Open AccessLimited-angle CT reconstruction with generalized shrinkage operators as regularizers
Author(s) -
Xun Deng,
Xing Zhao,
Mengfei Li,
Hongwei Li
Publication year - 2021
Publication title -
inverse problems and imaging
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.755
H-Index - 40
eISSN - 1930-8345
pISSN - 1930-8337
DOI - 10.3934/ipi.2021019
Subject(s) - piecewise , mathematics , smoothing , shrinkage , norm (philosophy) , prior probability , algorithm , computer science , geometry , pure mathematics , mathematical analysis , statistics , bayesian probability , political science , law
Limited-angle reconstruction is a very important but challenging problem in the field of computed tomography (CT) which has been extensively studied for many years. However, some difficulties still remain. Based on the theory of visible and invisible boundary developed by Quinto et.al, we propose a reconstruction model for limited-angle CT, which encodes the visible edges as priors to recover the invisible ones. The new model utilizes generalized shrinkage operators as regularizers to perform edge-preserving smoothing such that the visible edges are employed as anchors to recover piecewise-constant or piecewise-smooth reconstructions, while noises and artifacts are suppressed or removed. This work extends our previous research on limited-angle reconstruction which employs gradient \begin{document}$ \ell_0 $\end{document} and \begin{document}$ \ell_1 $\end{document} norm regularizers. The effectiveness of the proposed model and its corresponding solving algorithm shall be verified by numerical experiments with simulated data as well as real data.