A fast algorithm for high order total variation minimization based interior tomography

Subtitle:

Article type: Research Article

Authors: Zhao, Zhenhua^a | Yang, Jiansheng^{a; b; *} | Jiang, Ming^{a; c; d}

Affiliations: [a] LMAM, School of Mathematical Sciences, Peking University, Beijing, China | [b] Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, China | [c] Beijing International Center for Mathematical Research, Peking University, Beijing, China | [d] Cooperative Medianet Innovation Center, Shanghai Jiao Tong University, Shanghai, China

Correspondence: [*] Corresponding author: Jiansheng Yang, LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China. Tel.: +86 10 6275 9626; Fax: +86 10 6275 1801; E-mail: jsyang@pku.edu.cn

Abstract: Interior tomography as a promising X-ray imaging technique has received increasing attention in medical imaging field. In our previous works, we proposed a high-order total variation (HOT) minimization method for interior tomography and proved that the region of interest (ROI) can be reconstructed accurately by minimizing the HOT if the object image is piecewise polynomial within the ROI. In this paper, we propose a modified HOT (MHOT) and develop a fast MHOT minimization algorithm for interior tomography, based on split Bregman iteration and ordered-subset simultaneous algebraic reconstruction techniques (OS-SART). Numerical simulation demonstrates that our algorithm is computationally efficient and can be applied to obtain high-quality reconstructed image.

Keywords: Interior tomography, MHOT, l_1-regularized problem, split bregman iteration, OS-SART

DOI: 10.3233/XST-150494

Journal: Journal of X-Ray Science and Technology, vol. 23, no. 3, pp. 349-364, 2015