Dynamic SPECT reconstruction from few projections: a sparsity enforced matrix factorization approach. (21st January 2015)

• Record Type: Journal Article
• Authors: Ding, Qiaoqiao; Zan, Yunlong; Huang, Qiu; Zhang, Xiaoqun
• Is Part Of: Inverse problems. Volume 31:Number 2(2015:Feb.)
• Publication Date: 2015-01-21
• Subjects: dynamic SPECT -- low rank matrix factorization -- Kurdyka-Łojasiewicz property -- sparsity -- total variation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/2/025004
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The reconstruction of dynamic images from few projection data is a challenging problem, especially when noise is present and when the dynamic images are vary fast. In this paper, we propose a variational model, sparsity enforced matrix factorization (SEMF), based on low rank matrix factorization of unknown images and enforced sparsity constraints for representing both coefficients and bases. The proposed model is solved via an alternating iterative scheme for which each subproblem is convex and involves the efficient alternating direction method of multipliers (ADMM). The convergence of the overall alternating scheme for the nonconvex problem relies upon the Kurdyka–Łojasiewicz property, recently studied by Attouch et al (2010 Math. Oper. Res. 35 438 ) and Attouch et al (2013 Math. Program. 137 91 ). Finally our proof-of-concept simulation on 2D dynamic images shows the advantage of the proposed method compared to conventional methods.