LJKProbability & Statistics Seminar

On Thursday December 7 2017 at 14h00 in Room 106  IMAG Building

Seminary of Mr Guillaume GARRIGOS (École Normale Supérieure)

Iterative regularization for general inverse problems

Summary

In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and datafit terms. We were particularly motivated by dealing with nonsmooth datafit terms, such like a KullbackLiebler divergence, or an L1 distance. We treat these problems by designing an algorithm, based on a primaldual diagonal descent method, designed to solve hierarchical optimization problems. The key point of our approach is that, in presence of noise, the number of iterations of our algorithm acts as a regularization parameter. In practice this means that the algorithm must be stopped after a certain number of iterations. This is what is called regularization by early stopping, an approach which gained in popularity in statistical learning. Our main results establishes convergence and stability of our algorithm, and are illustrated by experiments on image denoising, comparing our approach with a more classical Tikhonov regularization method.
Keywords: statistical learning, inverse problems, regularization, optimization, primaldual algorithm, early stopping.
