title: Relaxed ordered-subset algorithm for penalized-likelihood image restoration.
abstract: The expectation-maximization (EM) algorithm for maximum-likelihood image recovery is guaranteed to converge, but it converges slowly. Its ordered-subset version (OS-EM) is used widely in tomographic image reconstruction because of its order-of-magnitude acceleration compared with the EM algorithm, but it does not guarantee convergence. Recently the ordered-subset, separable-paraboloidal-surrogate (OS-SPS) algorithm with relaxation has been shown to converge to the optimal point while providing fast convergence. We adapt the relaxed OS-SPS algorithm to the problem of image restoration. Because data acquisition in image restoration is different from that in tomography, we employ a different strategy for choosing subsets, using pixel locations rather than projection angles. Simulation results show that the relaxed OS-SPS algorithm can provide an order-of-magnitude acceleration over the EM algorithm for image restoration. This new algorithm now provides the speed and guaranteed convergence necessary for efficient image restoration.
authors.affiliation: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109, USA. ssotthiv@umich.edu
authors.forename: Saowapak
authors.initials: S
authors.lastname: Sotthivirat
authors.forename: Jeffrey A
authors.initials: JA
authors.lastname: Fessler