TOTAL VARIATION DENOISING USING POSTERIOR EXPECTATION

Total Variation image denoising, generally formulated in a variational setting, can be seen as a Maximum A Posteri- ori (MAP) Bayesian estimate relying on a simple explicit image prior. In this formulation, the denoised image is the most likely image of the posterior distribution, which fa- vors regularity and produces staircasing artifacts: in regions where smooth-varying intensities would be expected, con- stant zones appear separated by artificial boundaries. In this paper, we propose to use the Least Square Error (LSE) cri- terion instead of the MAP. This leads to a new denoising method called TV-LSE, that produces more realistic images by computing the expectation of the posterior distribution. We describe a Monte-Carlo Markov Chain algorithm based on Metropolis scheme, and provide an efficient convergence criterion. We also discuss the properties of TV-LSE, and show in particular that it does not suffer from the staircas- ing effect.