Cartoon-Texture Image Decomposition Using Blockwise Low-Rank Texture Characterization

Using a novel characterization of texture, we propose an image decomposition technique that can effectively decomposes an image into its cartoon and texture components. The characterization rests on our observation that the texture component enjoys a blockwise low-rank nature with possible overlap and shear, because texture, in general, is globally dissimilar but locally well patterned. More specifically, one can observe that any local block of the texture component consists of only a few individual patterns. Based on this premise, we first introduce a new convex prior, named the block nuclear norm (BNN), leading to a suitable characterization of the texture component. We then formulate a cartoon-texture decomposition model as a convex optimization problem, where the simultaneous estimation of the cartoon and texture components from a given image or degraded observation is executed by minimizing the total variation and BNN. In addition, patterns of texture extending in different directions are extracted separately, which is a special feature of the proposed model and of benefit to texture analysis and other applications. Furthermore, the model can handle various types of degradation occurring in image processing, including blur+missing pixels with several types of noise. By rewriting the problem via variable splitting, the so-called alternating direction method of multipliers becomes applicable, resulting in an efficient algorithmic solution to the problem. Numerical examples illustrate that the proposed model is very selective to patterns of texture, which makes it produce better results than state-of-the-art decomposition models.