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-likeliho od a version of the convexity technique developed by De Pierro for emi ssion tomography. The new class includes the single-coordinate ascent (SCA) algorithm and Lange's convex algorithm for transmission tomograp hy as special cases, The new grouped-coordinate ascent (GCA) algorithm s in the class overcome several limitations associated with previous a lgorithms, 1) Fewer exponentiations are required than in the transmiss ion maximum likelihood-expectation maximization (ML-EM) algorithm or i n the SCA algorithm, 2) The algorithms intrinsically accommodate nonne gativity; constraints, unlike many gradient-based methods, 3) The algo rithms are easily parallelizable, unlike the SCA algorithm and perhaps line-search algorithms, We show that the GCA algorithms converge fast er than the SCA algorithm, even on conventional workstations, An examp le from a low-count positron emission tomography (PET) transmission sc an illustrates the method.