Learning to compress ergodic sources

A novel image decomposing algorithm is proposed in this paper, it can separate images into texture and cartoon parts under the complicated background. The main idea is the use of two appropriate dictionaries, one for the representation of textures, and the other for the cartoon parts assumed to be piecewise-smooth. The cartoon parts in the image can be sparsely represented by the local Ridgelet and the local Discrete Cosine transform is appropriate representation for texture parts. Furthermore, the use of Basic-Pursuit and Total-Variation regularization methods leads to the desired separation, along with noise removal as a by-product. The experiment results show that the image decomposition by the method is according with the human visual system.