Alternating Minimization Algorithms for Convex Minimization Problem with Application to Image Deblurring and Denoising

In this paper, we propose algorithm to restore blurred and noisy images based on the discretized total variation minimization technique. The proposed method is based on an alternating technique for image deblurring and denoising. Start by finding an approximate image using a Tikhonov regularization method. This corresponds to a deblurring process with possible artifacts and noise remaining. In the denoising step, we use fast iterative shrinkage-thresholding algorithm (SFISTA) or fast gradient-based algorithm (FGP). 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.