LIMITED TOMOGRAPHY RECONSTRUCTION VIA TIGHT FRAME AND SIMULTANEOUS SINOGRAM EXTRAPOLATION

作     者：Jae Kyu Choi Bin Dong Xiaoqun Zhang 

作者机构：Institute of Natural Sciences Shanghai Jiao Tong University Shanghai China Beijing International Center for Mathematical Research Peking University Beijing China Institute of Natural Sciences School of Mathematical Sciences and MOE-LSC Shanghai Jiao Tong University Shanghai China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2016年第34卷第6期

页      面：575-589页

核心收录：

学科分类：07[理学] 

基　　金：国家自然科学基金 Sino-German center grant 国家973计划 

主　　题：X-ray computed tomography Limited tomography Wavelet frame Data driventight frame Bregmanized operator splitting algorithm Sinogram extrapolation. 

摘      要：X-ray computed tomography （CT） is one of widely used diagnostic tools for medical and dental tomographic imaging of the human body. However, the standard filtered back- projection reconstruction method requires the complete knowledge of the projection data. In the case of limited data, the inverse problem of CT becomes more ill-posed, which makes the reconstructed image deteriorated by the artifacts. In this paper, we consider two dimensional CT reconstruction using the projections truncated along the spatial direc- tion in the Radon domain. Over the decades, the numerous results including the sparsity model based approach has enabled the reconstruction of the image inside the region of interest （ROI） from the limited knowledge of the data. However, unlike these existing methods, we try to reconstruct the entire CT image from the limited knowledge of the sinogram via the tight frame regularization and the simultaneous sinogram extrapolation. Our proposed model shows more promising numerical simulation results compared with the existing sparsity model based approach.