'Institute of Electrical and Electronics Engineers (IEEE)'
Doi
Abstract
No convergent ordered subsets (OS) type image
reconstruction algorithms for transmission 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 incremental expectation maximization (EM)
approach (Hsiao et al., 2002). This paper generalizes the incremental
EM approach by introducing a general framework that
we call “incremental optimization transfer.” Like incremental 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 transmission tomography. The general approach is
applicable to both monoenergetic and polyenergetic transmission
scans as well as to other image reconstruction problems. We
propose a particular incremental optimization transfer method
for (nonconcave) penalized-likelihood (PL) transmission image
reconstruction by using separable paraboloidal surrogates (SPS).
Results show that the new “transmission incremental optimization
transfer (TRIOT)” algorithm is faster than nonincremental
ordinary SPS and even OS-SPS yet is convergent.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85800/1/Fessler200.pd