Image Cartoon-texture Decomposition Via Regularization Based Sparse Representations

Image decomposition is an important research area in the field of image processing. This topic mainly studies how to decompose a natural image into several components, and each component contains specific informations. According to different applications, the target component can be extracted and processed freely. Due to the fact that different components have different properties, the subsequent processing(including compression, recovery, recognition, classification and so on) engaged in different component will greatly improve the performance and reduce the burden of data storage and computing.In this paper, we mainly study the cartoon-texture image decomposition problem. That is how to decompose a natural image into two parts: cartoon(structure) and texture. Various models and algorithms focused on this problem are proposed and discussed. Donoho’s research group put forward a decomposition model(MCA) which is based on 1lnorm sparse representation. The original 0lnorm model was proved to be NP-hard, Donoho’s research group propose to relax 0l norm minimization problem to the 1lnorm minimization problem. The 1lnorm of coefficient vector was applied to measure its sparse degree. At each iteration, TV-regularizer was applied to the structural part, so that the adjusted structure part matches its corresponding original structure better. Finally, they give an algorithm known as morphological component analysis(MCA) to solve the model. The algorithm uses iterative soft threshold algorithm to process the coefficients after the transformation through appropriate dictionary. The reason is that different components have different morphological specificity. The corresponding component under a certain dictionary is sparse, and not sparse under another dictionary. After an iterative threshold procession on the coefficients under the corresponding dictionary, the corresponding component can be obtained correctly.However, according to some new research achievements in the field of sparse representation, 1lregularization is not the optimal approximation to sparse representation. Inspired by 1 2l regularization model and half threshold operator, we innovatively introduce the 1 2l regularization and half threshold operator into image cartoon-texture decomposition model, and give a new algorithm which is based on iterative half threshold operator to solve the model. The algorithm can obtain better approximation solution to the sparse representation problem. In addition, the recently proposed non-convex lp(0 <p <1)regularization has been proved to be a better approximation to sparse representation problem, and bring about more sparse solution. The generalized lp norm is introduced into the decomposition model, the generalized iterative shrinkage algorithm was presented to search the optimal solution. A large number of numerical experiments show that the 1 2l regularization based model and the lp(0 <p <1)regularization based model is more robust to image decomposition problem and can achieve better performances.