Abstract: Maximizing some form of Poisson likelihood (either
with or without penalization) is central to image reconstruction
algorithms in emission tomography. In this paper we introduce
NMML, a non-monotonic algorithm for maximum likelihood
PET image reconstruction. NMML offers a simple and flexible
procedure that also easily incorporates standard convex regularization
for doing penalized likelihood estimation. A vast number
image reconstruction algorithms have been developed for PET,
and new ones continue to be designed. Among these, methods
based on the expectation maximization (EM) and ordered-subsets
(OS) framework seem to have enjoyed the greatest popularity.
Our method NMML differs fundamentally from methods based
on EM: i) it does not depend on the concept of optimization transfer
(or surrogate functions); and ii) it is a rapidly converging nonmonotonic
descent procedure. The greatest strengths of NMML,
however, are its simplicity, efficiency, and scalability, which
make it especially attractive for tomographic reconstruction. We
provide a theoretical analysis NMML, and empirically observe
it to outperform standard EM based methods, sometimes by
orders of magnitude. NMML seamlessly allows integreation of
penalties (regularizers) in the likelihood. This ability can prove to
be crucial, especially because with the rapidly rising importance
of combined PET/MR scanners, one will want to include more
“prior” knowledge into the reconstruction.
Citation
- A New Non-monotonic Algorithm for PET image reconstruction
S. Sra, D. Kim, I. Dhillon, B. Schölkopf.
In IEEE Medical Imaging Conference (MIC), October 2009.
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