Image Restoration and Noise Reduction with Context-Dependent Wavelet Graph and ADMM Optimization

We represent the image noise reduction and restoration problems as context-dependent graphs and propose algorithms to derive the optimal graphs by the alternating direction method of multipliers (ADMM) method. An image is spatially decomposed into smooth regions and singular regions, consisting of edges and textures. The graph representing a smooth region is defined in the image domain, while that representing a singular region is defined in the wavelet domain. The optimal graphs are formulated as the solutions of constrained optimization problems over sparse graphs, where the sparseness is imposed on the edges. The graphs on the wavelet domain are solved in a hierarchical layer structure. The convergence and complexity of the algorithms have been studied. Simulation experiments demonstrate that the results of our algorithms are superior to the state-of-the-art algorithms for image noise reduction and restoration.