A Non-Local Dual-Domain Approach to Cartoon and Texture Decomposition

This paper addresses the problem of cartoon and texture decomposition. Microtextures being characterized by their power spectrum, we propose to extract cartoon and texture components from the information provided by the power spectrum of image patches. The contribution of texture to the spectrum of a patch is detected as statistically significant spectral components with respect to a null hypothesis modeling the power spectrum of a non-textured patch. The null-hypothesis model is built upon a coarse cartoon representation obtained by a basic yet fast filtering algorithm of the literature. Hence the term "dual domain": the coarse decomposition is obtained in the spatial domain and is an input of the proposed spectral approach. The statistical model is also built upon the power spectrum of patches with similar textures across the image. The proposed approach therefore falls within the family of non-local methods. Experimental results are shown in various application areas, including canvas pattern removal in fine arts painting, or periodic noise removal in remote sensing imaging.