An alternating iterative algorithm for image deblurring and denoising problems

In this paper, a modified l1 minimization model for image delurring and denoising problems is considered. To solve the proposed l1 minimization model, we present an efficient alternative iterative algorithm in which the fast iterative shrinkge-thresholding method (FISTA) and the well known dual approach for solving the denosing problems are alternately employed. Besides, we prove the convergence of the proposed algorithm. Numerical results demonstrate the efficiency and viability of the proposed algorithm to restore the degraded images.