A new linearized split Bregman iterative algorithm for image reconstruction in sparse-view X-ray computed tomography.pdfVIP

Computers and Mathematics with Applications 71 (2016) 1537–1559 Contents lists available at ScienceDirect Computers and Mathematics with Applications journal homepage: /locate/camwa A new linearized split Bregman iterative algorithm for image reconstruction in sparse-view X-ray computed tomography Chong Chen, Guoliang Xu ? LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, PR China article info Article history: Received 15 June 2015 Received in revised form 15 November 2015 Accepted 9 January 2016 Available online 26 March 2016 Keywords: Linearized split Bregman iteration Compressed sensing Robust image reconstruction Sparse views X-ray computed tomography abstract In this paper, a new linearized split Bregman iterative algorithm is proposed for sparseview X-ray computed tomography, which can avoid solving a large-scale and unstructured linear system in each iteration. Remarkably, our method can be generalized to efficiently resolve some other image processing and analysis models, for instance, the robust com- pressed sensing, the total variation-?1, and the ?1–?1. We also give rigorous proofs for the convergence of the proposed method under appropriate conditions for the aforementioned problems. Experimental results demonstrate that our algorithm has better performance in terms of reconstruction quality, effectiveness and robustness, compared with some other methods (e.g. gradient-flow-based semi-implicit finite element method, split Bregman, etc.) for the robust image reconstruction in sparse-view X-ray computed tomography. ? 2016 Elsevier Ltd. All rights reserved. 1. Introduction Motivations. In modern commercial X-ray computed tomography (CT) imaging, the projections are generally detected at a large number (about 984) of views from the patient for high-quality image reconstruction by currently analyticbased algorithms, for instance, filtered back-projection (FBP) method [1–4]. However, data coll