Incremental optimization transfer algorithms: application to transmission tomography

Abstract

N o convergent ordered subsets (OS) type image reconstruction algorithms for tomography have been proposed to date. In contrast, in emission tomography, there are two known families of convergent OS algorithms: methods that use relaxation parameters (Ahn and Fessler, 2003), and methods based on the expectation maximization (EM) approach (Hsiao et al., 2002). This paper generalizes the incre- mental EM approach by introducing a general framework that we call incremental optimization transfer. Like EM methods, the proposed algorithms accelerate convergence speeds and ensure global convergence (to a stationary point) under mild regularity conditions without requiring inconvenient relaxation parameters. The general optimization transfer framework enables the use of a very broad family of non-EM surrogate functions. In particular, this paper provides the first convergent OS-type algorithm for tomography. The general approach is applicable to both monoenergetic and polyenergetic scans as well as to other image reconstruction problems. We propose a particular optimization transfer method for (nonconcave) penalized-likelihood (PL) image reconstruction by using separable paraboloidal surrogates (SPS). Results show that the new transmission optimiza- tion transfer (TRIOT) algorithm is faster than nonincremental ordinary SPS and even OS-SPS yet is convergent.