging easy. SW for each tissue voxel is the result of applying over most other image smoothing problems. First, there the smoothing kernel to the binary mask that designates are multiple image volumes such that voxels in the same voxels classified as tissue with a 1 and non-tissue voxels spatial location will have the same classification. The with 0. This is true since the within-tissue class weights second is that there are extreme voxel intensity differ- get multiplied by the mask image value of one, whereas ences between voxels of different classifications for some the weights for voxels outside our mask are multiplied image volumes. While thresholding the mean image and by zero. Smoothing the binary image is then simply the the difference of the maximum and minimum images is sum of the weights that are within class, i.e. SW. While a simple but powerful way of identifying vascular voxels, we made the above argument for voxels classified as tis- more sophisticated methods have been presented for the sue, the same argument can be made in general for any identification of arteries and veins [18]. Hence Masked classification. Smoothing makes use of the easy access to a mask image To summarize, the smoothing process for a given of the tissue regions that adaptive smoothing or bilateral image, Im , is: 1) create an image mask, Msk, with 1 orig filters fail to utilize. values at voxel locations representing tissue, and 0 otherwise; 2) Create Im by setting all non-tissue masked Masked smoothing algorithm voxels of Im to zero; 3) Apply the desired smoothing orig Smoothing methods typically use a weighted sum of to Im and Msk, creating Sm(Im )and Sm masked masked voxels within the smoothing neighborhood of a given (Msk); 4) Create the “Masked Smoothing” image by set- tissue voxel, V , to assign a new value to V . The weights ting tissue voxels to the voxel-wise quotient Sm x x are all nonnegative and sum to one. The smoothing (Im )/Sm (Msk), and non-tissue voxels to their ori- masked neighborhood for a given tissue voxel will, in general, in- ginal values. By using a separable smoothing kernel in clude voxels of different segmentation classes–such as a Step 3) the Masked Smoothing method will be orders of Wack et al. BMC Medical Imaging 2014, 14:28 Page 3 of 11 http://www.biomedcentral.com/1471-2342/14/28 magnitude faster than directly using the 3D kernel for Smoothing can be used to separately smooth both the calculation. the object and object background. Masked smoothing assertions Simulation experiment We developed Masked Smoothing as an alternative to basic Parameters Gaussian smoothing, which we term “Simple Smoothing”, We created a simulated volume that included a tissue re- and a method where the vessel voxels are set to zero prior gion; a long thin vascular region, which could be varied in to smoothing in an attempt to minimize the impact on tis- intensity and width; and a border that was set to zero. The sue voxels, which we term “Removed Smoothing”.Webe- dimension of the simulated volume was 100×100×100, lieve that if Simple Smoothing, Removed Smoothing, and and used voxel sizes of 0.4 × 0.4 × 0.4 mm. Each simula- Masked Smoothing are used to process the same image, tion used the following parameters: then tissue voxels that neighbor vessel voxels will best maintain their true value with Masked Smoothing. Further- 1) Intensity ratio: The intensity ratio is the ratio more, we believe that the differences between smoothing between the value assigned to vascular voxels and methods can lead to meaningful consequences in the deter- the tissue region. The tissue value was set to 50. The mination of critical CT perfusion parameters. That is, if simulations used intensity ratios of: 2 to 1, 3 to 1, each smoothing method is applied to the individual time and 4 to 1, which correspond to vascular voxel frames of a CT perfusion scan, then tissue voxels that are values of 100, 150, and 200. located near vessel voxels will have significant and mean- 2) SNR: Gaussian noise was added to all simulation ingful differences in the resulting values of CBF, CBV and iterations. The standard deviation for the noise TTP depending on the smoothing method used. generator was set to 50, 25, and ~16.6, which corresponded to SNR values 1, 2, and 3 (lowest noise). Methods 3) Vessel width: Is the cross-sectional width of the The Masked Smoothing method was tested against two vascular region. Values used were: .8, 1.6, 2.4 mm. smoothing methods (Simple and Removed Smoothing) 4) Smoothing kernel –FWHM: The isotropic Gaussian that are similar, but which do not limit the smoothing to smoothing kernel size was set to Full Width Half tissue voxels. The smoothing methods were tested using Max (FWHM) values of 1, 2, and 4 mm. simulated data, phantom data, and anonymized CT per- fusion data from patients. The simulations provide a Iteration framework for determining the noise reduction and bias For each iteration of a simulation run: for each method. The phantom data allows us to test for bias using real scanner data. The CT perfusion data 1) The simulated volume was formed with intensity from 23 patients allows an assessment of the impact of values of tissue voxels set to 50. Vascular voxels bias caused by smoothing the CT Perfusion time series were selected according to “Vessel Width”, and images on the calculation of CBF, CBV, and TTP. assigned an intensity value according to the variable “Intensity Ratio”. Smoothing methods 2) Gaussian noise was added at a level determined by The three smoothing methods were implemented in the Signal to Noise Ratio (SNR), Figure 1, image a. Matlab (Mathworks, Natick, MA) using Gaussian smooth- 3) All three smoothing methods were applied. All ing kernels: methods used the same Gaussian kernel with the kernel size determined from the variable “Kernel 1) Simple Smoothing: The unmodified image volume is FWHM”, Figure 1, images b-d. smoothed using a Gaussian kernel. 4) The value at a tissue location located midway along, 2) Removed Smoothing: The vascular voxels are set to and directly next to, the vascular voxels was selected zero, and the image is smoothed as in (1) above. and the value with noise and smoothing applied was 3) Masked Smoothing: First, Simple Smoothing is recorded. Figure 2 shows the intensity profile for the performed on the binary tissue mask. Second, the different smoothing methods for a vertical line voxel-by-voxel ratio of the Removed Smoothing passing through the images of Figure 1. image and the smoothed tissue mask image (i.e. the result of the first step of this method) is returned as Assessment the Masked Smoothing image. Voxel values outside 500 iterations were used to determine the mean and of the tissue mask are assigned the original image standard deviation for a selected tissue voxel that neigh- value, except for the phantom experiment. We used bored the vessel voxels for different settings of parame- this case to also demonstrate that Masked ters. Since in-tissue values in all cases were set to 50, the Wack et al. BMC Medical Imaging 2014, 14:28 Page 4 of 11 http://www.biomedcentral.com/1471-2342/14/28 parameter set allowing for examination of deviation from the expected tissue value of 50 for each smooth- ing method. CT phantom experiment Thirty image volumes of a CT phantom were collected using a Phillips Gemini PET/CT; 0.5 mm thickness, 0 in- crement, 80 kV, 125 mAs, collimation: 32×1.25 l, rota- tion time: 0.5 sec, FOV 250, 512 matrix, with voxel size 0.49 × 0.49 × 0.5 mm. All three methods of smoothing, using a 5 × 5 × 5 mm Gaussian kernel, were applied to Figure 1 Simulation vessel with tissue background – raw and the first image volume. Additionally, the mean across smoothed images. Top Left rectangle is the raw image from the simulation. Top Right rectangle is of Simple Smoothing applied to images volumes was calculated, which was used as the the raw image. Bottom Left rectangle is of Removed Smoothing reference because of the reduced noise characteristics. applied to the raw image and the Bottom Right rectangle is of One slice is shown for each smoothing method, and the Masked Smoothing applied to the raw image. A smoothing kernel mean (Figure 3). Two lines were chosen that passed of 2 mm was used for each, with a vessel size of 2 mm and a raw through a large and small object identified on the CT. image Signal to Noise level of 2. The line profiles for these lines are shown in Figures 4 and 5. Finally a line of 41 pixels in length was identified calculated mean value from 500 iterations even if a high directly above of the larger object. The mean and stand- level of noise is added is expected to be very close to 50 ard deviation was calculated for this set of voxels across unless a bias is present. The four parameters (Intensity Ra- all 30 image volumes (i.e. 30 × 41 voxels), for the Simple tio, SNR, Vessel Width, and Smoothing Kernel FWHM) andMaskedsmoothing methods, andcomparedtothe were individually varied using the values given above for mean and standard deviation calculated from the each. When one parameter was varied the other values 41 voxels of the mean image. To demonstrate a vari- were set to default values (Intensity Ratio = 2 to 1, SNR = 2, ation from the simulation experiment, we performed Vessel Width = 1.6 mm, and FWHM = 2 mm). One masked smoothing, separately, to both the non-object simulation run (500 iterations) was performed for each region and object region. Figure 2 Vertical line profile for smoothing methods from Figure 1. The boundary and vessel voxels are identical for the Masked Smoothing and original values, since Masked Smoothing was only applied to the tissue values. The Simple and Removed smoothing methods had identical results except near the vessel voxels. The Simple Smoothing method over estimates the true value of the tissue near the vessel and underestimates the true value near the boundary. The Removed Smoothing methods underestimates the true value both near the boundary and vessel. For points away from both the boundary and vessel the three smoothing methods gave identical results. The smoothing kernel applied was 2 x 2 x 2 mm for all methods. Wack et al. BMC Medical Imaging 2014, 14:28 Page 5 of 11 http://www.biomedcentral.com/1471-2342/14/28 Influence of smoothing method on CBF, CBV, and TTP values Twenty-three CT perfusion studies were selected from the Neurosurgery department’s stroke research database, at the University at Buffalo. Each dataset consisted of nineteen CT perfusion volumes from a Toshiba Aquilion ONE, 320 slice scanner (with voxel sizes of .42×.42×.5 mm) which were collected from patients pre- senting with symptoms of a stroke. Images were converted from Dicom to NifTI format, and corrected for motion using SPM8 (www.fil.ion.ucl.ac.uk/spm). Image volumes were “skull striped”, and vascular voxels were identified using in-house software written in Matlab. The middle cerebral artery was automatically identified and a center portion was segmented and used for the arterial input function. A similar procedure was used to select the sagit- tal sinus, and these values were used to ensure the proper scaling of the arterial input function. A parametric image of CBF values was calculated using the maximum slope method, while a CBV image was calculated using the inte- Figure 3 Image slice from phantom study: raw, mean, and gral of tracer activity divided by the integral of arterial smoothed images. Top left image is a slice from the first of 30 activity. image volumes. Top right image is the mean of the same slice Tissue voxels immediately adjacent to a selected artery across all image volumes. Lower left image is the same slice as the were selected by performing a voxel-wise dilation of the upper left but with Gaussian smoothing applied. Lower right image is the same slice as the upper left but with Masked Smoothing applied. voxels representing a selected artery followed by an intersection with the tissue masks resulting in the elim- ination of the vascular voxels. For each smoothing method we calculated CBF, CBV, and TTP values for the selected neighboring tissue voxels, using a Gaussian ker- nel size of 4 × 4 × 4 mm, FWHM. Mean and voxel-wise Figure 4 Intensity profile for line passing through the large object seen in Figure 3. Simple Gaussian smoothing underestimates the raw values for the object, but overestimates the values neighboring the object. Values neighboring the object have a small increase in value, which is related to the underlying neighboring voxels being correlated as a result of the reconstruction process. Notice that Masked Smoothing was applied both to the background and the object. Wack et al. BMC Medical Imaging 2014, 14:28 Page 6 of 11 http://www.biomedcentral.com/1471-2342/14/28 Figure 5 Intensity profile for line passing through the small object seen in Figure 3. The line profile has similar behavior near the object as in Figure 4. Likewise, it can be seen that both smoothing methods give identical results away from the object. statistics were calculated to examine differences in CBF, intensity ratio was varied and the other variables were CBV, and TTP due to the smoothing method used. fixed, all smoothing methods provided over a 10 fold de- crease of the standard deviation (Table 1). For the Sim- ple Smoothing method the tissue mean increased with Ethics an increase in intensity of the neighboring vessel voxels. This project is approved by the University at Buffalo The Simple Smoothing method has a 100% increase Health Sciences Institutional Review Board. (bias) for the tissue mean for the highest level of vessel voxel intensity (4 to 1). The Removed Smoothing Results method showed a bias which lowered the value (~28% Simulation experiment decrease) and was unaffected by changes in the intensity Figure 2 displays line profiles, each corresponding to a of neighboring vessel voxels. The Masked Smoothing vertical line across each image of Figure 1, to demon- method did not show any significant bias in the calcula- strate the effects of the Simple, Removed, and Masked tion of the mean tissue value. The standard deviation Smoothing methods. resulting from the Removed Smoothing was slightly lower than the standard deviation of from the Simple Simulation experiment intensity ratio and Masked Smoothing approaches. Tissue mean and standard deviation results for different Intensity Ratios are provided in Table 1. When the Simulation experiment – SNR Table 1 Simulation—intensity ratio: mean values and Tissue mean and standard deviation results for different (standard deviation) SNRs are provided in Table 2. The Simple Smoothing Method\Intensity ratio 1.5 to 1 2 to 1 4 to 1 method showed an upward bias, while the Removed Noise – No smoothing 49.7 (25.1) 50.3 (25.0) 49.0 (25.7) Smoothing method exhibited a downward bias. The Simple smoothing 58.2 (1.6) 66.3 (1.6) 99.3 (1.7) biases were essentially identical for all three noise con- ditions. The standard deviation decreased with a de- Removed smoothing 33.6 (1.3) 33.5 (1.3) 33.5 (1.4) crease in the level of noise (increase of SNR) used in Masked smoothing 50.0 (1.9) 50.0 (1.9) 50.0 (2.1) the simulation for all smoothing methods. The standard As the ratio of the intensity of the arterial voxels compared to tissue voxels deviation was markedly smaller for all smoothing increased, the values from Masked Smoothing and Removed Smoothing held constant. However, the removed smoothing values were significantly reduced methods compared to the non-smoothed images. The compared to their true underlying value of 50. Masked Smoothing values were Masked Smoothingmethoddid not showabias in the equal to their true underlying value in all cases. Tissue voxels for the Simple Smoothing method increased with the increase in the arterial ratio. calculation of the mean tissue value. Wack et al. BMC Medical Imaging 2014, 14:28 Page 7 of 11 http://www.biomedcentral.com/1471-2342/14/28 Table 2 Simulation—SNR: mean values and (standard Table 4 Simulation—smoothing kernel FWHM: mean deviation) values and (standard deviation) Method\SNR 1 2 3 (least noise) Method\kernel FWHM 1 2 4 mm Noise – No smoothing 53.6 (49.0) 49.9 (27.1) 50.8 (16.9) Noise – No smoothing 51.7 (25.1) 49.9 (25.9) 50.0 (24.0) Simple smoothing 66.4 (3.3) 66.4 (1.6) 60.4 (1.1) Simple smoothing 64.6 (4.1) 66.4 (1.6) 60.4 (0.6) Removed smoothing 33.6 (2.6) 33.6 (1.3) 33.6 (0.8) Removed smoothing 35.7 (3.6) 33.6 (1.3) 39.6 (0.5) Masked smoothing 50.0 (3.9) 49.9 (1.9) 50.0 (1.3) Masked smoothing 50.2 (5.1) 50.0 (2.0) 50.0 (0.7) The standard deviation values were lower for low SNR than for high SNR. Only the Masked Smoothing method had mean values close to the true Standard deviation values were slightly poorer for the Masked Smoothing underlying value of 50. Standard deviation values decreased as the kernel method, which is explained by fewer voxels being averaged because size increased. non-tissue voxels were excluded. Phantom data experiment Simulation experiment: change of vessel diameter The line profiles passing through the small and large ob- Tissue mean and standard deviation results for different ject show that each smoothing method is essentially iden- vessel widths are provided in Table 3. When the width tical for voxels away from the object (Figures 4 and 5). of the simulated vessel increased, the Simple Smoothing However, where the profiles cross through the object, the method biased the mean tissue value to greater levels, Simple Smoothing method has significantly lower valued while the Removed Smoothing method biased the mean voxels than the reference, i.e. mean across all image vol- value to lesser values. The Masked Smoothing method umes. In contrast, for several voxels on either side of the did not show any bias associated with the mean tissue object, the Simple Smoothing method has higher intensity value. All smoothing methods greatly reduced the stand- values than the reference. The Masked Smoothing method ard deviation of the results. has values close to the reference both for voxels located within the object, and outside of the object. We notice that there are a few voxels at either side of the object Simulation experiment: change of smoothing kernel FWHM where the reference values lay between central values for The Simple Smoothing method yielded an upward bias for the object and background. This is an indication of the tissue mean values, while the Removed Smoothing method limitation in the scanner resolution and reflects partial yielded a downward bias. The magnitude of the bias de- volume and an inherent smoothness of the raw data. Simi- creased with increased filter size. Masked Smoothing dis- lar effects are seen for the line profile passing through the played no significant bias of the tissue mean value. For all smaller object. methods, the standard deviation of the smoothed tissue The mean and standard deviation for the 41 voxel line value decreased when the Smoothing Kernel FWHM in- parallel and adjacent to the large object, for all 30 collected creased. Mean and standard deviation values for our three image volumes was 6.90 (13.08) HU. With Simple Smooth- FWHM values and three smoothing methods is provided ing, using 5 × 5 × 5 mm Gaussian kernel, the mean in- in Table 4. creased to 29.78 HU, but the standard deviation decreased to 1.76. With the corresponding Masked Smoothing ap- plied the mean equaled 8.26 HU, i.e. much closer to the All reported biases original. Further, the standard deviation equaled 1.96 HU, For all simulations the number of iterations was 500, close to same value seen with Simple Smoothing. and the standard deviation was relatively small com- pared to the size of the bias. Hence, all biases reported Patient CT perfusion data – calculation of CBF, CBV, and above were strongly significant (p < 0.0001). TTP values The ROIs of the tissue voxel that neighbored vascular voxels, formed for each of the 23 datasets had a mean size Table 3 Simulation—vessel width: mean values and of 376,575 voxels, and was used for determining the mean (standard deviation) parameter values. The calculated values for CBF, CBV, Method\Vessel diameter 1 2 3 mm and TTP, for the three smoothing methods are reported in Noise – No smoothing 51.2 (26.0) 50.2 (24.5) 48.5 (25.5) Table 5. Mean values for CBV were greater than 50% Simple smoothing 61.3 (1.6) 66.5 (1.7) 68.6 (1.6) higher, and CBF were greater than 100% higher, for the Removed smoothing 38.8 (1.4) 33.6 (1.4) 31.6 (1.3) Simple Smoothing method than the Masked Smoothing Masked smoothing 50.0 (1.8) 50.1 (2.0) 50.1 (2.1) method. Mean values for both CBV and CBF were both Masked Smoothing is much closer to the true value of 50 than either of the more than 30% lower for the Removed Smoothing method other smoothing methods. The standard deviation values are markedly better than the Masked Smoothing method. The mean TTP for all smoothing methods than the No Smoothing data. A clear bias is evident for the Simple and Removed Smoothing methods. values for all smoothing methods were similar. Wack et al. BMC Medical Imaging 2014, 14:28 Page 8 of 11 http://www.biomedcentral.com/1471-2342/14/28 Table 5 Mean Parametric values for subjects’ CT not introduce bias (as opposed to the Removed and perfusion scan data Simple Smoothing methods), is easy to implement, and Method\Parameter CBF (ml/(cc x min)) CBV (ml/cc) TTP (min) executes fast enough to allow clinical use, we advocate its use over the other methods for the smoothing of CT per- Simple smooth 1.48 .112 .52 fusion images. Removed smooth .35 .029 .54 Masked smooth .67 .048 .54 Study design CBF and CBV values were higher and lower than would be expected We used simulated data to test the performance charac- physiologically for the Simple and Removed Smoothing methods, respectively. Time to Peak (TTP) values were similar for all methods. teristics of the three smoothing methods in situations where the smoothing neighborhood for a tissue voxel in- All voxel-by-voxel comparisons for CBF, CBV, and TTP cluded the much higher valued vessel voxels. In all simu- were significantly different (p < < .0001, paired t-test) for lations the tissue and vessel intensity values remained all pairwise comparisons of Simple Smoothing, Removed constant, allowing us to measure the effect of varying Smoothing, and Masked Smoothing methods, with the ex- vessel characteristics (both vessel size and tracer concen- ception of TTP calculated from Removed and Masked tration), the effect of varying SNR, and influence of the Smoothing. Identical results (voxel by voxel) were found smoothing kernel FWHM. Using phantom imaging we in comparing TTP calculated from volumes smoothed were able to further show potential biases caused by the with the Removed Smoothing and Masked Smoothing different smoothing methods. Using real world data methods. Despite finding a significant difference between from 23 patients, we also compared Simple, Masked, TTP calculated with Simple Smoothing and either Re- and Removed Smoothing to examine whether the theor- moved or Masked Smoothing, the magnitude of the differ- etical improvement seen on simulations can have a real ence was very small (1.14 seconds, while the time between life impact in the calculation of CBF, CBV, and TTP. volumes was 3 seconds). For illustration, we display the Using this approach we not only showed that Masked results of the three smoothing methods for one slice using Smoothing did not have the bias of the other methods, an 8 × 8 × 8 mm kernel (Figure 6). but we also demonstrated the large practical impact this Execution time of the Masked Smoothing method was has on determining physiological parametric images for 66 seconds for the 512×512×320×19 voxel CT perfusion CBF and CBV. image volume using a Gaussian Filter with size 2 × 2 × 2 mm FWHM, which required a 25 × 25 × 21 voxel ker- Change of intensity ratio/vessel width nel. Execution time using an 8 × 8 × 8 mm FWHM Our simulation experiments indicate that the Simple Gaussian filter, which required a kernel of 99×99×93 Smoothing method has a large upward bias for tissue voxels, was 81 seconds. Execution time was measured voxels surrounding a vessel that increases as the inten- using “tic” and “toc” Matlab functions, on a multi-user sity of the vessel voxel increases. By setting the vessel Dell PowerEdge R710 server with Dual 2.4 GHz proces- voxels to zero for the purpose of smoothing, the Re- sors, and 48 GB RAM. moved Smoothing method has a downward bias for tissue voxels neighboring a vessel voxel that is both fixed and in- Discussion dependent of the vessel voxel’s intensity level. The Masked Our simulation and phantom data show that the Simple Smoothing method avoided bias by compensating for vox- (i.e. ordinary Gaussian smoothing) and Removed Smooth- els set to zero. Increasing the vessel width increased the ing introduce a significant bias to tissue voxels that neigh- bias for the Simple Smoothing method, which reflects that bor vessels, whereas our Masked Smoothing method did a greater number of high intensity vessel voxels are within not introduce a bias. Our experiment using patient data the smoothing neighborhood of the tissue voxel. The Re- revealed that the bias of the Simple and Removed moved Smoothing method also increased its bias (down- Smoothing methods had a large impact on the calculation ward) with an increase in vessel size. This is reasonable, of CBF and CBV. The Removed Smoothing method had since for a given smoothing neighborhood the Removed the lowest values for CBF and CBV and were influenced Smoothing method would have a greater number of vas- by factoring in zero values in the place of neighboring vas- cular voxels set to zero as the vessel width increases. cular values. The Simple Smoothing method had in- Again, by compensating for voxels that were set to zero creased CBF and CBV values for tissue voxels that the Masked Smoothing method did not exhibit a bias. neighbor vessels that were not physiologically reasonable. The Masked Smoothing method had physiologically rea- Change of SNR/smoothing kernel FWHM sonable values for CBF and CBV, between the extremes All smoothing methods provided a large decrease in the returned by the Removed and Simple smoothing methods noise level. Increasing the noise level caused an increase (Table 5). Given that the Masked Smoothing method does in the standard deviation measured for all methods, but Wack et al. BMC Medical Imaging 2014, 14:28 Page 9 of 11 http://www.biomedcentral.com/1471-2342/14/28 Figure 6 Simple, Removed, and Masked Smoothing images, with sample line profile. Top row: Simple and Removed Smoothing images; Bottom row: Masked Smoothing image and the line profile of each along the line connecting the edge marks of the images. The line profile of the Masked Smoothing image preserves the high intensity value for a vessel that is crossed near the line center, whereas the peak is much smaller for the Simple Smoothing method, and smallest for the Removed Smoothing method. The Simple Smoothing method has much higher values around the peak, due to the smoothing of the vessel’s intensity into neighboring tissue. Along the right edge the Masked Smoothing method maintained the higher intensity values of the tissue, whereas the Simple and Removed Smoothing methods have lower values that are influenced by surrounding zero values. An 8x8x8 mm smoothing kernel was selected for this illustration to simplify the line profile. had no effect on the calculated mean value. Increasing the vessel, hence lessening the influence of the vessel it- the filter kernel for all methods reduced the measured self. As in all cases, the Masked Smoothing exhibited no standard deviation. Increasing the filter size from 1 mm significant bias. to 2 mm increased the bias for both Simple and Re- moved Smoothing. However, increasing the smoothing Influence of smoothing method on the calculation of CBF, kernel further to 4 mm resulted in the smallest bias. The CBV, and TTP change in bias reflects the weighted proportion of voxels Smoothing is a critical noise reduction pre-processing that are within the smoothing neighborhood. With the step prior to the calculation of physiologic parameters as 4 mm smoothing kernel, the smoothing is incorporating we have demonstrated previously using simulations a significant number of voxels from the “other-side” of [19-21]. The CBF and CBV derived from the Simple and Wack et al. BMC Medical Imaging 2014, 14:28 Page 10 of 11 http://www.biomedcentral.com/1471-2342/14/28 Removed Smoothing methods differed, approximately, Conclusion by a factor of four for tissue voxels close to vessels, thus We demonstrated that the Masked Smoothing method ex- demonstrating the critical importance of the smoothing ecutes rapidly and can readily integrate into existing method. The CBF and CBV values, calculated using the smoothing kernels. The Masked Smoothing method does Masked Smoothing method, were in-between and signifi- not introduce a bias in situations where nearby voxels cantly different from the other smoothing methods, and have a different classification and a large difference in in- closest to physiologically expected values. Since the tensity values. This accuracy, coupled with speed, gives the Masked Smoothing approach showed no bias on the simu- Masked Smoothing method the potential to significantly lated data, we believe these CBF and CBV values are the improve the clinical processing of perfusion imaging. most accurate. The TTP values for the Removed and Competing interests Masked Smoothing were identical because the time activ- The authors declare they have no competing interests. ity curves for a given voxel will only differ by a scaling multiple, and were close to the Simple Smoothing method. Authors’ contributions DSW developed the algorithm and developed software for the experiments. DSW and KFS drafted the manuscript. KFS, KVS, and AHS set criteria for and Filter selection identified appropriate scans for inclusion. All authors participated in the We used a Gaussian smoothing kernel for our implemen- experimental design, and have read and approved the final manuscript. tation because it is commonly used for medical images, Acknowledgements and allows for fast implementations because it is separ- The authors wish to thank Carmen Mieles, RTCT at WNY PET/CT, for her able. Our 3D execution times for an entire volume was technical expertise and assistance for the phantom data collection. significantly faster than a 2D TIPs bilateral filter on a sin- Author details gle slice. Klotz and König [5] also applied smoothing sep- Dept. of Nuclear Medicine and Center for Positron Emission Tomography, arately on brain and vascular voxels. Their approach used The University at Buffalo, State University of New York, Buffalo, NY, USA. multiple applications of a mean filter, whereas we utilized Dept. of Neurosurgery and Toshiba Stroke and Vascular Research Center, The University at Buffalo, State University of New York, Buffalo, NY, USA. a Gaussian kernel. Our approach would also work with School of Medicine, The University at Buffalo, State University of New York, mean filters, since they are also separable. There are very Buffalo, NY, USA. fast methods for implementing mean filters; and further- Received: 26 July 2013 Accepted: 7 August 2014 more, multiple passes of a mean filter can be used to ap- Published: 21 August 2014 proximate a Gaussian filter. However, internal timings during development favored our approach. References 1. Kudo K, Terae S, Katoh C, Oka M, Shiga T, Tamaki N, Miyasaka K: Quantitative cerebral blood flow measurement with dynamic perfusion CT using the Segmentation and segmentation vascular-pixel elimination method: comparison with H215O positron The Masked Smoothing method assumes that satisfac- emission tomography. AJNR Am J Neuroradiol 2003, 24(3):419–426. tory segmentation is available. However, if the thickness 2. König M, Bültmann E, Bode-Schnurbus L, Koenen D, Mielke E, Heuser L: Image quality in CT perfusion imaging of the brain. Eur Radiol 2007, between planes is high then partial volume effects may 17(1):39–47. hinder segmentation. If a vessel voxel were to be classi- 3. Kudo K, Sasaki M, Yamada K, Momoshima S, Utsunomiya H, Shirato H, fied as a tissue voxel, then neighboring tissue voxels will Ogasawara K: Differences in CT Perfusion Maps Generated by Different Commercial Software: Quantitative Analysis by Using Identical Source be biased upward, especially as the tracer concentration Data of Acute Stroke Patients1. Radiology 2010, 254(1):200. peaks in the vessel. However, this bias cannot exceed the 4. Sasaki M, Kudo K, Oikawa H: CT perfusion for acute stroke: current concepts bias from using Simple Smoothing. Because of the quan- on technical aspects and clinical applications. Elsevier; 2006:30–36. 5. Klotz E, Konig M: Perfusion measurements of the brain: using dynamic CT titation, some voxels partially represent both underlying for the quantitative assessment of cerebral ischemia in acute stroke. Eur tissue and vessel. This is not a problem in practice. If J Radiol 1999, 30(3):170–184. this voxel is excluded, the estimate for a nearby tissue 6. Saint-Marc P, Chen J, Medioni G: Adaptive smoothing: a general tool for early vision. IEEE Trans Pattern Anal Mach Intell 1991, 13(6):618–624. voxel proceeds without using the value. If the voxel is 7. Nagao M, Matsuyama T: Edge preserving smoothing. Computer graphics included, then a neighboring voxel may be biased and image processing 1979, 9(4):394–407. upward, but the effect will be minimal since the voxel 8. Fang M, Qian J: Adaptive edge-preserving smoothing filter. In Google Patents. 1998. US Patent: 08/672,194, Publication date: June 23. partially represents tissue and thus will not reach espe- 9. Alvarez L, Guichard F, Lions PL, Morel JM: Axioms and fundamental cially high intensity levels. This is similar to the situation equations of image processing. Archive for rational mechanics and analysis seen with the phantom data, where the mean of the raw 1993, 123(3):199–257. 10. Alvarez L, Lions PL, Morel JM: Image selective smoothing and edge data shows a gradual increase to the higher intensity detection by nonlinear diffusion. II SIAM Journal on numerical analysis object. In this case the Masked Smoothing best approxi- 1992, 29(3):845–866. mated the best estimate of the true value found by cal- 11. Angenent S, Pichon E, Tannenbaum A: Mathematical methods in medical image processing. Bulletin of the American Mathematical Society 2006, culating the mean across 30 image volumes. Finally, our 43(3):365–396. method allows both the arterial and tissue regions to be 12. Chan TF, Shen J, Vese L: Variational PDE models in image processing. smoothed separately. Notices AMS 2003, 50:14–26. Wack et al. BMC Medical Imaging 2014, 14:28 Page 11 of 11 http://www.biomedcentral.com/1471-2342/14/28 13. Garcia D: Robust smoothing of gridded data in one and higher dimensions with missing values. Computational Statistics & Data Analysis 2010, 54(4):1167–1178. 14. Paris S, Durand F: A fast approximation of the bilateral filter using a signal processing approach. International Journal of Computer Vision 2009, 81(1):24–52. 15. Paris S, Kornprobst P, Tumblin J: Bilateral filtering. Theory and applications, Foundations and Trends in Computer Graphics and Vision 2009, 4(1):1–73. 16. Mendrik A, Vonken E, Dankbaar JW, Prokop M, Van Ginneken B: Noise filtering in thin-slice 4D cerebral CT perfusion scans. SPIE Proceedings; 2010. 17. Mendrik AM, Vonken E, van Ginneken B, de Jong HW, Riordan A, van Seeters T, Smit EJ, Viergever MA, Prokop M: TIPS bilateral noise reduction in 4D CT perfusion scans produces high-quality cerebral blood flow maps. Phys Med Biol 2011, 56:3857. 18. Mendrik A, Vonken E, van Ginneken B, Smit E, Waaijer A, Bertolini G, Viergever MA, Prokop M: Automatic segmentation of intracranial arteries and veins in four-dimensional cerebral CT perfusion scans. Med Phys 2010, 37:2956. 19. Fisher J: Improvements in Computed Tomography Perfusion Output using Complex Singular Value Decomposition and the Maximum Slope Algorithm. Master’s Thesis, Boston University, School of Medicine; 2014. 20. Wack DS, Badgaiyan RD: Complex singular value decomposition based noise reduction of dynamic PET images. Current Medical Imaging Reviews 2011, 7(2):113–117. 21. Snyder K, Seals K, Wack D: Using simulations to explore the characteristics of CT perfusion calculations in the assessment of stroke. Current Medical Imaging Reviews 2014, 10(3). In press. doi:10.1186/1471-2342-14-28 Cite this article as: Wack et al.: Masked smoothing using separable kernels for CT perfusion images. BMC Medical Imaging 2014 14:28. 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Masked smoothing using separable kernels for CT perfusion images

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Springer Journals
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Copyright © 2014 by Wack et al.; licensee BioMed Central Ltd.
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Medicine & Public Health; Imaging / Radiology
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1471-2342
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10.1186/1471-2342-14-28
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25145879
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Abstract

Background: CT perfusion images have a high contrast ratio between voxels representing different anatomy, such as tissue or vessels, which makes image segmentation of tissue and vascular regions relatively easy. However, grey and white matter tissue regions have relatively low values and can suffer from poor signal to noise ratios. While smoothing can improve the image quality of the tissue regions, the inclusion of much higher valued vascular voxels can skew the tissue values. It is thus desirable to smooth tissue voxels separately from other voxel types, as has been previously implemented using mean filter kernels. We created a novel Masked Smoothing method that performs Gaussian smoothing restricted to tissue voxels. Unlike previous methods, it is implemented as a combination of separable kernels and is therefore fast enough to consider for clinical work, even for large kernel sizes. Methods: We compare our Masked Smoothing method to alternatives using Gaussian smoothing on an unaltered image volume and Gaussian smoothing on an image volume with vascular voxels set to zero. Each method was tested on simulation data, collected phantom data, and CT perfusion data sets. We then examined tissue voxels for bias and noise reduction. Results: Simulation and phantom experiments demonstrate that Masked Smoothing does not bias the underlying tissue value, whereas the other smoothing methods create significant bias. Furthermore, using actual CT perfusion data, we demonstrate significant differences in the calculated CBF and CBV values dependent on the smoothing method used. Conclusion: The Masked Smoothing is fast enough to allow eventual clinical usage and can remove the bias of tissue voxel values that neighbor blood vessels. Conversely, the other Gaussian smoothing methods introduced significant bias to the tissue voxels. Background SNR within tissue regions is relatively low. Spatial CT perfusion imaging uses many high resolution scans smoothing is often applied to trade high spatial reso- in a dynamic series to determine parametric image maps lution for improved SNR characteristics. However, regu- of Cerebral Blood Flow (CBF), Cerebral Blood Volume lar smoothing overestimates many tissue voxels due to (CBV), and Time to Peak (TTP), among other data nearby, high-valued vascular voxels. types. A characteristic of CT image volumes is the high While the importance of smoothing has been noted in contrast ratio of voxel intensity values located in skull the literature, it usually receives little discussion [2-4]. (or calcified regions) versus tissue regions, which can ex- Klotz and König gave a brief but important description ceed 15:1. Furthermore, with the injection of a tracer, of their smoothing method as a “running mean smooth- voxels representing vascular regions may have intensity ing procedure that operates separately on brain and vas- values greater than four times higher than neighboring cular pixels” [5] (pg 173). As such, their approach tissue regions. Kudo et al. demonstrated that the inclu- operated in 2D and avoided blurring from smoothing sion of vascular voxels could overestimate CBF [1]. The high valued vascular pixels into tissue regions. Our method also operates separately on brain and vascular pixels, however we use a Gaussian kernel. Furthermore, * Correspondence: dswack@buffalo.edu Dept. of Nuclear Medicine and Center for Positron Emission Tomography, our Masked Smoothing method can execute quickly, The University at Buffalo, State University of New York, Buffalo, NY, USA even when applied as 3D, by utilizing a combination of Full list of author information is available at the end of the article © 2014 Wack et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Wack et al. BMC Medical Imaging 2014, 14:28 Page 2 of 11 http://www.biomedcentral.com/1471-2342/14/28 separable kernels. This offers an improvement in execu- high valued vessel voxel. This inclusion will have a ten- tion time of a few orders of magnitude relative to what dency to artificially increase the smoothed value found could be achieved otherwise. at V from the true underlying tissue value. Our goal is A “separable” 3D smoothing kernel can be expressed to apply smoothing by only using voxels of like classes. as the outer product of three vectors, and 3D smoothing Excluding voxels of a different class could be achieved can be applied as three successive 1D smoothings in the by setting their weight values to zero, while rescaling the x, y, and z directions. While Gaussian kernels and mean weights of same class voxels so they sum to one. kernels are separable, they do not remain separable if We define sum of weights (SW) for V as the sum of they must exclude vascular voxels. Our method over- all weights of voxels that are both within the area of the comes this hurdle. smoothing kernel and the mask of the same tissue re- gion (without rescaling). SW will equal one if the all the Related methods voxels within the smoothing neighborhood of V are all Many smoothing methods are “adaptive” [6] and arrive of the same class as V . Otherwise SW will be less than at an optimal solution through the progressive refine- one. The reciprocal of SW (1/SW) can be used to rescale ment of an initial solution. Some methods preserve the weights so that they sum to one. edges [7,8], similar to our desire to separate vessel and Setting some weights to zero and rescaling the tissue voxels. Other methods consider the first or second remaining weights associated with each voxel within the spatial derivatives [9-12] or use the Discreet Cosine smoothing neighborhood of Vx is computationally cum- Transform [13]. A strength is these methods do not bersome. We can simplify the computation by making need a priori knowledge, such as voxel classifications [8]. two changes: 1) Rather than resetting the smoothing A 4D extension of bilateral filters varies the weight of kernel weight values of voxels outside of our tissue mask neighboring voxels according to distance and intensity, to zero, we instead set voxel values outside of our tissue or “similarity” differences [14,15], and has been applied mask to zero. 2) Rather than rescaling the individual to CT perfusion scans [16]. The TIPS (Time Intensity weights within our mask by 1/SW, we rescale the Profile Similarity) bilateral filter method [17] calculates weighted sum of voxel values by (1/SW), employing the the similarity of neighboring pixels across all image distributive property. That is, if SW is known for each frames. While this reduces processing time to some de- voxel, then smoothing the image with non-tissue voxels gree, the TIPS bilateral smoothing kernel is not strictly set to zero and dividing voxel by voxel by SW will result separable. While TIPS offers great flexibility in express- in the desired with-in class masked smoothing. Post- ing the smoothing formulation, its execution time [17], smoothing, non-tissue voxels can be set to zero, replaced even applied as a 2D filter, is much slower than what by their original values, or smoothed separately. can be achieved using separable 3D kernels. Fortunately, calculating SW for each tissue voxel is There are two advantages of CT perfusion imaging easy. SW for each tissue voxel is the result of applying over most other image smoothing problems. First, there the smoothing kernel to the binary mask that designates are multiple image volumes such that voxels in the same voxels classified as tissue with a 1 and non-tissue voxels spatial location will have the same classification. The with 0. This is true since the within-tissue class weights second is that there are extreme voxel intensity differ- get multiplied by the mask image value of one, whereas ences between voxels of different classifications for some the weights for voxels outside our mask are multiplied image volumes. While thresholding the mean image and by zero. Smoothing the binary image is then simply the the difference of the maximum and minimum images is sum of the weights that are within class, i.e. SW. While a simple but powerful way of identifying vascular voxels, we made the above argument for voxels classified as tis- more sophisticated methods have been presented for the sue, the same argument can be made in general for any identification of arteries and veins [18]. Hence Masked classification. Smoothing makes use of the easy access to a mask image To summarize, the smoothing process for a given of the tissue regions that adaptive smoothing or bilateral image, Im , is: 1) create an image mask, Msk, with 1 orig filters fail to utilize. values at voxel locations representing tissue, and 0 otherwise; 2) Create Im by setting all non-tissue masked Masked smoothing algorithm voxels of Im to zero; 3) Apply the desired smoothing orig Smoothing methods typically use a weighted sum of to Im and Msk, creating Sm(Im )and Sm masked masked voxels within the smoothing neighborhood of a given (Msk); 4) Create the “Masked Smoothing” image by set- tissue voxel, V , to assign a new value to V . The weights ting tissue voxels to the voxel-wise quotient Sm x x are all nonnegative and sum to one. The smoothing (Im )/Sm (Msk), and non-tissue voxels to their ori- masked neighborhood for a given tissue voxel will, in general, in- ginal values. By using a separable smoothing kernel in clude voxels of different segmentation classes–such as a Step 3) the Masked Smoothing method will be orders of Wack et al. BMC Medical Imaging 2014, 14:28 Page 3 of 11 http://www.biomedcentral.com/1471-2342/14/28 magnitude faster than directly using the 3D kernel for Smoothing can be used to separately smooth both the calculation. the object and object background. Masked smoothing assertions Simulation experiment We developed Masked Smoothing as an alternative to basic Parameters Gaussian smoothing, which we term “Simple Smoothing”, We created a simulated volume that included a tissue re- and a method where the vessel voxels are set to zero prior gion; a long thin vascular region, which could be varied in to smoothing in an attempt to minimize the impact on tis- intensity and width; and a border that was set to zero. The sue voxels, which we term “Removed Smoothing”.Webe- dimension of the simulated volume was 100×100×100, lieve that if Simple Smoothing, Removed Smoothing, and and used voxel sizes of 0.4 × 0.4 × 0.4 mm. Each simula- Masked Smoothing are used to process the same image, tion used the following parameters: then tissue voxels that neighbor vessel voxels will best maintain their true value with Masked Smoothing. Further- 1) Intensity ratio: The intensity ratio is the ratio more, we believe that the differences between smoothing between the value assigned to vascular voxels and methods can lead to meaningful consequences in the deter- the tissue region. The tissue value was set to 50. The mination of critical CT perfusion parameters. That is, if simulations used intensity ratios of: 2 to 1, 3 to 1, each smoothing method is applied to the individual time and 4 to 1, which correspond to vascular voxel frames of a CT perfusion scan, then tissue voxels that are values of 100, 150, and 200. located near vessel voxels will have significant and mean- 2) SNR: Gaussian noise was added to all simulation ingful differences in the resulting values of CBF, CBV and iterations. The standard deviation for the noise TTP depending on the smoothing method used. generator was set to 50, 25, and ~16.6, which corresponded to SNR values 1, 2, and 3 (lowest noise). Methods 3) Vessel width: Is the cross-sectional width of the The Masked Smoothing method was tested against two vascular region. Values used were: .8, 1.6, 2.4 mm. smoothing methods (Simple and Removed Smoothing) 4) Smoothing kernel –FWHM: The isotropic Gaussian that are similar, but which do not limit the smoothing to smoothing kernel size was set to Full Width Half tissue voxels. The smoothing methods were tested using Max (FWHM) values of 1, 2, and 4 mm. simulated data, phantom data, and anonymized CT per- fusion data from patients. The simulations provide a Iteration framework for determining the noise reduction and bias For each iteration of a simulation run: for each method. The phantom data allows us to test for bias using real scanner data. The CT perfusion data 1) The simulated volume was formed with intensity from 23 patients allows an assessment of the impact of values of tissue voxels set to 50. Vascular voxels bias caused by smoothing the CT Perfusion time series were selected according to “Vessel Width”, and images on the calculation of CBF, CBV, and TTP. assigned an intensity value according to the variable “Intensity Ratio”. Smoothing methods 2) Gaussian noise was added at a level determined by The three smoothing methods were implemented in the Signal to Noise Ratio (SNR), Figure 1, image a. Matlab (Mathworks, Natick, MA) using Gaussian smooth- 3) All three smoothing methods were applied. All ing kernels: methods used the same Gaussian kernel with the kernel size determined from the variable “Kernel 1) Simple Smoothing: The unmodified image volume is FWHM”, Figure 1, images b-d. smoothed using a Gaussian kernel. 4) The value at a tissue location located midway along, 2) Removed Smoothing: The vascular voxels are set to and directly next to, the vascular voxels was selected zero, and the image is smoothed as in (1) above. and the value with noise and smoothing applied was 3) Masked Smoothing: First, Simple Smoothing is recorded. Figure 2 shows the intensity profile for the performed on the binary tissue mask. Second, the different smoothing methods for a vertical line voxel-by-voxel ratio of the Removed Smoothing passing through the images of Figure 1. image and the smoothed tissue mask image (i.e. the result of the first step of this method) is returned as Assessment the Masked Smoothing image. Voxel values outside 500 iterations were used to determine the mean and of the tissue mask are assigned the original image standard deviation for a selected tissue voxel that neigh- value, except for the phantom experiment. We used bored the vessel voxels for different settings of parame- this case to also demonstrate that Masked ters. Since in-tissue values in all cases were set to 50, the Wack et al. BMC Medical Imaging 2014, 14:28 Page 4 of 11 http://www.biomedcentral.com/1471-2342/14/28 parameter set allowing for examination of deviation from the expected tissue value of 50 for each smooth- ing method. CT phantom experiment Thirty image volumes of a CT phantom were collected using a Phillips Gemini PET/CT; 0.5 mm thickness, 0 in- crement, 80 kV, 125 mAs, collimation: 32×1.25 l, rota- tion time: 0.5 sec, FOV 250, 512 matrix, with voxel size 0.49 × 0.49 × 0.5 mm. All three methods of smoothing, using a 5 × 5 × 5 mm Gaussian kernel, were applied to Figure 1 Simulation vessel with tissue background – raw and the first image volume. Additionally, the mean across smoothed images. Top Left rectangle is the raw image from the simulation. Top Right rectangle is of Simple Smoothing applied to images volumes was calculated, which was used as the the raw image. Bottom Left rectangle is of Removed Smoothing reference because of the reduced noise characteristics. applied to the raw image and the Bottom Right rectangle is of One slice is shown for each smoothing method, and the Masked Smoothing applied to the raw image. A smoothing kernel mean (Figure 3). Two lines were chosen that passed of 2 mm was used for each, with a vessel size of 2 mm and a raw through a large and small object identified on the CT. image Signal to Noise level of 2. The line profiles for these lines are shown in Figures 4 and 5. Finally a line of 41 pixels in length was identified calculated mean value from 500 iterations even if a high directly above of the larger object. The mean and stand- level of noise is added is expected to be very close to 50 ard deviation was calculated for this set of voxels across unless a bias is present. The four parameters (Intensity Ra- all 30 image volumes (i.e. 30 × 41 voxels), for the Simple tio, SNR, Vessel Width, and Smoothing Kernel FWHM) andMaskedsmoothing methods, andcomparedtothe were individually varied using the values given above for mean and standard deviation calculated from the each. When one parameter was varied the other values 41 voxels of the mean image. To demonstrate a vari- were set to default values (Intensity Ratio = 2 to 1, SNR = 2, ation from the simulation experiment, we performed Vessel Width = 1.6 mm, and FWHM = 2 mm). One masked smoothing, separately, to both the non-object simulation run (500 iterations) was performed for each region and object region. Figure 2 Vertical line profile for smoothing methods from Figure 1. The boundary and vessel voxels are identical for the Masked Smoothing and original values, since Masked Smoothing was only applied to the tissue values. The Simple and Removed smoothing methods had identical results except near the vessel voxels. The Simple Smoothing method over estimates the true value of the tissue near the vessel and underestimates the true value near the boundary. The Removed Smoothing methods underestimates the true value both near the boundary and vessel. For points away from both the boundary and vessel the three smoothing methods gave identical results. The smoothing kernel applied was 2 x 2 x 2 mm for all methods. Wack et al. BMC Medical Imaging 2014, 14:28 Page 5 of 11 http://www.biomedcentral.com/1471-2342/14/28 Influence of smoothing method on CBF, CBV, and TTP values Twenty-three CT perfusion studies were selected from the Neurosurgery department’s stroke research database, at the University at Buffalo. Each dataset consisted of nineteen CT perfusion volumes from a Toshiba Aquilion ONE, 320 slice scanner (with voxel sizes of .42×.42×.5 mm) which were collected from patients pre- senting with symptoms of a stroke. Images were converted from Dicom to NifTI format, and corrected for motion using SPM8 (www.fil.ion.ucl.ac.uk/spm). Image volumes were “skull striped”, and vascular voxels were identified using in-house software written in Matlab. The middle cerebral artery was automatically identified and a center portion was segmented and used for the arterial input function. A similar procedure was used to select the sagit- tal sinus, and these values were used to ensure the proper scaling of the arterial input function. A parametric image of CBF values was calculated using the maximum slope method, while a CBV image was calculated using the inte- Figure 3 Image slice from phantom study: raw, mean, and gral of tracer activity divided by the integral of arterial smoothed images. Top left image is a slice from the first of 30 activity. image volumes. Top right image is the mean of the same slice Tissue voxels immediately adjacent to a selected artery across all image volumes. Lower left image is the same slice as the were selected by performing a voxel-wise dilation of the upper left but with Gaussian smoothing applied. Lower right image is the same slice as the upper left but with Masked Smoothing applied. voxels representing a selected artery followed by an intersection with the tissue masks resulting in the elim- ination of the vascular voxels. For each smoothing method we calculated CBF, CBV, and TTP values for the selected neighboring tissue voxels, using a Gaussian ker- nel size of 4 × 4 × 4 mm, FWHM. Mean and voxel-wise Figure 4 Intensity profile for line passing through the large object seen in Figure 3. Simple Gaussian smoothing underestimates the raw values for the object, but overestimates the values neighboring the object. Values neighboring the object have a small increase in value, which is related to the underlying neighboring voxels being correlated as a result of the reconstruction process. Notice that Masked Smoothing was applied both to the background and the object. Wack et al. BMC Medical Imaging 2014, 14:28 Page 6 of 11 http://www.biomedcentral.com/1471-2342/14/28 Figure 5 Intensity profile for line passing through the small object seen in Figure 3. The line profile has similar behavior near the object as in Figure 4. Likewise, it can be seen that both smoothing methods give identical results away from the object. statistics were calculated to examine differences in CBF, intensity ratio was varied and the other variables were CBV, and TTP due to the smoothing method used. fixed, all smoothing methods provided over a 10 fold de- crease of the standard deviation (Table 1). For the Sim- ple Smoothing method the tissue mean increased with Ethics an increase in intensity of the neighboring vessel voxels. This project is approved by the University at Buffalo The Simple Smoothing method has a 100% increase Health Sciences Institutional Review Board. (bias) for the tissue mean for the highest level of vessel voxel intensity (4 to 1). The Removed Smoothing Results method showed a bias which lowered the value (~28% Simulation experiment decrease) and was unaffected by changes in the intensity Figure 2 displays line profiles, each corresponding to a of neighboring vessel voxels. The Masked Smoothing vertical line across each image of Figure 1, to demon- method did not show any significant bias in the calcula- strate the effects of the Simple, Removed, and Masked tion of the mean tissue value. The standard deviation Smoothing methods. resulting from the Removed Smoothing was slightly lower than the standard deviation of from the Simple Simulation experiment intensity ratio and Masked Smoothing approaches. Tissue mean and standard deviation results for different Intensity Ratios are provided in Table 1. When the Simulation experiment – SNR Table 1 Simulation—intensity ratio: mean values and Tissue mean and standard deviation results for different (standard deviation) SNRs are provided in Table 2. The Simple Smoothing Method\Intensity ratio 1.5 to 1 2 to 1 4 to 1 method showed an upward bias, while the Removed Noise – No smoothing 49.7 (25.1) 50.3 (25.0) 49.0 (25.7) Smoothing method exhibited a downward bias. The Simple smoothing 58.2 (1.6) 66.3 (1.6) 99.3 (1.7) biases were essentially identical for all three noise con- ditions. The standard deviation decreased with a de- Removed smoothing 33.6 (1.3) 33.5 (1.3) 33.5 (1.4) crease in the level of noise (increase of SNR) used in Masked smoothing 50.0 (1.9) 50.0 (1.9) 50.0 (2.1) the simulation for all smoothing methods. The standard As the ratio of the intensity of the arterial voxels compared to tissue voxels deviation was markedly smaller for all smoothing increased, the values from Masked Smoothing and Removed Smoothing held constant. However, the removed smoothing values were significantly reduced methods compared to the non-smoothed images. The compared to their true underlying value of 50. Masked Smoothing values were Masked Smoothingmethoddid not showabias in the equal to their true underlying value in all cases. Tissue voxels for the Simple Smoothing method increased with the increase in the arterial ratio. calculation of the mean tissue value. Wack et al. BMC Medical Imaging 2014, 14:28 Page 7 of 11 http://www.biomedcentral.com/1471-2342/14/28 Table 2 Simulation—SNR: mean values and (standard Table 4 Simulation—smoothing kernel FWHM: mean deviation) values and (standard deviation) Method\SNR 1 2 3 (least noise) Method\kernel FWHM 1 2 4 mm Noise – No smoothing 53.6 (49.0) 49.9 (27.1) 50.8 (16.9) Noise – No smoothing 51.7 (25.1) 49.9 (25.9) 50.0 (24.0) Simple smoothing 66.4 (3.3) 66.4 (1.6) 60.4 (1.1) Simple smoothing 64.6 (4.1) 66.4 (1.6) 60.4 (0.6) Removed smoothing 33.6 (2.6) 33.6 (1.3) 33.6 (0.8) Removed smoothing 35.7 (3.6) 33.6 (1.3) 39.6 (0.5) Masked smoothing 50.0 (3.9) 49.9 (1.9) 50.0 (1.3) Masked smoothing 50.2 (5.1) 50.0 (2.0) 50.0 (0.7) The standard deviation values were lower for low SNR than for high SNR. Only the Masked Smoothing method had mean values close to the true Standard deviation values were slightly poorer for the Masked Smoothing underlying value of 50. Standard deviation values decreased as the kernel method, which is explained by fewer voxels being averaged because size increased. non-tissue voxels were excluded. Phantom data experiment Simulation experiment: change of vessel diameter The line profiles passing through the small and large ob- Tissue mean and standard deviation results for different ject show that each smoothing method is essentially iden- vessel widths are provided in Table 3. When the width tical for voxels away from the object (Figures 4 and 5). of the simulated vessel increased, the Simple Smoothing However, where the profiles cross through the object, the method biased the mean tissue value to greater levels, Simple Smoothing method has significantly lower valued while the Removed Smoothing method biased the mean voxels than the reference, i.e. mean across all image vol- value to lesser values. The Masked Smoothing method umes. In contrast, for several voxels on either side of the did not show any bias associated with the mean tissue object, the Simple Smoothing method has higher intensity value. All smoothing methods greatly reduced the stand- values than the reference. The Masked Smoothing method ard deviation of the results. has values close to the reference both for voxels located within the object, and outside of the object. We notice that there are a few voxels at either side of the object Simulation experiment: change of smoothing kernel FWHM where the reference values lay between central values for The Simple Smoothing method yielded an upward bias for the object and background. This is an indication of the tissue mean values, while the Removed Smoothing method limitation in the scanner resolution and reflects partial yielded a downward bias. The magnitude of the bias de- volume and an inherent smoothness of the raw data. Simi- creased with increased filter size. Masked Smoothing dis- lar effects are seen for the line profile passing through the played no significant bias of the tissue mean value. For all smaller object. methods, the standard deviation of the smoothed tissue The mean and standard deviation for the 41 voxel line value decreased when the Smoothing Kernel FWHM in- parallel and adjacent to the large object, for all 30 collected creased. Mean and standard deviation values for our three image volumes was 6.90 (13.08) HU. With Simple Smooth- FWHM values and three smoothing methods is provided ing, using 5 × 5 × 5 mm Gaussian kernel, the mean in- in Table 4. creased to 29.78 HU, but the standard deviation decreased to 1.76. With the corresponding Masked Smoothing ap- plied the mean equaled 8.26 HU, i.e. much closer to the All reported biases original. Further, the standard deviation equaled 1.96 HU, For all simulations the number of iterations was 500, close to same value seen with Simple Smoothing. and the standard deviation was relatively small com- pared to the size of the bias. Hence, all biases reported Patient CT perfusion data – calculation of CBF, CBV, and above were strongly significant (p < 0.0001). TTP values The ROIs of the tissue voxel that neighbored vascular voxels, formed for each of the 23 datasets had a mean size Table 3 Simulation—vessel width: mean values and of 376,575 voxels, and was used for determining the mean (standard deviation) parameter values. The calculated values for CBF, CBV, Method\Vessel diameter 1 2 3 mm and TTP, for the three smoothing methods are reported in Noise – No smoothing 51.2 (26.0) 50.2 (24.5) 48.5 (25.5) Table 5. Mean values for CBV were greater than 50% Simple smoothing 61.3 (1.6) 66.5 (1.7) 68.6 (1.6) higher, and CBF were greater than 100% higher, for the Removed smoothing 38.8 (1.4) 33.6 (1.4) 31.6 (1.3) Simple Smoothing method than the Masked Smoothing Masked smoothing 50.0 (1.8) 50.1 (2.0) 50.1 (2.1) method. Mean values for both CBV and CBF were both Masked Smoothing is much closer to the true value of 50 than either of the more than 30% lower for the Removed Smoothing method other smoothing methods. The standard deviation values are markedly better than the Masked Smoothing method. The mean TTP for all smoothing methods than the No Smoothing data. A clear bias is evident for the Simple and Removed Smoothing methods. values for all smoothing methods were similar. Wack et al. BMC Medical Imaging 2014, 14:28 Page 8 of 11 http://www.biomedcentral.com/1471-2342/14/28 Table 5 Mean Parametric values for subjects’ CT not introduce bias (as opposed to the Removed and perfusion scan data Simple Smoothing methods), is easy to implement, and Method\Parameter CBF (ml/(cc x min)) CBV (ml/cc) TTP (min) executes fast enough to allow clinical use, we advocate its use over the other methods for the smoothing of CT per- Simple smooth 1.48 .112 .52 fusion images. Removed smooth .35 .029 .54 Masked smooth .67 .048 .54 Study design CBF and CBV values were higher and lower than would be expected We used simulated data to test the performance charac- physiologically for the Simple and Removed Smoothing methods, respectively. Time to Peak (TTP) values were similar for all methods. teristics of the three smoothing methods in situations where the smoothing neighborhood for a tissue voxel in- All voxel-by-voxel comparisons for CBF, CBV, and TTP cluded the much higher valued vessel voxels. In all simu- were significantly different (p < < .0001, paired t-test) for lations the tissue and vessel intensity values remained all pairwise comparisons of Simple Smoothing, Removed constant, allowing us to measure the effect of varying Smoothing, and Masked Smoothing methods, with the ex- vessel characteristics (both vessel size and tracer concen- ception of TTP calculated from Removed and Masked tration), the effect of varying SNR, and influence of the Smoothing. Identical results (voxel by voxel) were found smoothing kernel FWHM. Using phantom imaging we in comparing TTP calculated from volumes smoothed were able to further show potential biases caused by the with the Removed Smoothing and Masked Smoothing different smoothing methods. Using real world data methods. Despite finding a significant difference between from 23 patients, we also compared Simple, Masked, TTP calculated with Simple Smoothing and either Re- and Removed Smoothing to examine whether the theor- moved or Masked Smoothing, the magnitude of the differ- etical improvement seen on simulations can have a real ence was very small (1.14 seconds, while the time between life impact in the calculation of CBF, CBV, and TTP. volumes was 3 seconds). For illustration, we display the Using this approach we not only showed that Masked results of the three smoothing methods for one slice using Smoothing did not have the bias of the other methods, an 8 × 8 × 8 mm kernel (Figure 6). but we also demonstrated the large practical impact this Execution time of the Masked Smoothing method was has on determining physiological parametric images for 66 seconds for the 512×512×320×19 voxel CT perfusion CBF and CBV. image volume using a Gaussian Filter with size 2 × 2 × 2 mm FWHM, which required a 25 × 25 × 21 voxel ker- Change of intensity ratio/vessel width nel. Execution time using an 8 × 8 × 8 mm FWHM Our simulation experiments indicate that the Simple Gaussian filter, which required a kernel of 99×99×93 Smoothing method has a large upward bias for tissue voxels, was 81 seconds. Execution time was measured voxels surrounding a vessel that increases as the inten- using “tic” and “toc” Matlab functions, on a multi-user sity of the vessel voxel increases. By setting the vessel Dell PowerEdge R710 server with Dual 2.4 GHz proces- voxels to zero for the purpose of smoothing, the Re- sors, and 48 GB RAM. moved Smoothing method has a downward bias for tissue voxels neighboring a vessel voxel that is both fixed and in- Discussion dependent of the vessel voxel’s intensity level. The Masked Our simulation and phantom data show that the Simple Smoothing method avoided bias by compensating for vox- (i.e. ordinary Gaussian smoothing) and Removed Smooth- els set to zero. Increasing the vessel width increased the ing introduce a significant bias to tissue voxels that neigh- bias for the Simple Smoothing method, which reflects that bor vessels, whereas our Masked Smoothing method did a greater number of high intensity vessel voxels are within not introduce a bias. Our experiment using patient data the smoothing neighborhood of the tissue voxel. The Re- revealed that the bias of the Simple and Removed moved Smoothing method also increased its bias (down- Smoothing methods had a large impact on the calculation ward) with an increase in vessel size. This is reasonable, of CBF and CBV. The Removed Smoothing method had since for a given smoothing neighborhood the Removed the lowest values for CBF and CBV and were influenced Smoothing method would have a greater number of vas- by factoring in zero values in the place of neighboring vas- cular voxels set to zero as the vessel width increases. cular values. The Simple Smoothing method had in- Again, by compensating for voxels that were set to zero creased CBF and CBV values for tissue voxels that the Masked Smoothing method did not exhibit a bias. neighbor vessels that were not physiologically reasonable. The Masked Smoothing method had physiologically rea- Change of SNR/smoothing kernel FWHM sonable values for CBF and CBV, between the extremes All smoothing methods provided a large decrease in the returned by the Removed and Simple smoothing methods noise level. Increasing the noise level caused an increase (Table 5). Given that the Masked Smoothing method does in the standard deviation measured for all methods, but Wack et al. BMC Medical Imaging 2014, 14:28 Page 9 of 11 http://www.biomedcentral.com/1471-2342/14/28 Figure 6 Simple, Removed, and Masked Smoothing images, with sample line profile. Top row: Simple and Removed Smoothing images; Bottom row: Masked Smoothing image and the line profile of each along the line connecting the edge marks of the images. The line profile of the Masked Smoothing image preserves the high intensity value for a vessel that is crossed near the line center, whereas the peak is much smaller for the Simple Smoothing method, and smallest for the Removed Smoothing method. The Simple Smoothing method has much higher values around the peak, due to the smoothing of the vessel’s intensity into neighboring tissue. Along the right edge the Masked Smoothing method maintained the higher intensity values of the tissue, whereas the Simple and Removed Smoothing methods have lower values that are influenced by surrounding zero values. An 8x8x8 mm smoothing kernel was selected for this illustration to simplify the line profile. had no effect on the calculated mean value. Increasing the vessel, hence lessening the influence of the vessel it- the filter kernel for all methods reduced the measured self. As in all cases, the Masked Smoothing exhibited no standard deviation. Increasing the filter size from 1 mm significant bias. to 2 mm increased the bias for both Simple and Re- moved Smoothing. However, increasing the smoothing Influence of smoothing method on the calculation of CBF, kernel further to 4 mm resulted in the smallest bias. The CBV, and TTP change in bias reflects the weighted proportion of voxels Smoothing is a critical noise reduction pre-processing that are within the smoothing neighborhood. With the step prior to the calculation of physiologic parameters as 4 mm smoothing kernel, the smoothing is incorporating we have demonstrated previously using simulations a significant number of voxels from the “other-side” of [19-21]. The CBF and CBV derived from the Simple and Wack et al. BMC Medical Imaging 2014, 14:28 Page 10 of 11 http://www.biomedcentral.com/1471-2342/14/28 Removed Smoothing methods differed, approximately, Conclusion by a factor of four for tissue voxels close to vessels, thus We demonstrated that the Masked Smoothing method ex- demonstrating the critical importance of the smoothing ecutes rapidly and can readily integrate into existing method. The CBF and CBV values, calculated using the smoothing kernels. The Masked Smoothing method does Masked Smoothing method, were in-between and signifi- not introduce a bias in situations where nearby voxels cantly different from the other smoothing methods, and have a different classification and a large difference in in- closest to physiologically expected values. Since the tensity values. This accuracy, coupled with speed, gives the Masked Smoothing approach showed no bias on the simu- Masked Smoothing method the potential to significantly lated data, we believe these CBF and CBV values are the improve the clinical processing of perfusion imaging. most accurate. The TTP values for the Removed and Competing interests Masked Smoothing were identical because the time activ- The authors declare they have no competing interests. ity curves for a given voxel will only differ by a scaling multiple, and were close to the Simple Smoothing method. Authors’ contributions DSW developed the algorithm and developed software for the experiments. DSW and KFS drafted the manuscript. KFS, KVS, and AHS set criteria for and Filter selection identified appropriate scans for inclusion. All authors participated in the We used a Gaussian smoothing kernel for our implemen- experimental design, and have read and approved the final manuscript. tation because it is commonly used for medical images, Acknowledgements and allows for fast implementations because it is separ- The authors wish to thank Carmen Mieles, RTCT at WNY PET/CT, for her able. Our 3D execution times for an entire volume was technical expertise and assistance for the phantom data collection. significantly faster than a 2D TIPs bilateral filter on a sin- Author details gle slice. Klotz and König [5] also applied smoothing sep- Dept. of Nuclear Medicine and Center for Positron Emission Tomography, arately on brain and vascular voxels. Their approach used The University at Buffalo, State University of New York, Buffalo, NY, USA. multiple applications of a mean filter, whereas we utilized Dept. of Neurosurgery and Toshiba Stroke and Vascular Research Center, The University at Buffalo, State University of New York, Buffalo, NY, USA. a Gaussian kernel. Our approach would also work with School of Medicine, The University at Buffalo, State University of New York, mean filters, since they are also separable. There are very Buffalo, NY, USA. fast methods for implementing mean filters; and further- Received: 26 July 2013 Accepted: 7 August 2014 more, multiple passes of a mean filter can be used to ap- Published: 21 August 2014 proximate a Gaussian filter. However, internal timings during development favored our approach. References 1. 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Fisher J: Improvements in Computed Tomography Perfusion Output using Complex Singular Value Decomposition and the Maximum Slope Algorithm. Master’s Thesis, Boston University, School of Medicine; 2014. 20. Wack DS, Badgaiyan RD: Complex singular value decomposition based noise reduction of dynamic PET images. Current Medical Imaging Reviews 2011, 7(2):113–117. 21. Snyder K, Seals K, Wack D: Using simulations to explore the characteristics of CT perfusion calculations in the assessment of stroke. Current Medical Imaging Reviews 2014, 10(3). In press. doi:10.1186/1471-2342-14-28 Cite this article as: Wack et al.: Masked smoothing using separable kernels for CT perfusion images. BMC Medical Imaging 2014 14:28. 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BMC Medical ImagingSpringer Journals

Published: Aug 21, 2014

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