Cecile Louchet (Orleans): Total Variation denoising using posterior expectation
Tuesday, 24.01.2012 14:15 im Raum Besprechungsraum Numerik
Total variation image denoising was originally described 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.
In this talk we propose to transpose this denoising method into an estimation based on the posterior expectation, in order to better account for the global properties of the posterior distribution. Theoretical and numerical results are presented, which demonstrate in particular that images denoised with the proposed scheme do not suffer from the staircasing effect.
We then focus on the practical computation of TV-LSE, and propose an MCMC (Monte-Carlo Markov Chain) algorithm whose convergence is carefully analyzed. Both the model and the algorithm are flexible enough to be directly applied to other low-level image processing tasks, such as image deblurring and interpolation.
This is joint work with Lionel Moisan.