Fast Parallelizable Algorithms for Transmission Image Reconstruction

Abstract

Presents a new class of algorithm for penalized-likelihood reconstruction of attenuation maps from low-count transmission scans. The authors derive the algorithms by applying to the transmission log-likelihood a variation of the convexity technique developed by De Pierro for the emission case. The new algorithms overcome several limitations associated with previous algorithms. (1) Fewer exponentiations are required than in the transmission EM algorithm or in coordinate-ascent algorithms. (2) The algorithms intrinsically accommodate nonnegativity constraints, unlike many gradient-based methods. (3) The algorithms are easily parallelizable, unlike coordinate-ascent algorithms and perhaps line-search algorithms. The authors show that the algorithms converge faster than several alternatives, even on conventional workstations. They give examples from low-count PET transmission scans and from truncated fan-beam SPECT transmission scans.