Image restoration refers to the recovery of a clean sharp image from a noisy, and potentially blurred, observation. Based on the assumption that noise is additive and white, we propose a novel variational framework in order to enforce whiteness of the residue image. In particular, the proposed variational model uses Total Variation (TV) regularization (chosen simply for its popularity, any other regularizers could be substituted as well) and imposes the resemblance of the residue image to a white noise realization by constraining its autocorrelation function. The whiteness constraint constitutes the key novelty behind our approach. The restored image is efficiently computed by the constrained minimization of an energy functional using an Alternating Directions Methods of Multipliers (ADMM) procedure. Numerical examples show that the novel residue constraint indeed improves the quality of the computed restorations.