Regularization in Tomographic Reconstruction Using Proximal Forward-Backward Algorithm

Recently, there are many approaches to tomographic reconstruction that consist of minimizing the sum of a residual energy and a regularized function using some prior information. Usually great efforts are expended for specific models with different regularizations. In this paper, taking the advantage of the proximity operators and operator splitting in convex analytical tools, we provide a systematic analysis of such generic models. Then using proximal forward-backward method, an iterative algorithm is given to solve them. And we provide two examples with different regularized function to demonstrate how this generic tomographic construction scheme works.