Reducing Staircasing Artifacts in SPECT Reconstruction by an Infimal Convolution Regularization

Abstract

The purpose of this paper is to investigate the ability of the infimal convolution regularization in curing the staircasing artifacts of the TV model in the SPECT reconstruction. We formulate the problem of SPECT reconstruction with the infimal convolution regularization as a convex three-block optimization problem and characterize its solution by a system of fixed-point equations in terms of the proximity operator of the functions involved in its objective function. We then develop a novel fixed-point proximity algorithm based on the fixed-point equations. Moreover, we introduce a preconditioning matrix motivated by the classical MLEM (maximum-likelihood expectation maximization) algorithm. We prove convergence of the proposed algorithm. The numerical results are included to show that the infimal convolution regularization is capable of effectively reducing the staircasing artifacts, while maintaining comparable image quality in terms of the signal-to-noise ratio and coefficient recovery contrast.