Access the full text.
Sign up today, get DeepDyve free for 14 days.
A. Kondor (1983)
Method of convergent weights — An iterative procedure for solving Fredholm's integral equations of the first kindNuclear Instruments and Methods in Physics Research, 216
Bernard Silverman (1982)
On the Estimation of a Probability Density Function by the Maximum Penalized Likelihood MethodAnnals of Statistics, 10
G. Latham (1995)
Existence of EMS Solutions and a Priori EstimatesSIAM J. Matrix Anal. Appl., 16
Y. Vardi, L. Shepp, L. Kaufman (1985)
A Statistical Model for Positron Emission TomographyJournal of the American Statistical Association, 80
Bernard Silverman, M. Jones, J. Wilson, D. Nychka (1990)
A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomographyJournal of the royal statistical society series b-methodological, 52
P. Eggermont, V. LaRiccia (1995)
Maximum Smoothed Likelihood Density Estimation for Inverse ProblemsAnnals of Statistics, 23
D. Nychka (1990)
Some properties of adding a smoothing step to the EM algorithmStatistics & Probability Letters, 9
E. Levitan, G. Herman (1987)
A Maximum a Posteriori Probability Expectation Maximization Algorithm for Image Reconstruction in Emission TomographyIEEE Transactions on Medical Imaging, 6
I. Csiszár (1975)
$I$-Divergence Geometry of Probability Distributions and Minimization ProblemsAnnals of Probability, 3
J. Kemperman (1969)
On the Optimum Rate of Transmitting InformationAnnals of Mathematical Statistics, 40
H. Mülthei, B. Schorr, W. Törnig (1987)
On an iterative method for a class of integral equations of the first kindMathematical Methods in The Applied Sciences, 9
K. Lange (1990)
Convergence of EM image reconstruction algorithms with Gibbs smoothing.IEEE transactions on medical imaging, 9 4
L. Cruz-Orive (1983)
Distribution‐free estimation of sphere size distributions from slabs showing overprojection and truncation, with a review of previous methodsJournal of Microscopy, 131
H. Mülthei, B. Schorr, W. Törnig (1989)
On properties of the iterative maximum likelihood reconstruction methodMathematical Methods in The Applied Sciences, 11
E. Kosarev, V. Peskov, E. Podolyak (1983)
High resolution soft X-ray spectrum reconstruction by MWPC attenuation measurementsNuclear Instruments and Methods in Physics Research, 208
E. Kosarev (1990)
Shannon's superresolution limit for signal recoveryInverse Problems, 6
J. Wilson (1989)
A smoothed em algorithm for the solution of wicksell's corpuscle problemJournal of Statistical Computation and Simulation, 31
Y. Vardi, D. Lee (1993)
From image deblurring to optimal investments : maximum likelihood solutions for positive linear inverse problemsJournal of the royal statistical society series b-methodological, 55
J. Llacer, E. Veklerov (1989)
Feasible images and practical stopping rules for iterative algorithms in emission tomography.IEEE transactions on medical imaging, 8 2
We study a modification of the EMS algorithm in which each step of the EMS algorithm is preceded by a nonlinear smoothing step of the form $ {\cal N} f = \exp(S^{*}\log f) $ , where S is the smoothing operator of the EMS algorithm. In the context of positive integral equations (à la positron emission tomography) the resulting algorithm is related to a convex minimization problem which always admits a unique smooth solution, in contrast to the unmodified maximum likelihood setup. The new algorithm has slightly stronger monotonicity properties than the original EM algorithm. This suggests that the modified EMS algorithm is actually an EM algorithm for the modified problem. The existence of a smooth solution to the modified maximum likelihood problem and the monotonicity together imply the strong convergence of the new algorithm. We also present some simulation results for the integral equation of stereology, which suggests that the new algorithm behaves roughly like the EMS algorithm.
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2007
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.