The Application Of Correlated Sparsity In Image Restoration And Edge Detection

Image processing technology has developed rapidly in the last decades and has achieved great success. In recent years, sparse representation method becomes a hot topic in the field of image processing. The sparse representation method usually uses the l1, norm as its regularization term. We use optimal methods to obtain the solution when dealing with the relevant problems. The model has been used widely in image processing, compressed sensing and regression problems.However, the sparse solution obtained by the l1, regularization term will neglect the correlations among non-zero entries. Actually, correlations among non-zero entries exist widely and are very important in many applications. Therefore, many l1-like regularization terms have been proposed to overcome this shortcoming. For example, non-zero entries of the solution obtained by structural sparse terms always have structural correlations. Moreover, there are many efforts have been devoted in sparse-inducing regularization terms. The sparse-inducing regularization terms encode some prior knowledge of the image, the obtained solution thus will include the relevant prior knowledge.In image processing domain, we propose the sparse model and the relevant methods based on the correlated sparse regularization terms for image processing inverse problem.Where the most important step is how to construct an appropriate regularization term for the image processing problem to induce sparse solution. The main contributions of this paper are as follows:(1) Introducing the k-support norm it into the image gradient domain. The k-support norm itself has the correlation property. Therefore, the non-zero atoms obtained by the model that regularized with the k-support regularizer have the same characteristics due to the property of the k-support norm. Experiment results demonstrate the k-support regularization term can induce good sparse solution thus obtain good processing results.(2) Based on the continuity of edges and the gradient value around edges is bigger than smooth area, we design a l∞ type correlation sparse regularizer and introduce it into the image gradient domain. The ADMM method is used to solve this model and a sub-problem with the regularizer is settled by finding a flow solution of a quadratic min-cost flow problem. This model can be used in image denoising, deblurring and edge-detecting and can obtain good results.(3) Similar to (2), we also propose a l2 type correlation sparse regularizer and introducing it into the image gradient domain. We use ADMM method to settle the relevant model, a fast novel algorithm is proposed for computing the proximal operator when solving the sub-problem. The model with the l2 type regularizer performs well in image denoising, deblurring and edge detecting.