In this paper, we consider variational approaches to handle the multiplicative noise removal and deblurring problem. Based on rather reasonable physical blurring-noisy assumptions, we derive a new variational model for this issue. After the study of the basic properties, we propose to approximate it by a convex relaxation model which is a balance between the previous non-convex model and a convex model. The relaxed model is solved by an alternating minimization approach. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed method.

Total variation regularization has good performance in noise removal and edge preservation but lacks in texture restoration. Here we present a texture-preserving strategy to restore images contaminated by blur and noise. According to a texture detection strategy, we apply spatially adaptive fractional order diffusion. A fast algorithm based on the half-quadratic technique is used to minimize the resulting objective function. Numerical results show the effectiveness of our strategy.

This paper deals with two complementary methods in noisy image deblurring: a nonlinear shrinkage of wavelet-packets coefficients called FCNR and Rudin-Osher-Fatemi's variational method. The FCNR has for objective to obtain a restored image with a white noise. It will prove to be very efficient to restore an image after an invertible blur but limited in the opposite situation. Whereas the Total Variation based method, with its ability to reconstruct the lost frequencies by interpolation, is very well adapted to non-invertible blur, but that it tends to erase low contrast textures. This complementarity is highlighted when the methods are applied to the restoration of satellite SPOT images.