Spatially adaptive sparse representation prior for blind image restoration

Variation-based methods with different priors have been proven their ability in preserving edges for image restoration. Blind image decomposition is an inverse problem that is much harder to be solved than non-blind image decomposition from noisy images, commonly producing staircase effects in flat regions and smoothing fine structures. In this paper, we have tried to use spatially adaptive sparse representation (SASR) prior to restore a clean result from a blurred and noised image. In order to fastly and efficiently solve the SASR model, the alternating direction method of multipliers (ADMM) is firstly exploited to separate it into two subproblems. Then the final solution is alternatively optimized with the employment of fast Fourier transformation (FFT) and generalized soft-threshold formula. The experiments on both synthesized images and practical polluted images show that the proposed algorithm is effectiveness in quantitation and qualification, and is even better than state-of-the-arts.