Image Decomposition via Generalized Morphological Component Analysis and Split Bregman Algorithm

This paper describes a novel image decomposition algorithm based on sparse representation and split bregman algorithm. This algorithm is a direct extension of morphological component analysis(MCA), which is the typical sparse representation-based image decomposition method designed for the separation of linearly combined texture and cartoon layers in a given image. But when dealing with problems with additional regularization of constraint, such as extra image structure information(e.g. BV), the convergence rate of traditional MCA is slow. To resolve this problem, this article propose a generalized morphological component analysis(GMCA) method. The GMCA algorithm introduce multiple regularization to the traditional MCA, and build a fast algorithm via Split Bregman and proximal method. Experimental results show that this algorithm achieved better results via giving specific constraints on different component and get faster convergence rate.