Sparsity regularization for image reconstruction with Poisson data

Daniel J Lingenfelter; Jeffrey A. Fessler; Zhong He

doi:10.1117/12.816961

2 February 2009 Sparsity regularization for image reconstruction with Poisson data

Daniel J Lingenfelter, Jeffrey A. Fessler, Zhong He

Proceedings Volume 7246, Computational Imaging VII; 72460F (2009) https://doi.org/10.1117/12.816961
Event: IS&T/SPIE Electronic Imaging, 2009, San Jose, California, United States

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.

Citation Download Citation

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); https://doi.org/10.1117/12.816961

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available