TY - GEN
T1 - A new non-monotonic algorithm for PET image reconstruction
AU - Sra, Suvrit
AU - Kim, Dongmin
AU - Dhillon, Inderjit
AU - Schölkopf, Bernhard
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
KW - Convex optimization
KW - Emission tomography
KW - Non-monotonic maximum likelihood
KW - Ordered subsets expectation maximization (OS-EM)
KW - Penalized likelihood
KW - Transmission tomography
UR - http://www.scopus.com/inward/record.url?scp=77951191422&partnerID=8YFLogxK
U2 - 10.1109/NSSMIC.2009.5402060
DO - 10.1109/NSSMIC.2009.5402060
M3 - Conference contribution
AN - SCOPUS:77951191422
SN - 9781424439621
T3 - IEEE Nuclear Science Symposium Conference Record
SP - 2500
EP - 2502
BT - 2009 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2009
T2 - 2009 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2009
Y2 - 25 October 2009 through 31 October 2009
ER -