Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction

Abstract

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 tech- nique developed by De Pierro for emission tomography. The new class includes the single-coordinate ascent (SCA) algo- rithm and Lange's convex algorithm for transmission tomog- raphy as special cases. The new grouped-coordinate ascent (GCA) algorithms in the class overcome several limitations as- sociated with previous algorithms. (1) Fewer exponentiations are required than in the transmission 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 al- gorithm 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 illus- trates the method.