A SURE Approach for Digital Signal/Image Deconvolution Problems

In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is twofold. First, we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from Stein´s unbiased quadratic risk estimate. Secondly, the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not. New theoretical results concerning the calculation of the variance of the Stein´s risk estimate are also provided in this work. Simulations carried out on natural images show the good performance of our method with respect to conventional wavelet-based restoration methods.