A Convex Regularizer for Reducing Color Artifact in Color Image Recovery

We propose a new convex regularizer, named the local color nuclear norm (LCNN), for color image recovery. The LCNN is designed to promote a property inherent in natural color images - in which their local color distributions often exhibit strong linearity - and is thus expected to reduce color artifact effectively. In addition, the very nature of LCNN allows us to incorporate it into various types of color image recovery formulations, with the associated convex optimization problems solvable using proximal splitting techniques. Applications of LCNN are demonstrated with illustrative numerical examples.