Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction.
This paper presents a new class of algorithms for penalized-likelihood reconstruction of attenuation maps from low-count transmission scans. We derive the algorithms by applying to the transmission log-likelihood a version of the convexity technique developed by De Pierro for emission tomography. The new class includes the single-coordinate ascent (SCA) algorithm and Lange's convex algorithm for transmission tomography as special cases. The new grouped-coordinate ascent (GCA) algorithms in the class overcome several limitations associated with previous algorithms. 1) Fewer exponentiations are required than in the transmission maximum likelihood-expectation maximization (ML-EM) algorithm or in the SCA algorithm. 2) The algorithms intrinsically accommodate nonnegativity constraints, unlike many gradient-based methods. 3) The algorithms are easily parallelizable, unlike the SCA algorithm and perhaps line-search algorithms. We show that the GCA algorithms converge faster than the SCA algorithm, even on conventional workstations. An example from a low-count positron emission tomography (PET) transmission scan illustrates the method.
Fessler
J A
JA
University of Michigan, Ann Arbor 48109-2122, USA. fessler@umich.edu
Ficaro
E P
EP
Clinthorne
N H
NH
Lange
K
K
D000465:Algorithms; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D019047:Phantoms, Imaging; D013909:Thorax / Q000000981:diagnostic imaging; D014055:Tomography, Emission-Computed / Q000379:methods*; D015899:Tomography, Emission-Computed, Single-Photon / Q000379:methods*