Using Channel Representations in Regularization Terms: A Case Study on Image Diffusion

In this work we propose a novel non-linear diffusion filtering approach for images based on their channel representation. To derive the diffusion update scheme we formulate a novel energy functional using a soft-histogram representation of image pixel neighborhoods obtained from the channel encoding. The resulting Euler-Lagrange equation yields a non-linear robust diffusion scheme with additional weighting terms stemming from the channel representation which steer the diffusion process. We apply this novel energy formulation to image reconstruction problems, showing good performance in the presence of mixtures of Gaussian and impulse-like noise, e.g. missing data. In denoising experiments of common scalar-valued images our approach performs competitive compared to other diffusion schemes as well as state-of-the-art denoising methods for the considered noise types.