Share Email Print
cover

Proceedings Paper

Sparsity regularization for image reconstruction with Poisson data
Format Member Price Non-Member Price
PDF $14.40 $18.00

Paper Abstract

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.

Paper Details

Date Published: 3 February 2009
PDF: 10 pages
Proc. SPIE 7246, Computational Imaging VII, 72460F (3 February 2009); doi: 10.1117/12.816961
Show Author Affiliations
Daniel J Lingenfelter, Univ. of Michigan, Ann Arbor (United States)
Jeffrey A. Fessler, Univ. of Michigan, Ann Arbor (United States)
Zhong He, Univ. of Michigan, Ann Arbor (United States)


Published in SPIE Proceedings Vol. 7246:
Computational Imaging VII
Charles A. Bouman; Eric L. Miller; Ilya Pollak, Editor(s)

© SPIE. Terms of Use
Back to Top