Image decomposition using optimally sparse representations and a variational approach

Lingling Jiang, Xiangchu Feng, Haiqing Yin

Abstract: In this paper, a new method which combines the basis pursuit denoising algorithm (BPDN) and the total variation (TV) regularization scheme is presented for separating images into texture and cartoon parts. It is a modification of the model [1]. In this process, two appropriate dictionaries are used, one for the representation of texture parts-the dual tree complex wavelet transform (DT CWT) and the other for the cartoon parts-the second generation of curvelet transform. To direct the separation process and reduce the pseudo-Gibbs phenomenon, the curvelet transform is followed by a projected regularization method for cartoon parts. Experimental results show that new method cannot only decompose better for a given image but also reduce the runtime, in comparison to the MCA approach.