Image decomposition: separation of texture from piecewise smooth content

This paper presents a novel method for separating images into texture and piecewise smooth parts. The proposed approach is based on a combination of the Basis Pursuit Denoising (BPDN) algorithm and the Total-Variation (TV) regularization scheme. The basic idea promoted in this paper is the use of two appropriate dictionaries, one for the representation of textures, and the other for the natural scene parts. Each dictionary is designed for sparse representation of a particular type of image-content (either texture or piecewise smooth). The use of BPDN with the two augmented dictionaries leads to the desired separation, along with noise removal as a by-product. As the need to choose a proper dictionary for natural scene is very hard, a TV regularization is employed to better direct the separation process. Experimental results validate the algorithm's performance.