Explorations on anisotropic regularisation of dynamic inverse problems by bilevel optimisation



Benning, Martin, Schönlieb, Carola-Bibiane, Valkonen, Tuomo ORCID: 0000-0001-6683-3572 and Vlačić, Verner
(2016) Explorations on anisotropic regularisation of dynamic inverse problems by bilevel optimisation.

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Abstract

We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation strategy to compute the optimal regularisation parameters of such a model for the application of video denoising. The optimisation poses a challenge in itself, as the dependency on one of the regularisation parameters is non-linear such that the standard existence and convergence theory does not apply. Moreover, we analyse numerical results of the proposed parameter learning strategy based on three exemplary video sequences and discuss the impact of these results on the actual modelling of dynamic inverse problems.

Item Type: Article
Uncontrolled Keywords: math.NA, math.NA, 34A55, 49N45, 45Q05, G.1.8; G.1.6; I.2.10
Depositing User: Symplectic Admin
Date Deposited: 26 Apr 2017 08:09
Last Modified: 19 Jan 2023 07:05
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3007113