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Nonlocal Coherent Denoising of RF Data for Ultrasound Elastography

Nonlocal Coherent Denoising of RF Data for Ultrasound Elastography Hindawi Journal of Healthcare Engineering Volume 2018, Article ID 7979528, 9 pages https://doi.org/10.1155/2018/7979528 Research Article Nonlocal Coherent Denoising of RF Data for Ultrasound Elastography 1 1 2 1 P. Khavari , A. Asif, M. Boily, and H. Rivaz Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada Department of Diagnostic Radiology, McGill University, Montreal, QC, Canada Correspondence should be addressed to P. Khavari; p_khavar@encs.concordia.ca Received 16 January 2018; Accepted 30 April 2018; Published 24 June 2018 Academic Editor: Terry K. K. Koo Copyright © 2018 P. Khavari et al. )is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Ultrasound elastography infers mechanical properties of living tissues from ultrasound radiofrequency (RF) data recorded while the tissues are undergoing deformation. A challenging yet critical step in ultrasound elastography is to estimate the tissue displacement (or, equivalently the time delay estimate) fields from pairs of RF data. )e RF data are often corrupted with noise, which causes the displacement estimator to fail in many in vivo experiments. To address this problem, we present a nonlocal, coherent denoising approach based on Bayesian estimation to reduce the impact of noise. Despite incoherent denoising al- gorithms that smooth the B-mode images, the proposed denoising algorithm is used to suppress noise while maintaining useful information such as speckle patterns. We refer to the proposed approach as COherent Denoising for Elastography (CODE) and evaluate its performance when CODE is used in conjunction with the two state-of-art elastography algorithms, namely: (i) GLobal Ultrasound Elastography (GLUE) and (ii) Dynamic Programming Analytic Minimization elastography (DPAM). Our results show that CODE substantially improves the strain result of both GLUE and DPAM. At the heart of both GLUE and DPAM is an energy 1.Introduction minimization approach to determine TDE’s. A dynamic Ultrasound elastography determines the viscoelastic prop- programming approach is used in both cases to compute erties of tissues and is useful for diagnosis of pathology and TDE’s first at a coarse pixel level. )e resolution of the TDE’s is then enhanced to the finer subpixel level through ana- for aiding surgeons in the operating room. Broadly speaking, ultrasound elastography can be grouped into two categories lytical minimization. Given that RF ultrasound data can be [1–6]: dynamic elastography and quasi-static elastography. corrupted by several factors such as thermal and electronic In this paper, we focus on two state-of-art free-hand pal- noise, there is a need to compensate for noise in the RF data. pations and quasi-static elastographic approaches, namely, Traditional filtering techniques, such as the convolution with GLobal Ultrasound Elastography(GLUE) [7] and Real-Time a Gaussian kernel, use local continuity in the images to reduce Regularized Ultrasound Elastography (DPAM) [8]. Both noise. A new class of denoising algorithms, referred to as approaches use successive pairs of frames of ultrasound RF nonlocal means (NLM) [9], considers data from a much larger data to estimate the tissue displacement (also referred to as “nonlocal” region for denoising. NLM relies on redundancy time delay estimates (TDE)). )e derivative of TDE provides in images and uses the weighted average of most similar an estimate of the induced strain that represents the stiffness intraframe pixels within a large nonlocal neighbourhood to eliminate noise. or softness of the tissue being imaged. Figure 1 illustrates the steps involved in quasi-static ultrasound elastography Most NLM-based denoising approaches [10–12] remove with the handheld device shown on the left handside and noise from processed output of the RF data, which is referred the displacement field estimates defined using the two to as B-mode images in ultrasound literature. NLM denois- frames on the right. ing reduces speckle pattern and generates smooth B-mode 2 Journal of Healthcare Engineering Ultrasound probe Before deformation I Aer deformation I 1 2 Lateral (z) 12 … jn … 12 … jn … 1 1 Axial (x) 2 2 . . . . . . (i, j) . . . . . . (i + a , j + l ) i,j i,j Tissue (a) (b) (c) Figure 1: Illustration of ultrasound elastography. (a) A handheld device that induces an external stimulus into the tissues. (b, c) Two successive frames I and I of RF data. —e goal of ultrasound elastography was to šnd the displacement (a ,l ) for each pixel (i, j) in the 1 2 i,j i,j I RF frame. images. Ultrasound speckle is useful in several image analysis 2. Quasi-Static Elastography: GLUE and DPAM techniques, such as ultrasound elastography [13, 14], free- Both DPAM and GLUE are quasi-static approaches based on hand sensorless 3D ultrasound [15, 16], and quantitative the optimization of a regularized cost function to determine ultrasound [17]. In this work, we focus on ultrasound tissue displacements. —ey both aim at šnding the axial and elastography. lateral displacements (a and l) of all samples of RF data as In this paper, we present an alternate approach, wherein shown in Figure 1. DPAM uses dynamic programming (DP) the NLM denoising algorithm is applied directly to raw RF to šrst estimate the integer displacement of a seed-line in data instead of processed B-mode images. We refer to the terms of the number of pixels and then applies analytical proposed approach as COherent Denoising for Elastography minimization (AM) to šne tune the estimated displacement (CODE) and evaluate its performance on in vivo liver ablation to the subpixel level. —e strain image is obtained using the data when used in conjunction with two commonly used spatial di›erentiation of the displacement šeld. GLUE also elastography algorithms, namely: (i) GLobal Ultrasound uses DP for estimating the integer tissue displacements and Elastography (GLUE) [7] and (ii) Dynamic Programming rešnes the estimates to subpixels for the entire image si- Analytic Minimization elastography (DPAM) [8]. CODE multaneously. In other words, GLUE solves an optimization exploits the complete set of information in the RF domain, function where both axial and lateral displacements of every some of which is likely to be lost in the processing steps used sample of the RF frame are unknowns, that is, in the order of to generate the B-mode images. It is, therefore, our intuition a million variables. —is is in contrast to DPAM, which that CODE would result in superior denoising results. Using rešnes the estimates line-by-line. —e strain image again is information in RF data to generate visually informative calculated based on the di›erentiation of displacement map B-mode images is challenging [18]. To illustrate the superi- similar to DPAM. Although GLUE and DPAM perform well ority of CODE, both mathematical analysis and experimental in most cases, they may not converge to the correct solution results are included in the paper. Our comparisons corrob- in the presence of excessive noise. In the next section, we orate our intuition and verify the usefulness of CODE. present our denoising approach used to reduce the impact of —e rest of this paper is organized as follows. In Section noise in the RF domain. 2, we introduce GLUE and DPAM as representative quasi- static elastography approaches. Section 3 provides back- ground on nonlocal denoising and introduces CODE as 3. The Nonlocal Denoising Approach a Bayesian estimator. In Section 4, we explore the ability of CODE on simulation data. Experimental results using —e central idea behind this paper is to apply coherent phantom and in vivo data are included in Section 5. Finally, denoising on RF data. Unlike incoherent denoising ap- we conclude the paper in Section 6. proaches that process the B-mode images to remove noise Journal of Healthcare Engineering 3 (resulting in spatial averaging and signišcant loss of speckle x x j,1 j,1 patterns), the proposed approach retains speckle patterns. x x j,2 j,2 We šrst outline NLM, which is followed by a description of x x x j j,3 j,3 the CODE algorithm, including an analytical justišcation of x x j,4 j,4 why CODE provides better denoising results. x x j,5 j,5 x x j,6 j,6 3.1. Nonlocal Means. Let v(i) be the observed value of the x x j,7 j,7 x x x discretized image for pixel i and u(i) be its true value. Due to i j,8 j,8 the presence of noise n(i), we have x x j,9 j,9 v(i) u(i)+ n(i). (1) To simplify our explanation, we focus on 1D signals, but our results are generalizable to 2D images. In fact, the ex- perimental results included in Section 4 are for 2D phantom and in vivo liver ablation data. To denoise the image for each pixel i, NLM searches a reference area of the image within Figure 2: Illustration for the patch and vectorized indices used in a rectangular search window Δ , which is centered around the proposed CODE approach for n  9. pixel i (Figure 2). A neighbourhood N of known dimension is selected around pixel i and compared to neighbourhood N around pixel j for all j ∈Δ . For pixel i, weight w(i, j) is j i assigned to each pixel j. —e value of pixel i is then replaced by We now provide an analytical explanation of why NLM denoising is adapted for the RF domain. Let g(x) and o(x) NLM[v](i)  w(i, j) ∗ v(j). (2) be vectorized ground truth and observed patches of size n j∈Δ centered at pixel x of RF data (Figure 2). We dešne them as —e distance metric is proportional to the square of the g(x) g(x ) with x ∈ N (x) and o(x) o(x ), where k k g k x ∈ N (x) and  N ,N are the neighbourhoods Euclidian distance between the two patches. —e weight is k o o g √ √ then calculated as (patches) of size ( n × n ) around the central pixel x in 2 ground truth and observed images. Our goal is to derive the       vN − v N     1 i j 2,a Bayesian estimator g(x) for patch g(x) based on the observed (3) w(i, j) exp − .  2  patch o(x). Dešning the optimal estimator by minimizing the Z  h  posterior expected loss as Based on (3), it is clear that the weight is the convo- E[L(g(x), g (x))]   [L(g(x), g(x))]p(g(x)|o(x)), lution of a Gaussian with standard deviation a > 0 and the g(x)∈Γ squared Euclidean distance between two neighbourhoods (5) v(N ) − v(N ) , for N and N . —e smoothing parameter i j i j h controls the contribution of the Gaussian-Euclidean where Γ constitutes all possible outcomes of g(x), the loss distance exponent in the weights. —e normalization factor function is given by Z for pixel i is given by   L(g(x), g (x))  g(x) − g(x) . (6) vN  − vN   i j 2,a (4) Z(i) exp − ,  2   h  j∈Δ Substituting (6) in (5), the optimal Bayesian estimator is where the weight is normalized to ensure that the dynamic range g (x)  arg min 2 opt g(x) − g(x) p(g(x)|o(x)) of the NLM[v](i) is the same as that of its counterpart v(i).  g(x) g(x) (7) g(x)p(g(x)|o(x)). 3.2. e Proposed Bayesian CODE Framework. Noise in g(x) ultrasound B-mode images originates from piezoelectric sensors and data acquisition card. Depending on the ap- Equation (7) can be expressed as plication, the level of noise can even be higher. For example, p(g(x), o(x)) g (x)  g(x) ablation treatment generates heat and microbubbles that opt p(o(x)) g(x) severely deteriorate RF data [19–21]. Both logarithmic (8) compression and envelope detection steps, applied to derive g(x)p(o(x)|g(x))p(g(x)) g(x) the B-mode image, are nonlinear operations that complicate measurement noise added by sensors and acquisition card. p(o(x)|g(x))p(g(x)) g(x) Our CODE approach eliminates noise introduced by sensors and acquisition card before the nonlinear logarithmic com- Only a subset of Γ is accessible in the search region of the pression and envelope detection by applying NLM directly to central pixel x . We refer to this subset as the search region, RF ultrasound data. SR(x) g (x), g (x), g (x), ... , g (x) . Assuming that 1 2 3 K 4 Journal of Healthcare Engineering (a) (b) (c) (d) (e) Figure 3: Field II simulation results. )e noisy input has substantially less contrast than the ground truth image. NLM is designed to remove speckle and therefore substantially reduces image detail. CODE output is closest to the ground truth. (a) Ground truth, (b) noisy, (c) NLM, (d) Gaussian on RF, and (e) CODE. cardinality of SR is K and p(g(x)) is uniformly distributed, )erefore, the adapted filter for denoising the RF data that is, p(g (x)) � 1/K, for all(0 ≤ i ≤ K), (8) simplifies to (CODE) is � � K 2 � � 􏼌 � � 2 − 􏼐 o x −o x􏼁 /2σ 􏼑 􏼌 � ( ) � K i j 􏽐 g􏼐x 􏼑p􏼐o x􏼁 􏼌g􏼐x 􏼑􏼑 g x􏼁 � 􏽘 exp o􏼐x 􏼑, j i j i j j�1 C x 􏽢 � 􏼌 g x􏼁 , (9) i j�1 i 􏼌 􏽐 p􏼐o x􏼁 􏼌g􏼐x 􏼑􏼑 j�1 i j (14) � � K � � � � 2 − o x −o x /2σ 􏼐� ( ) 􏼁 � 􏼑 i j where g 􏽢(x ) is the optimal estimator based on the uniform with C x􏼁 � 􏽘 exp . distribution assumption. Given the ground truth is not j�1 accessible, we substitute the observed value of the neigh- )is filter is based on the noise statistics of RF data. bourhood patches to get CODE is, therefore, the optimal denoising approach for 􏽐 o􏼐x 􏼑p􏼐o x􏼁 o􏼐x 􏼑􏼑 removing noise in (11) within the RF domain. j�1 j i j 􏽢 􏼌 g x􏼁 � . (10) i 􏼌 Kevrann et al. [12] and Coupe et al. [10] have developed 􏽐 p􏼐o x􏼁 􏼌o􏼐x 􏼑􏼑 j�1 i j similar Bayesian estimators but for reducing the speckles pattern in the B-mode image. Aligned with the mathematical Given that the noise in the RF data is modelled as an Bayesian estimator, the properties of noise in RF data show additive Gaussian noise [22, 23], we have the usefulness of CODE for removing noise from the RF ultrasound data. o(x) � g(x) + v(x), (11) where v(x) is the additive white Gaussian noise with vari- 4. Simulation Validation for Code ance σ . By assuming that the likelihood can be factorized as To assess the performance of the CODE approach, the Field 􏼌 II [24] software is used to simulate RF data from a lesion p􏼐o x􏼁 o􏼐x 􏼑􏼑 � 􏽙 p􏼒o􏼐x 􏼑 o􏼐x 􏼑􏼓, 􏼌 (12) i j i,k j,k phantom of size 60, 50, and 10 mm in axial, lateral, and out- k�1 of-plane directions, respectively. )e phantoms consist of where x ∈ N(x ) and x ∈ N(x ) are the counterpart two classes of background and target tissues. To determine i,k i j,k j pixels in the patches with central pixels x and x . )ere- the precision and sensitivity of the CODE, three different i j fore, p(o(x )|o(x )) is multivariant normal distributed setups with 5, 10, and 15 scatterers per resolution cell dis- i j p(o(x )|o(x )) ∼ N(o(x ), σ I ). Notation I is the identity tributed randomly within the phantom are used. Different i j j n n matrix. )us, the filter in (10) can be adapted to remove the realizations for each group of scatterers are generated. )e noise of RF data as RF output of Field II is corrupted by adding additive white � � K � � Gaussian noise with a SNR of 5 dB. � � 2 − 􏼐�o x −o x􏼁 � /h 􏼑 ( i) j g 􏽢 x􏼁 � 􏽘 exp o􏼐x 􏼑, i j Figure 3 shows the results of NLM applied to B-mode C x􏼁 j�1 images. As expected, NLM performs incoherent averaging (13) and removes speckle pattern. )is is desired for many ap- � � K � � � � 2 − 􏼐�o x −o x􏼁 � /h 􏼑 ( i) j plications such as segmentation and registration [25], but with C x􏼁 � 􏽘 exp . not in elastography. Figure 3 also shows the results of ap- j�1 plying a Gaussian kernel to the RF data. Since averaging is Equation (13) is also known as the NLM algorithm. By performed in the RF domain, the speckle pattern is retained. Finally, the results of CODE denoising are also shown in this considering the normal distributed assumption, (13) can be 2 2 adapted for denoising the RF data by replacing h � 2σ . figure, which visually outperforms other methods in terms of Journal of Healthcare Engineering 5 6000 6000 6000 5000 5000 5000 4000 4000 3000 3000 3000 2000 2000 2000 1000 1000 1000 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 NLM Gaussian CODE Ground truth Ground truth Ground truth Noisy data Noisy data Noisy data (a) (b) (c) Figure 4: (a) Histograms of NLM, ground truth, and noisy data. (b) Histograms of Gaussian denoising, ground truth, and noisy data. Finally, (c) is the same as (b) except the histogram of NLM replaced by that of CODE. Table 1: Values of chi-square and SSD for reconstructed images.. Chi SSD Scatterer NLM Gaussian CODE NLM Gaussian CODE 5/mm 9702.33 167.78 95.49 76250.03 2240.55 2119.90 10/mm 86361.68 253.65 60.18 7482.55 2242.51 1909.44 15/mm 6108.31 294.90 27.63 7961.00 2300.42 1536.20 —e ground truth was obtained from a Field II simulation Table 2: Using Field II ground truth for evaluation of NRMSE for similarity to the original B-mode image. Figure 4 compares di›erent denoising and noisy images. the histogram of the B-mode of these three images. Since the 3 3 3 Method 5/mm 10/mm 15/mm distribution of noise-free image (ground truth) is known, we Noisy 0.1501 0.1298 0.1284 used the following chi-square test as a quantitative pa- NLM 0.3210 0.3208 0.3182 rameter for comparison: Gaussian 0.1595 0.1478 0.1442 O − E 2 t t CODE 0.1354 0.1216 0.1203 χ   , (15) t1 where O is the observed value, E is the expected value, and t t 5. Phantom and In Vivo Elastography m is the number of bins (256 bins of grey levels for simulated We study 3 di›erent cases of phantom data, in vivo liver images). —e chi-squared criterion for distribution and sum ablation data, and tendon data for both GLUE and DPAM. of squared di›erence (SSD) between original and šltered —e results are provided in Figures 5–10. —e window size of images using NLM, Gaussian with kernel width of 5 and 3 provides correct strain map, for CODE meanwhile requires smoothing parameter 1, and CODE with search region 21, the minimum computational budget. To be fair in com- kernel width 5, and smoothing parameter 5, are compared in parison, the window size is the same for both NLM and Table 1. In both cases (chi-squared and SSD), CODE out- Gaussian denoising. performs the conventional NLM approach and Gaussian Phantom data in Figures 5 and 6 are obtained from denoising applied directly on RF data, as demonstrated in a CIRS breast phantom (Norfolk, VA) under free-hand theory in Section 3.2. palpation. —ere is excessive out-of-plane motion between Moreover, with respect to simulations in Field II, the the two processed images, and therefore, the DP step fails. ground truth is available to study error variance of all 3 dis- —is leads to failure in both DPAM and GLUE, which is tributions of scatterers. —e error variance is measured using apparent as black horizontal artifacts in (a), (c) and black normalized root mean square error (NRMSE) dešned as artifact at right down corner of (d) for both mentioned n m I (i, j) − G(i, j) /(m ∗ n) i1 j1 d šgures. However, CODE removes the noise from the RF data NRMSE G, I  , and leads to a strain image with low noise and high contrast. max(G) − min(G) —e phantom contains a cyst in the middle with certain (16) elasticity surrounded by another tissue. —ose artifacts as where G is ground truth of Field II, I is either noisy image described are failing to depict the tissue around the cyst or or denoised version using NLM or Gaussian denoising. the cyst elasticity by showing di›erent elasticities. Table 2 shows that the error variance for the CODE method Patient data in Figures 7 and 8 were acquired from is minimum in comparison with other denoising. a patient undergoing open-surgical radiofrequency thermal 6 Journal of Healthcare Engineering 0.1 0.1 0.08 0.08 0.06 0.06 0.04 0.04 0.02 0.02 0 52 10 15 20 5 0 10 20 Width (mm) Width (mm) (a) (b) 0.1 0.1 5 5 0.08 0.08 10 10 0.06 0.06 0.04 0.04 20 20 25 25 0.02 0.02 05 10 15 20 25 05 10 15 20 25 Width (mm) Width (mm) (c) (d) Figure 5: Denoising results for phantom data: (a) DPAM alone; (b) DPAM with CODE; (c) DPAM with Gaussian; (d) DPAM with NLM. For CODE, the dimension of the search window is (11 × 11), size of the neighbourhood is (3 × 3), and the smoothing parameter h is set to 11. For (c), the kernel size is (3 × 3) and smoothing parameter is 1. For (d), the NLM properties are set as (b), but they are applied on B-mode. 0.08 0.08 0.07 0.07 0.06 0.06 10 10 0.05 0.05 15 15 0.04 0.04 20 20 0.03 0.03 0.02 0.02 0 52 10 20 5 0 10 20 Width (mm) Width (mm) (a) (b) 0.08 0.08 5 5 0.07 0.07 10 0.06 10 0.06 0.05 0.05 15 15 0.04 0.04 20 20 0.03 0.03 25 25 0.02 0.02 05 10 15 20 25 05 10 15 20 25 Width (mm) Width (mm) (c) (d) Figure 6: Denoising results for phantom data: (a) GLUE alone; (b) GLUE with CODE; (c) GLUE with Gaussian; (d) GLUE with NLM. For CODE, the dimension of the search window is (11 × 11), size of the neighbourhood is (3 × 3), and the smoothing parameter h is set to 11. For (c), the kernel size is (3 × 3) and smoothing parameter is 1. For (d), the NLM properties are set as (b), but it is applied on B-mode. ablation for primary or secondary liver cancer. —ese data are able to get the correct strain map for patient data. —e are available online [8]. —e Institutional Ethical Review ablation operation coagulates the tissue, which makes the Board at Johns Hopkins University approved all experi- tissue sti›er. —e coagulated tissue is often referred to as mental procedures involving human subjects. For the pa- ablation lesion, and its size should be bigger than the tumor tient data, ablation procedure generates substantial amount to ensure that the entire tumor is ablated. —e strain images of noise in the RF data [19–21]. As a result of excessive noise, in Figures 7(b) and 8(b) clearly show the ablation lesion as DP fails, which generates the horizontal black and white a dark region with low strain (i.e., hard). CODE helps to bands in the top left of (a), (c), and (d). Although the en- remove noise in RF data, which leads to less noisy strain vironment is extremely noisy, the well-adapted CODE images. Such strain images can help the surgeon to minimize method denoises the RF data in a way that both algorithms the cancer recurrence rate. However, NLM and Gaussian fail Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Journal of Healthcare Engineering 7 0.02 0.02 0.015 0.015 20 20 0.01 0.01 30 30 0.005 0.005 40 40 0 0 0 10 20 0 5 10 15 20 25 Width (mm) Width (mm) (a) (b) 0.02 0.02 10 10 0.015 0.015 0.01 0.01 0.005 0.005 0 0 05 10 15 20 25 05 10 15 20 25 Width (mm) Width (mm) (c) (d) Figure 7: Same as Figure 5 except in vivo liver ablation, patient data are used: (a) DPAM alone; (b) DPAM with CODE; (c) DPAM with Gaussian; (d) DPAM with NLM. 0.02 0.02 0.015 0.015 20 20 0.01 0.01 30 30 0.005 0.005 40 40 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Width (mm) Width (mm) (a) (b) 0.02 0.02 10 10 0.015 0.015 20 20 0.01 0.01 30 30 0.005 0.005 40 40 0 0 05 10 15 20 25 05 10 15 20 25 Width (mm) Width (mm) (c) (d) Figure 8: Same as Figure 6 except in vivo liver ablation, patient data are used: (a) GLUE alone; (b) GLUE with CODE; (c) DPAM alone; (d) DPAM with CODE. to reconstruct the strain map and show sudden changes in frequency of 40 MHz. )e results are shown in Figures 9 and tissue that are misleading and violate tissue continuity. 10. )e probe is held stationary, and the subject flexes his We also evaluate CODE on data collected from patellar knee joint during data collection. CODE removes the noise tendon. )ese data were collected at the PERFORM Centre in the RF data and results in a more meaningful strain image. at Concordia University. Ethics approval was obtained for this study from Quebec’s Ministere de la Sante et des Ser- 6. Conclusions vices Sociaux, and all subjects signed a consent form to participate. Data are collected using an Alpinion ECube In this paper, we have proposed a denoising algorithm, ultrasound machine (Bothell, WA) with a L3-12 linear referred to as the CODE (COherent Denoising for Elas- transducer at the centre frequency of 11 MHz with sampling tography) approach for ultrasound elastography. CODE is Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) 8 Journal of Healthcare Engineering 0.02 0.02 0.015 0.015 10 0.01 0.01 0.005 15 0.005 0 0 1 20 0 10 20 Width (mm) Width (mm) (a) (b) 0.02 0.02 5 5 0.015 0.015 10 10 0.01 0.01 15 15 0.005 0.005 0 10 20 0 10 20 Width (mm) Width (mm) (c) (d) Figure 9: Same as Figure 5 except in vivo liver ablation, patient tendon data are used: (a) DPAM alone; (b) DPAM with CODE; (c) DPAM with Gaussian; (d) DPAM with NLM. 0.02 0.02 0.015 0.015 2 0.01 0.01 0.005 0.005 0 0 1 20 1 20 Width (mm) Width (mm) (a) (b) 0.02 0.02 1 1 0.015 0.015 2 0.01 2 0.01 0.005 0.005 3 3 0 0 0 10 20 0 10 20 Width (mm) Width (mm) (c) (d) Figure 10: Same as Figure 6 except in vivo liver ablation, patient tendon data are used: (a) GLUE alone; (b) GLUE with CODE; (c) GLUE with Gaussian; (d) GLUE with NLM. applied directly to the RF data and has the ability to other constraints. Some of the data used in this paper are eliminate noise, while retaining relevant speckle patterns. available online [8]. —is is demonstrated using phantom and experiments based on in vivo clinical data. —e results of CODE are used for Conflicts of Interest GLUE and DPAM, which verišes the e›ectiveness of the —e authors declare that they have no con¦icts of interest. proposed CODE. More clinical studies are needed to fully verify the benešts of the CODE algorithm. Acknowledgments —e authors would like to thank Julian Lee from Alpinion Data Availability USA for technical help. —e liver data were collected at —e data collected for this publication cannot be shared Johns Hopkins Hospital. —e authors would like to thank online due to the requirements of the ethics approval and the principal investigators Drs. E. Boctor, M. Choti, and Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) 00 Journal of Healthcare Engineering 9 [16] H. Rivaz, R. Zellars, G. 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Nonlocal Coherent Denoising of RF Data for Ultrasound Elastography

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Copyright © 2018 P. Khavari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Journal of Healthcare Engineering Volume 2018, Article ID 7979528, 9 pages https://doi.org/10.1155/2018/7979528 Research Article Nonlocal Coherent Denoising of RF Data for Ultrasound Elastography 1 1 2 1 P. Khavari , A. Asif, M. Boily, and H. Rivaz Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada Department of Diagnostic Radiology, McGill University, Montreal, QC, Canada Correspondence should be addressed to P. Khavari; p_khavar@encs.concordia.ca Received 16 January 2018; Accepted 30 April 2018; Published 24 June 2018 Academic Editor: Terry K. K. Koo Copyright © 2018 P. Khavari et al. )is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Ultrasound elastography infers mechanical properties of living tissues from ultrasound radiofrequency (RF) data recorded while the tissues are undergoing deformation. A challenging yet critical step in ultrasound elastography is to estimate the tissue displacement (or, equivalently the time delay estimate) fields from pairs of RF data. )e RF data are often corrupted with noise, which causes the displacement estimator to fail in many in vivo experiments. To address this problem, we present a nonlocal, coherent denoising approach based on Bayesian estimation to reduce the impact of noise. Despite incoherent denoising al- gorithms that smooth the B-mode images, the proposed denoising algorithm is used to suppress noise while maintaining useful information such as speckle patterns. We refer to the proposed approach as COherent Denoising for Elastography (CODE) and evaluate its performance when CODE is used in conjunction with the two state-of-art elastography algorithms, namely: (i) GLobal Ultrasound Elastography (GLUE) and (ii) Dynamic Programming Analytic Minimization elastography (DPAM). Our results show that CODE substantially improves the strain result of both GLUE and DPAM. At the heart of both GLUE and DPAM is an energy 1.Introduction minimization approach to determine TDE’s. A dynamic Ultrasound elastography determines the viscoelastic prop- programming approach is used in both cases to compute erties of tissues and is useful for diagnosis of pathology and TDE’s first at a coarse pixel level. )e resolution of the TDE’s is then enhanced to the finer subpixel level through ana- for aiding surgeons in the operating room. Broadly speaking, ultrasound elastography can be grouped into two categories lytical minimization. Given that RF ultrasound data can be [1–6]: dynamic elastography and quasi-static elastography. corrupted by several factors such as thermal and electronic In this paper, we focus on two state-of-art free-hand pal- noise, there is a need to compensate for noise in the RF data. pations and quasi-static elastographic approaches, namely, Traditional filtering techniques, such as the convolution with GLobal Ultrasound Elastography(GLUE) [7] and Real-Time a Gaussian kernel, use local continuity in the images to reduce Regularized Ultrasound Elastography (DPAM) [8]. Both noise. A new class of denoising algorithms, referred to as approaches use successive pairs of frames of ultrasound RF nonlocal means (NLM) [9], considers data from a much larger data to estimate the tissue displacement (also referred to as “nonlocal” region for denoising. NLM relies on redundancy time delay estimates (TDE)). )e derivative of TDE provides in images and uses the weighted average of most similar an estimate of the induced strain that represents the stiffness intraframe pixels within a large nonlocal neighbourhood to eliminate noise. or softness of the tissue being imaged. Figure 1 illustrates the steps involved in quasi-static ultrasound elastography Most NLM-based denoising approaches [10–12] remove with the handheld device shown on the left handside and noise from processed output of the RF data, which is referred the displacement field estimates defined using the two to as B-mode images in ultrasound literature. NLM denois- frames on the right. ing reduces speckle pattern and generates smooth B-mode 2 Journal of Healthcare Engineering Ultrasound probe Before deformation I Aer deformation I 1 2 Lateral (z) 12 … jn … 12 … jn … 1 1 Axial (x) 2 2 . . . . . . (i, j) . . . . . . (i + a , j + l ) i,j i,j Tissue (a) (b) (c) Figure 1: Illustration of ultrasound elastography. (a) A handheld device that induces an external stimulus into the tissues. (b, c) Two successive frames I and I of RF data. —e goal of ultrasound elastography was to šnd the displacement (a ,l ) for each pixel (i, j) in the 1 2 i,j i,j I RF frame. images. Ultrasound speckle is useful in several image analysis 2. Quasi-Static Elastography: GLUE and DPAM techniques, such as ultrasound elastography [13, 14], free- Both DPAM and GLUE are quasi-static approaches based on hand sensorless 3D ultrasound [15, 16], and quantitative the optimization of a regularized cost function to determine ultrasound [17]. In this work, we focus on ultrasound tissue displacements. —ey both aim at šnding the axial and elastography. lateral displacements (a and l) of all samples of RF data as In this paper, we present an alternate approach, wherein shown in Figure 1. DPAM uses dynamic programming (DP) the NLM denoising algorithm is applied directly to raw RF to šrst estimate the integer displacement of a seed-line in data instead of processed B-mode images. We refer to the terms of the number of pixels and then applies analytical proposed approach as COherent Denoising for Elastography minimization (AM) to šne tune the estimated displacement (CODE) and evaluate its performance on in vivo liver ablation to the subpixel level. —e strain image is obtained using the data when used in conjunction with two commonly used spatial di›erentiation of the displacement šeld. GLUE also elastography algorithms, namely: (i) GLobal Ultrasound uses DP for estimating the integer tissue displacements and Elastography (GLUE) [7] and (ii) Dynamic Programming rešnes the estimates to subpixels for the entire image si- Analytic Minimization elastography (DPAM) [8]. CODE multaneously. In other words, GLUE solves an optimization exploits the complete set of information in the RF domain, function where both axial and lateral displacements of every some of which is likely to be lost in the processing steps used sample of the RF frame are unknowns, that is, in the order of to generate the B-mode images. It is, therefore, our intuition a million variables. —is is in contrast to DPAM, which that CODE would result in superior denoising results. Using rešnes the estimates line-by-line. —e strain image again is information in RF data to generate visually informative calculated based on the di›erentiation of displacement map B-mode images is challenging [18]. To illustrate the superi- similar to DPAM. Although GLUE and DPAM perform well ority of CODE, both mathematical analysis and experimental in most cases, they may not converge to the correct solution results are included in the paper. Our comparisons corrob- in the presence of excessive noise. In the next section, we orate our intuition and verify the usefulness of CODE. present our denoising approach used to reduce the impact of —e rest of this paper is organized as follows. In Section noise in the RF domain. 2, we introduce GLUE and DPAM as representative quasi- static elastography approaches. Section 3 provides back- ground on nonlocal denoising and introduces CODE as 3. The Nonlocal Denoising Approach a Bayesian estimator. In Section 4, we explore the ability of CODE on simulation data. Experimental results using —e central idea behind this paper is to apply coherent phantom and in vivo data are included in Section 5. Finally, denoising on RF data. Unlike incoherent denoising ap- we conclude the paper in Section 6. proaches that process the B-mode images to remove noise Journal of Healthcare Engineering 3 (resulting in spatial averaging and signišcant loss of speckle x x j,1 j,1 patterns), the proposed approach retains speckle patterns. x x j,2 j,2 We šrst outline NLM, which is followed by a description of x x x j j,3 j,3 the CODE algorithm, including an analytical justišcation of x x j,4 j,4 why CODE provides better denoising results. x x j,5 j,5 x x j,6 j,6 3.1. Nonlocal Means. Let v(i) be the observed value of the x x j,7 j,7 x x x discretized image for pixel i and u(i) be its true value. Due to i j,8 j,8 the presence of noise n(i), we have x x j,9 j,9 v(i) u(i)+ n(i). (1) To simplify our explanation, we focus on 1D signals, but our results are generalizable to 2D images. In fact, the ex- perimental results included in Section 4 are for 2D phantom and in vivo liver ablation data. To denoise the image for each pixel i, NLM searches a reference area of the image within Figure 2: Illustration for the patch and vectorized indices used in a rectangular search window Δ , which is centered around the proposed CODE approach for n  9. pixel i (Figure 2). A neighbourhood N of known dimension is selected around pixel i and compared to neighbourhood N around pixel j for all j ∈Δ . For pixel i, weight w(i, j) is j i assigned to each pixel j. —e value of pixel i is then replaced by We now provide an analytical explanation of why NLM denoising is adapted for the RF domain. Let g(x) and o(x) NLM[v](i)  w(i, j) ∗ v(j). (2) be vectorized ground truth and observed patches of size n j∈Δ centered at pixel x of RF data (Figure 2). We dešne them as —e distance metric is proportional to the square of the g(x) g(x ) with x ∈ N (x) and o(x) o(x ), where k k g k x ∈ N (x) and  N ,N are the neighbourhoods Euclidian distance between the two patches. —e weight is k o o g √ √ then calculated as (patches) of size ( n × n ) around the central pixel x in 2 ground truth and observed images. Our goal is to derive the       vN − v N     1 i j 2,a Bayesian estimator g(x) for patch g(x) based on the observed (3) w(i, j) exp − .  2  patch o(x). Dešning the optimal estimator by minimizing the Z  h  posterior expected loss as Based on (3), it is clear that the weight is the convo- E[L(g(x), g (x))]   [L(g(x), g(x))]p(g(x)|o(x)), lution of a Gaussian with standard deviation a > 0 and the g(x)∈Γ squared Euclidean distance between two neighbourhoods (5) v(N ) − v(N ) , for N and N . —e smoothing parameter i j i j h controls the contribution of the Gaussian-Euclidean where Γ constitutes all possible outcomes of g(x), the loss distance exponent in the weights. —e normalization factor function is given by Z for pixel i is given by   L(g(x), g (x))  g(x) − g(x) . (6) vN  − vN   i j 2,a (4) Z(i) exp − ,  2   h  j∈Δ Substituting (6) in (5), the optimal Bayesian estimator is where the weight is normalized to ensure that the dynamic range g (x)  arg min 2 opt g(x) − g(x) p(g(x)|o(x)) of the NLM[v](i) is the same as that of its counterpart v(i).  g(x) g(x) (7) g(x)p(g(x)|o(x)). 3.2. e Proposed Bayesian CODE Framework. Noise in g(x) ultrasound B-mode images originates from piezoelectric sensors and data acquisition card. Depending on the ap- Equation (7) can be expressed as plication, the level of noise can even be higher. For example, p(g(x), o(x)) g (x)  g(x) ablation treatment generates heat and microbubbles that opt p(o(x)) g(x) severely deteriorate RF data [19–21]. Both logarithmic (8) compression and envelope detection steps, applied to derive g(x)p(o(x)|g(x))p(g(x)) g(x) the B-mode image, are nonlinear operations that complicate measurement noise added by sensors and acquisition card. p(o(x)|g(x))p(g(x)) g(x) Our CODE approach eliminates noise introduced by sensors and acquisition card before the nonlinear logarithmic com- Only a subset of Γ is accessible in the search region of the pression and envelope detection by applying NLM directly to central pixel x . We refer to this subset as the search region, RF ultrasound data. SR(x) g (x), g (x), g (x), ... , g (x) . Assuming that 1 2 3 K 4 Journal of Healthcare Engineering (a) (b) (c) (d) (e) Figure 3: Field II simulation results. )e noisy input has substantially less contrast than the ground truth image. NLM is designed to remove speckle and therefore substantially reduces image detail. CODE output is closest to the ground truth. (a) Ground truth, (b) noisy, (c) NLM, (d) Gaussian on RF, and (e) CODE. cardinality of SR is K and p(g(x)) is uniformly distributed, )erefore, the adapted filter for denoising the RF data that is, p(g (x)) � 1/K, for all(0 ≤ i ≤ K), (8) simplifies to (CODE) is � � K 2 � � 􏼌 � � 2 − 􏼐 o x −o x􏼁 /2σ 􏼑 􏼌 � ( ) � K i j 􏽐 g􏼐x 􏼑p􏼐o x􏼁 􏼌g􏼐x 􏼑􏼑 g x􏼁 � 􏽘 exp o􏼐x 􏼑, j i j i j j�1 C x 􏽢 � 􏼌 g x􏼁 , (9) i j�1 i 􏼌 􏽐 p􏼐o x􏼁 􏼌g􏼐x 􏼑􏼑 j�1 i j (14) � � K � � � � 2 − o x −o x /2σ 􏼐� ( ) 􏼁 � 􏼑 i j where g 􏽢(x ) is the optimal estimator based on the uniform with C x􏼁 � 􏽘 exp . distribution assumption. Given the ground truth is not j�1 accessible, we substitute the observed value of the neigh- )is filter is based on the noise statistics of RF data. bourhood patches to get CODE is, therefore, the optimal denoising approach for 􏽐 o􏼐x 􏼑p􏼐o x􏼁 o􏼐x 􏼑􏼑 removing noise in (11) within the RF domain. j�1 j i j 􏽢 􏼌 g x􏼁 � . (10) i 􏼌 Kevrann et al. [12] and Coupe et al. [10] have developed 􏽐 p􏼐o x􏼁 􏼌o􏼐x 􏼑􏼑 j�1 i j similar Bayesian estimators but for reducing the speckles pattern in the B-mode image. Aligned with the mathematical Given that the noise in the RF data is modelled as an Bayesian estimator, the properties of noise in RF data show additive Gaussian noise [22, 23], we have the usefulness of CODE for removing noise from the RF ultrasound data. o(x) � g(x) + v(x), (11) where v(x) is the additive white Gaussian noise with vari- 4. Simulation Validation for Code ance σ . By assuming that the likelihood can be factorized as To assess the performance of the CODE approach, the Field 􏼌 II [24] software is used to simulate RF data from a lesion p􏼐o x􏼁 o􏼐x 􏼑􏼑 � 􏽙 p􏼒o􏼐x 􏼑 o􏼐x 􏼑􏼓, 􏼌 (12) i j i,k j,k phantom of size 60, 50, and 10 mm in axial, lateral, and out- k�1 of-plane directions, respectively. )e phantoms consist of where x ∈ N(x ) and x ∈ N(x ) are the counterpart two classes of background and target tissues. To determine i,k i j,k j pixels in the patches with central pixels x and x . )ere- the precision and sensitivity of the CODE, three different i j fore, p(o(x )|o(x )) is multivariant normal distributed setups with 5, 10, and 15 scatterers per resolution cell dis- i j p(o(x )|o(x )) ∼ N(o(x ), σ I ). Notation I is the identity tributed randomly within the phantom are used. Different i j j n n matrix. )us, the filter in (10) can be adapted to remove the realizations for each group of scatterers are generated. )e noise of RF data as RF output of Field II is corrupted by adding additive white � � K � � Gaussian noise with a SNR of 5 dB. � � 2 − 􏼐�o x −o x􏼁 � /h 􏼑 ( i) j g 􏽢 x􏼁 � 􏽘 exp o􏼐x 􏼑, i j Figure 3 shows the results of NLM applied to B-mode C x􏼁 j�1 images. As expected, NLM performs incoherent averaging (13) and removes speckle pattern. )is is desired for many ap- � � K � � � � 2 − 􏼐�o x −o x􏼁 � /h 􏼑 ( i) j plications such as segmentation and registration [25], but with C x􏼁 � 􏽘 exp . not in elastography. Figure 3 also shows the results of ap- j�1 plying a Gaussian kernel to the RF data. Since averaging is Equation (13) is also known as the NLM algorithm. By performed in the RF domain, the speckle pattern is retained. Finally, the results of CODE denoising are also shown in this considering the normal distributed assumption, (13) can be 2 2 adapted for denoising the RF data by replacing h � 2σ . figure, which visually outperforms other methods in terms of Journal of Healthcare Engineering 5 6000 6000 6000 5000 5000 5000 4000 4000 3000 3000 3000 2000 2000 2000 1000 1000 1000 0 0 0 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 NLM Gaussian CODE Ground truth Ground truth Ground truth Noisy data Noisy data Noisy data (a) (b) (c) Figure 4: (a) Histograms of NLM, ground truth, and noisy data. (b) Histograms of Gaussian denoising, ground truth, and noisy data. Finally, (c) is the same as (b) except the histogram of NLM replaced by that of CODE. Table 1: Values of chi-square and SSD for reconstructed images.. Chi SSD Scatterer NLM Gaussian CODE NLM Gaussian CODE 5/mm 9702.33 167.78 95.49 76250.03 2240.55 2119.90 10/mm 86361.68 253.65 60.18 7482.55 2242.51 1909.44 15/mm 6108.31 294.90 27.63 7961.00 2300.42 1536.20 —e ground truth was obtained from a Field II simulation Table 2: Using Field II ground truth for evaluation of NRMSE for similarity to the original B-mode image. Figure 4 compares di›erent denoising and noisy images. the histogram of the B-mode of these three images. Since the 3 3 3 Method 5/mm 10/mm 15/mm distribution of noise-free image (ground truth) is known, we Noisy 0.1501 0.1298 0.1284 used the following chi-square test as a quantitative pa- NLM 0.3210 0.3208 0.3182 rameter for comparison: Gaussian 0.1595 0.1478 0.1442 O − E 2 t t CODE 0.1354 0.1216 0.1203 χ   , (15) t1 where O is the observed value, E is the expected value, and t t 5. Phantom and In Vivo Elastography m is the number of bins (256 bins of grey levels for simulated We study 3 di›erent cases of phantom data, in vivo liver images). —e chi-squared criterion for distribution and sum ablation data, and tendon data for both GLUE and DPAM. of squared di›erence (SSD) between original and šltered —e results are provided in Figures 5–10. —e window size of images using NLM, Gaussian with kernel width of 5 and 3 provides correct strain map, for CODE meanwhile requires smoothing parameter 1, and CODE with search region 21, the minimum computational budget. To be fair in com- kernel width 5, and smoothing parameter 5, are compared in parison, the window size is the same for both NLM and Table 1. In both cases (chi-squared and SSD), CODE out- Gaussian denoising. performs the conventional NLM approach and Gaussian Phantom data in Figures 5 and 6 are obtained from denoising applied directly on RF data, as demonstrated in a CIRS breast phantom (Norfolk, VA) under free-hand theory in Section 3.2. palpation. —ere is excessive out-of-plane motion between Moreover, with respect to simulations in Field II, the the two processed images, and therefore, the DP step fails. ground truth is available to study error variance of all 3 dis- —is leads to failure in both DPAM and GLUE, which is tributions of scatterers. —e error variance is measured using apparent as black horizontal artifacts in (a), (c) and black normalized root mean square error (NRMSE) dešned as artifact at right down corner of (d) for both mentioned n m I (i, j) − G(i, j) /(m ∗ n) i1 j1 d šgures. However, CODE removes the noise from the RF data NRMSE G, I  , and leads to a strain image with low noise and high contrast. max(G) − min(G) —e phantom contains a cyst in the middle with certain (16) elasticity surrounded by another tissue. —ose artifacts as where G is ground truth of Field II, I is either noisy image described are failing to depict the tissue around the cyst or or denoised version using NLM or Gaussian denoising. the cyst elasticity by showing di›erent elasticities. Table 2 shows that the error variance for the CODE method Patient data in Figures 7 and 8 were acquired from is minimum in comparison with other denoising. a patient undergoing open-surgical radiofrequency thermal 6 Journal of Healthcare Engineering 0.1 0.1 0.08 0.08 0.06 0.06 0.04 0.04 0.02 0.02 0 52 10 15 20 5 0 10 20 Width (mm) Width (mm) (a) (b) 0.1 0.1 5 5 0.08 0.08 10 10 0.06 0.06 0.04 0.04 20 20 25 25 0.02 0.02 05 10 15 20 25 05 10 15 20 25 Width (mm) Width (mm) (c) (d) Figure 5: Denoising results for phantom data: (a) DPAM alone; (b) DPAM with CODE; (c) DPAM with Gaussian; (d) DPAM with NLM. For CODE, the dimension of the search window is (11 × 11), size of the neighbourhood is (3 × 3), and the smoothing parameter h is set to 11. For (c), the kernel size is (3 × 3) and smoothing parameter is 1. For (d), the NLM properties are set as (b), but they are applied on B-mode. 0.08 0.08 0.07 0.07 0.06 0.06 10 10 0.05 0.05 15 15 0.04 0.04 20 20 0.03 0.03 0.02 0.02 0 52 10 20 5 0 10 20 Width (mm) Width (mm) (a) (b) 0.08 0.08 5 5 0.07 0.07 10 0.06 10 0.06 0.05 0.05 15 15 0.04 0.04 20 20 0.03 0.03 25 25 0.02 0.02 05 10 15 20 25 05 10 15 20 25 Width (mm) Width (mm) (c) (d) Figure 6: Denoising results for phantom data: (a) GLUE alone; (b) GLUE with CODE; (c) GLUE with Gaussian; (d) GLUE with NLM. For CODE, the dimension of the search window is (11 × 11), size of the neighbourhood is (3 × 3), and the smoothing parameter h is set to 11. For (c), the kernel size is (3 × 3) and smoothing parameter is 1. For (d), the NLM properties are set as (b), but it is applied on B-mode. ablation for primary or secondary liver cancer. —ese data are able to get the correct strain map for patient data. —e are available online [8]. —e Institutional Ethical Review ablation operation coagulates the tissue, which makes the Board at Johns Hopkins University approved all experi- tissue sti›er. —e coagulated tissue is often referred to as mental procedures involving human subjects. For the pa- ablation lesion, and its size should be bigger than the tumor tient data, ablation procedure generates substantial amount to ensure that the entire tumor is ablated. —e strain images of noise in the RF data [19–21]. As a result of excessive noise, in Figures 7(b) and 8(b) clearly show the ablation lesion as DP fails, which generates the horizontal black and white a dark region with low strain (i.e., hard). CODE helps to bands in the top left of (a), (c), and (d). Although the en- remove noise in RF data, which leads to less noisy strain vironment is extremely noisy, the well-adapted CODE images. Such strain images can help the surgeon to minimize method denoises the RF data in a way that both algorithms the cancer recurrence rate. However, NLM and Gaussian fail Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Journal of Healthcare Engineering 7 0.02 0.02 0.015 0.015 20 20 0.01 0.01 30 30 0.005 0.005 40 40 0 0 0 10 20 0 5 10 15 20 25 Width (mm) Width (mm) (a) (b) 0.02 0.02 10 10 0.015 0.015 0.01 0.01 0.005 0.005 0 0 05 10 15 20 25 05 10 15 20 25 Width (mm) Width (mm) (c) (d) Figure 7: Same as Figure 5 except in vivo liver ablation, patient data are used: (a) DPAM alone; (b) DPAM with CODE; (c) DPAM with Gaussian; (d) DPAM with NLM. 0.02 0.02 0.015 0.015 20 20 0.01 0.01 30 30 0.005 0.005 40 40 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Width (mm) Width (mm) (a) (b) 0.02 0.02 10 10 0.015 0.015 20 20 0.01 0.01 30 30 0.005 0.005 40 40 0 0 05 10 15 20 25 05 10 15 20 25 Width (mm) Width (mm) (c) (d) Figure 8: Same as Figure 6 except in vivo liver ablation, patient data are used: (a) GLUE alone; (b) GLUE with CODE; (c) DPAM alone; (d) DPAM with CODE. to reconstruct the strain map and show sudden changes in frequency of 40 MHz. )e results are shown in Figures 9 and tissue that are misleading and violate tissue continuity. 10. )e probe is held stationary, and the subject flexes his We also evaluate CODE on data collected from patellar knee joint during data collection. CODE removes the noise tendon. )ese data were collected at the PERFORM Centre in the RF data and results in a more meaningful strain image. at Concordia University. Ethics approval was obtained for this study from Quebec’s Ministere de la Sante et des Ser- 6. Conclusions vices Sociaux, and all subjects signed a consent form to participate. Data are collected using an Alpinion ECube In this paper, we have proposed a denoising algorithm, ultrasound machine (Bothell, WA) with a L3-12 linear referred to as the CODE (COherent Denoising for Elas- transducer at the centre frequency of 11 MHz with sampling tography) approach for ultrasound elastography. CODE is Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) 8 Journal of Healthcare Engineering 0.02 0.02 0.015 0.015 10 0.01 0.01 0.005 15 0.005 0 0 1 20 0 10 20 Width (mm) Width (mm) (a) (b) 0.02 0.02 5 5 0.015 0.015 10 10 0.01 0.01 15 15 0.005 0.005 0 10 20 0 10 20 Width (mm) Width (mm) (c) (d) Figure 9: Same as Figure 5 except in vivo liver ablation, patient tendon data are used: (a) DPAM alone; (b) DPAM with CODE; (c) DPAM with Gaussian; (d) DPAM with NLM. 0.02 0.02 0.015 0.015 2 0.01 0.01 0.005 0.005 0 0 1 20 1 20 Width (mm) Width (mm) (a) (b) 0.02 0.02 1 1 0.015 0.015 2 0.01 2 0.01 0.005 0.005 3 3 0 0 0 10 20 0 10 20 Width (mm) Width (mm) (c) (d) Figure 10: Same as Figure 6 except in vivo liver ablation, patient tendon data are used: (a) GLUE alone; (b) GLUE with CODE; (c) GLUE with Gaussian; (d) GLUE with NLM. applied directly to the RF data and has the ability to other constraints. Some of the data used in this paper are eliminate noise, while retaining relevant speckle patterns. available online [8]. —is is demonstrated using phantom and experiments based on in vivo clinical data. —e results of CODE are used for Conflicts of Interest GLUE and DPAM, which verišes the e›ectiveness of the —e authors declare that they have no con¦icts of interest. proposed CODE. More clinical studies are needed to fully verify the benešts of the CODE algorithm. Acknowledgments —e authors would like to thank Julian Lee from Alpinion Data Availability USA for technical help. —e liver data were collected at —e data collected for this publication cannot be shared Johns Hopkins Hospital. —e authors would like to thank online due to the requirements of the ethics approval and the principal investigators Drs. E. Boctor, M. Choti, and Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) Depth (mm) 00 Journal of Healthcare Engineering 9 [16] H. Rivaz, R. Zellars, G. Hager, G. Fichtinger, and E. Boctor, G. Hager who provided the data. )is research has been “9c-1 beam steering approach for speckle characterization and provided by two NSERC Discovery Grants RGPIN-2015- out-of-plane motion estimation in real tissue,” in Proceedings 04136 and 228415. of the Ultrasonics Symposium, 2007, pp. 781–784, IEEE, New York, NY, USA, October 2007. References [17] M. L. Oelze and J. Mamou, “Review of quantitative ultra- sound: Envelope statistics and backscatter coefficient imaging [1] J. Ophir, S. K. Alam, B. Garra et al., “Elastography: ultrasonic and contributions to diagnostic ultrasound,” IEEE Trans- estimation and imaging of the elastic properties of tissues,” actions on Ultrasonics, Ferroelectrics, and Frequency Control, Proceedings of the Institution of Mechanical Engineers, Part H: vol. 63, no. 2, pp. 336–351, 2016. Journal of Engineering in Medicine, vol. 213, no. 3, pp. 203– [18] C. Wachinger, T. Klein, and N. 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