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A Block Nonlocal TV Method for Image Restoration

In this paper, we propose a block nonlocal total variation (TV) regularization method for image restoration. We extend the existing nonlocal TV method in two aspects: first, some block nonlocal operators are introduced to extend the point-based nonlocal diffusion as a block-based nonlocal diffusion process; second, the weighting function in the nonlocal method can be adaptively determined by the cost functional itself. The proposed method is derived from a block-based maximum a posteriori estimation. By the assumption of the self-similarity of small patches, we formulate a regularization term as a log-likelihood functional of a mixture model. To optimize this regularization term efficiently, we employ the idea of the expectation maximum algorithm and give a variational framework to propose a block-based nonlocal TV regularization. The weighting function occurring in our model can be regarded as a probability of the similarity for image patches, and it can be updated adaptively according to the newest esti...