Automatic Parameter Selection Based on Residual Whiteness for Convex Non-convex Variational Restoration

Image restoration is a well-known ill-posed inverse problem whose aim is to recover a sharp clean image from the corresponding blur- and noise-corrupted observation. Variational methods penalize solutions deemed undesirable by incorporating regularization techniques. A popular strategy relies on using sparsity promoting regularizers; it is well known that, in general, nonconvex regularizers hold the potential for promoting sparsity more effectively than convex regularizers. Recently a new class of convex non-convex (CNC) variational models has been proposed which includes a general parametric nonconvex nonseparable regularizer. However, the performance of this approach depends critically on the regularization parameter. In this paper we propose to use a parametric CNC variational restoration model within a bilevel framework, where the parameter is tuned by minimizing a measure of the restoration residual whiteness. Some preliminary numerical experiments are shown which indicate the effectiveness of the proposal.