Image Recovery Via Hybrid Sparse Representations: A Deterministic Annealing Approach

Local smoothness and nonlocal similarity have both led to sparsity prior useful to image recovery applications. In this paper, we propose to combine the strengths of local and nonlocal sparse representations by Bayesian model averaging (BMA) where sparsity offers a plausible approximation of model posterior probabilities. An iterative thresholding-based image recovery algorithm using hybrid sparse representations is developed and its convergence property is analyzed using the theory of fixed point. Since nonlocal sparsity based on clustering relationship is nonconvex, we have borrowed the powerful idea of deterministic annealing (DA) to optimize the algorithm performance. It can be shown that as temperature decreases, our algorithm is capable of traversing different states of image structures (e.g., smooth regions, regular edges and textures). Fully reproducible experimental results are reported to support the effectiveness of the proposed image recovery algorithm.