Compressive Sensing Total-Variation Primal-Dual Algorithms for Image Reconstruction

Image reconstruction remains a challenging task in image processing. In this letter, a compressive sensing total-variation primal-dual (CTPD) algorithm is developed for image reconstruction. The proposed CTPD algorithm involves minimization of a multi-term cost function with sparse and total-variation composite regularization. Instead of finding its optimal solution directly, this minimization problem is first cast into a convex-concave saddle point optimization problem, which can be solved by using a proximal primal-dual iteration algorithm with several simple sub-steps, each producing low complexity solvers. Moreover, in order to speed-up convergence, an accelerated version of the CTPD (A-CTPD) algorithm is also presented. In the A-CTPD algorithm, the primal-dual iteration is reformulated as a fixed-point iteration, which allows the use of an Anderson acceleration technique for faster convergence without sacrificing image reconstruction accuracy. Several numerical experiments demonstrate the efficiency of our proposed algorithms in comparison with other algorithms such as least squares (LS), the least absolute shrinkage and selection operator (LASSO), total variation (TV) image reconstruction, the alternating direction method of multipliers (ADMM), or fast iterative shrinkage-thresholding algorithm (FISTA).