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.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
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.