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- W1971478618 abstract "This paper introduces a novel framework for the study of the total-variation model for image denoising. In the model, the denoised image is the proximity operator of the total-variation evaluated at a given noisy image. The total-variation can be viewed as the composition of a convex function (the ?1 norm for the anisotropic total-variation or the ?2 norm for the isotropic total-variation) with a linear transformation (the first-order difference operator). These two facts lead us to investigate the proximity operator of the composition of a convex function with a linear transformation. Under the assumption that the proximity operator of a given convex function (e.g., the ?1 norm or the ?2 norm) can be readily obtained, we propose a fixed-point algorithm for computing the proximity operator of the composition of the convex function with a linear transformation. We then specialize this fixed-point methodology to the total-variation denoising models. The resulting algorithms are compared with the Goldstein?Osher split-Bregman denoising algorithm. An important advantage of the fixed-point framework leads us to a convenient analysis for convergence of the proposed algorithms as well as a platform for us to develop efficient numerical algorithms via various fixed-point iterations. Our numerical experience indicates that the methods proposed here perform favorably." @default.
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- W1971478618 date "2011-03-17" @default.
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- W1971478618 title "Proximity algorithms for image models: denoising" @default.
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- W1971478618 doi "https://doi.org/10.1088/0266-5611/27/4/045009" @default.
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