Talk by Andreas Langer, University of Stuttgart

Spatially adaptive regularization for total variation minimization

Abstract

A good approximation of the original image from an observed image may be obtained by minimizing a functional that consists of a data-fidelity term, a regularization term, and a parameter, which balances data-fidelity and regularization. The proper choice of the parameter is delicate. In fact, large weights not only remove noise but also details in images, while small weights retain noise in homogeneous regions. However, since images consist of multiple objects of different scales, it is expected that a spatially varying weight would give better reconstructions than a scalar parameter. In this vein we present algorithms for computing a distributed weight. We study the convergence behaviour of the proposed algorithms and present numerical experiments for Gaussian noise removal, for impulsive noise removal, and for eliminating simultaneously mixed Gaussian-impulse noise.