Compressed sensing of sparsity-constrained total variation minimization for CT image reconstruction

Abstract

Sparse-view CT image reconstruction is becoming a potential strategy for radiation dose reduction of CT scans. Compressed sensing (CS) has been utilized to address this problem. Total Variation (TV) minimization, a method which can reduce streak artifacts and preserve object boundaries well, is treated as the most standard approach of CS. However, TV minimization cannot be solved by using classical differentiable optimization techniques such as the gradient method, because the expression of TV (TV norm) is non-differentiable. In early stages, approximated solving methods were proposed by changing TV norm to be differentiable in the way of adding a small constant in TV norm to enable the usage of gradient methods. But this reduces the power of TV in preserving accuracy object boundaries. Subsequently, approaches which can optimize TV norm exactly were proposed based on the convex optimization theory, such as generalizations of the iterative soft-thresholding (GIST) algorithm and Chambolle-Pock algorithm. However, these methods are simultaneous-iterative-type algorithms. It means that their convergence is rather slower compared with row-action-type algorithms. The proposed method, called sparsity-constrained total variation (SCTV), is developed by using the alternating direction method of multipliers (ADMM). On the method we succeeded in solving the main optimization problem by iteratively splitting the problem into processes of row-action-type algebraic reconstruction technique (ART) procedure and TV minimization procedure which can be processed using Chambolle’s projection algorithm. Experimental results show that the convergence speed of the proposed method is much faster than the conventional simultaneous iterative methods.