Limited-angle image reconstruction based on Mumford–Shah-like model and wavelet tight frames

Restricted by the scanning environment and the radiation exposure of computed tomography (CT), the obtained projection data are sometimes incomplete, which results in an ill-posed problem, such as a limited-angle image reconstruction. In such circumstance, the commonly used analytic and iterative algorithms, such as filtered back-projection and simultaneous algebraic reconstruction technique (SART), will not work well. Nowadays, a popular iterative image reconstruction algorithm (SART+TV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {SART}}+{\hbox {TV}}$$\end{document}) solving the optimization model based on the minimization of total variation (TV) of the image applies to the sparse-view reconstruction problem well; it is not effective on small limited-angle reconstruction problem, especially in aspect of suppressing slope artifacts when the limited-angle projection views are severely reduced. In this work, we develop a reconstruction model based on the Mumford–Shah-like model and wavelet tight frames that applies to limited-angle CT; and the corresponding iterative method is given. Numerical experiments and quantitative analysis demonstrate that our method outperforms SART and SART+TV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {SART}}+{\hbox {TV}}$$\end{document} in suppressing slope artifacts when the limited-angle projection views are severely decreased.