A Convex Variational Approach for Image Deblurring With Multiplicative Structured Noise

The restoration of images corrupted by blurring and structured noise has attracted growing attention in the domains of image processing and computer vision. However, many works only focus on the restoration of the images degraded by blurring and additive structured noise or multiplicative structured noise separately. It is still a challenge and an open problem to restore degraded images with blurring and multiplicative structured noise, simultaneously. In this paper, based on the total variation (TV), the statistical property of the Gamma noise and the maximum a posteriori (MAP) estimator, we obtain a convex variational model to recover blurred images with multiplicative structured noise. Especially, to get this convex model, we reformulate the prior assumption of the images degradation model by division instead of multiplication. For solving this convex model, an effective alternating direction method of multipliers (ADMM) is employed. Numerical experiments are presented to illustrate the effectiveness and efficiency of the proposed model.