XCT image reconstruction by a modified superiorized iteration and theoretical analysis. (1st November 2020)

• Record Type: Journal Article
• Authors: Luo, Shousheng; Zhang, Yanchun; Zhou, Tie; Song, Jinping; Wang, Yanfei
• Is Part Of: Optimization methods and software. Volume 35:Number 6(2020)
• Page Start: 1080
• Page End: 1097
• Publication Date: 2020-11-01
• Subjects: XCT image reconstruction -- algebraic method -- superiorization of iteration -- proximity perturbation; 92C55 -- 15A29 -- 65K10 -- 68U10; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1560442
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: In this paper, we propose an improved iteration superiorization method for X-ray computed tomography image reconstruction. We simplify the classic superiorized iteration by removing two constraints imposed on the perturbation. A novel method is proposed to determine the perturbation amount and direction for the superiorized iteration simultaneously. Some theoretical properties (convergence for instance) of the superiorized iteration sequence with the proposed perturbation are analysed. We present a general proof for the convergence of ART-like iterations with summable perturbations. In addition, we prove the convergence of simultaneous iterations without the summable perturbation assumption. Experiments on simulated and real data not only verify the theoretical result but also show that the proposed algorithm is superior to the classic superiorized iteration and can reconstruct desirable images.