Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints

TL;DR

This paper introduces a dynamic sampling optimization algorithm that efficiently learns optimal parameters for TV denoising models with multiple noise distributions, addressing computational challenges posed by large databases and nonsmooth PDE constraints.

Contribution

It proposes a novel dynamic sampling scheme combined with a quasi-Newton method for efficient bilevel optimization in TV denoising with multiple noise types.

Findings

Reduces computational costs in parameter learning for TV denoising.

Achieves accurate solutions despite nonsmooth PDE constraints.

Effectively handles large databases through dynamic sampling.

Abstract

We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way.