Variational Model with Nonstandard Growth Condition in Image Restoration and Contrast Enhancement

We propose a new variational model in Sobolev-Orlicz spaces with non-standard growth conditions of the objective functional and discuss its applications to the simultaneous contrast enhancement and denoising of color images. The characteristic feature of the proposed model is that we deal with a constrained non-convex minimization problem that lives in variable Sobolev-Orlicz spaces where the variable exponent is unknown a priori and it depends on a particular function that belongs to the domain of the objective functional. In contrast to the standard approach, we do not apply any spatial regularization to the image gradient. We discuss the consistency of the variational model, give the scheme for its regularization, derive the corresponding optimality system, and propose an iterative algorithm for practical implementations.