Variational Image Denoising While Constraining the distribution of the residual

We present a denoising method aimed at restoring images corrupted by additive noise based on the assumption that the distribution of the noise process is known. The proposed variational model uses Total Variation (TV) regularization (chosen simply for its popularity, any other regularizer could be substituted as well) but constrains the distribution of the residual to t a given target noise distribution. The residual distribution constraint constitutes the key novelty behind our approach. The restored image is eciently computed by the constrained minimization of an energy functional using an Alternating Directions Methods of Multipliers (ADMM) procedure. Numerical examples show that the novel residual constraint indeed improves the quality of the image restorations.