Theoretical study on high order interior tomography

Article type: Research Article

Authors: Yang, Jiansheng | Cong, Wenxiang | Jiang, Ming^{; ;} | Wang, Ge

Affiliations: LMAM, School of Mathematical Sciences, Peking University, Beijing, China | Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Sciences, Virginia Tech, Blacksburg, VA, USA | Beijing International Center for Mathematical Research, Beijing, China

Note: [] 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: In this paper, we study a new type of high order interior problems characterized by high order differential phase shift measurement. This problem is encountered in local x-ray phase-contrast tomography. Here we extend our previous theoretical framework from interior CT to interior differential phase-contrast tomography, and establish the solution uniqueness in this context. We employ the analytic continuation method and high order total variation minimization which we developed in our previous work for interior CT, and prove that an image in a region of interest (ROI) can be uniquely reconstructed from truncated high order differential projection data if the image is known a priori in a sub-region of the ROI or the image is piecewise polynomial in the ROI. Preliminary numerical experiments support the theoretical finding.

Keywords: High order interior problem, ambiguity image, analytic function, high order total variation

DOI: 10.3233/XST-2012-00349

Journal: Journal of X-Ray Science and Technology, vol. 20, no. 4, pp. 423-436, 2012