科研之友
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摘要
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 estimation. In addition, we mathematically prove the existence of a minimizer for one of the proposed models. Compared with the nonlocal TV method, numerical results show that our method can greatly improve the quality of the restored images, especially under heavy noise.
