Image restoration using proximal-splitting methods

Abstract

In this paper, we focus on giving two fixed-point-like methods, using proximal operators, called forward-backward and Douglas-Rachford, for solving the restoration problem for grayscale images corrupted with Gaussian noise model. We discuss how to evaluate proximal operators and provide an example in reconstructed image. The main idea is to choose the classic variational model TV L1 for recovering a true image u from an observed image f contaminated with Gaussian noise. The objective function is a sum of two convex terms: the `1-norm data fidelity and the total variational regularization. The first term forces the final image to be not too far away from the initial image and the second term performs actually the noise reduction. Experimental results prove the efficiency of the proposed work by performing some test by changing the noise levels applied to different images. We notice that the Peak Signal-to-Noise Ratio (PSNR) is used to evaluate the quality of the restored images.