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Explorations on anisotropic regularisation of dynamic inverse problems by bilevel optimisation

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Martin Benning, Carola-Bibiane Schönlieb, Tuomo Valkonen, Verner Vlačić

Numerical Analysis · Submitted 3 Feb 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID1602.01278 (version 1)
Pith IDGJRNDW45, Pith's permanent record of this paper and its review
CitationCarola-Bibiane Sch\"onlieb, Martin Benning, Tuomo Valkonen, Verner Vla\v{c}i\'c. "Explorations on anisotropic regularisation of dynamic inverse problems by bilevel optimisation." arXiv:1602.01278 (2016). https://pith.science/paper/GJRNDW45
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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.89 · human participants 0.03 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.15 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. background 0.87 0.60 0.03 asserted 0.85
s1 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. method 0.56 0.94 0.12 asserted 1.00
s2 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. limitation 0.78 0.50 0.07 asserted 1.00
s3 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. contribution 0.58 0.95 0.18 asserted 0.96

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.96.

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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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.

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Cites as background 1 paper
  • Recently parameter learning in the context of functional variational regularisation models [ref] also entered the image processing community with works by the authors [ref] , Kunisch, Pock and co-workers [ref] , Chung et al. [ref] , Hintermüller et al. [ref] and others [ref] .

    Optimal Regularization Parameters for General-Form Tikhonov Regularization · Introduction · 0.85

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