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The posterior expectation of the Total Variation denoising model

Total variation image denoising was originally proposed by Rudin, Osher and Fatemi as a variational method, but it can be interpreted in a Bayesian framework as a Maximum A Posteriori estimate. This maximization aspect is partly responsible for the so-called “staircasing effect”, i.e. the outbreak of quasi-constant regions separated by sharp edges in the intensity map. We will show how this denoising method can be transposed into an estimation based on the posterior expectation, in order to better account for the global properties of the posterior distribution. We will present theoretical properties and numerical results, which demonstrate in particular that images denoised with the proposed scheme do not suffer from the staircasing effect.

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