Incoherent dictionary learning for sparse representation based image denoising

Dictionary learning for sparse representation has been an active topic in the field of image processing. Most existing dictionary learning schemes focus on the representation ability of the learned dictionary. However, according to the theory of compressive sensing, the mutual incoherence of the dictionary is of crucial role in the sparse coding. Thus incoherent dictionary is desirable to improve the performance of sparse representation based image restoration. In this paper, we propose a new incoherent dictionary learning model that minimizes the representation error and the mutual incoherence by incorporating the constraint of mutual incoherence into the dictionary update model. The optimal incoherent dictionary is achieved by seeking an optimization solution. An efficient algorithm is developed to solve the optimization problem iteratively. Experimental results on image denoising demonstrate that the proposed scheme achieves better recovery quality and converges faster than K-SVD while keeping lower computation complexity.