New risk bounds for two-dimensional total variation denoising

Jeudi 21 mars 14:00-15:00 - Subhajit Goswami - IHES

Résumé : Two-dimensional total variation denoising (TVD) is a widely used technique for image denoising. It is also an important non parametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to be nearly minimax
rate optimal for the class of functions with bounded variation. One of the main results I will discuss in this talk complements these worst case guarantees by investigating the adaptivity of the ideally tuned TVD estimator to functions which are piecewise constant on axis aligned rectangles. In particular, our result shows that, when the truth is piecewise constant, the ideally tuned TVD estimator performs significantly better than in the worst case. I will also talk about the issue of choosing the tuning parameter. In particular, we propose a fully data driven version of the TVD estimator which enjoys similar worst case risk guarantees as the ideally tuned TVD estimator. Based on a joint work with Sabyasachi Chatterjee (https://publish.illinois.edu/sabyasachi/).

New risk bounds for two-dimensional total variation denoising  Version PDF