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2 February 2009 Sparsity regularization for image reconstruction with Poisson data
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Proceedings Volume 7246, Computational Imaging VII; 72460F (2009)
Event: IS&T/SPIE Electronic Imaging, 2009, San Jose, California, United States
This work investigates three penalized-likelihood expectation maximization (EM) algorithms for image reconstruction with Poisson data where the images are known a priori to be sparse in the space domain. The penalty functions considered are the l1 norm, the l0 "norm", and a penalty function based on the sum of logarithms of pixel values,(see equation in PDF) Our results show that the l1 penalized algorithm reconstructs scaled versions of the maximum-likelihood (ML) solution, which does not improve the sparsity over the traditional ML estimate. Due to the singularity of the Poisson log-likelihood at zero, the l0 penalized EM algorithm is equivalent to the maximum-likelihood EM algorithm. We demonstrate that the penalty based on the sum of logarithms produces sparser images than the ML solution. We evaluated these algorithms using experimental data from a position-sensitive Compton-imaging detector, where the spatial distribution of photon-emitters is known to be sparse.
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Daniel J Lingenfelter, Jeffrey A. Fessler, and Zhong He "Sparsity regularization for image reconstruction with Poisson data", Proc. SPIE 7246, Computational Imaging VII, 72460F (2 February 2009);

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