Benning, Martin;
Bubba, Tatiana A;
Ratti, Luca;
Riccio, Danilo;
(2024)
Trust your source: quantifying source condition elements for variational regularisation methods.
IMA Journal of Applied Mathematics
, 89
(1)
pp. 12-43.
10.1093/imamat/hxae008.
Preview |
Text
Benning_Trust_your_source_Benning_et_al_accepted.pdf - Accepted Version Download (4MB) | Preview |
Abstract
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as the solution of convex minimisation problems that can be solved with first-order algorithms. We demonstrate the validity of our approach by testing it on two inverse problem case studies in machine learning and image processing: sparse coefficient estimation of a polynomial via LASSO regression and recovering an image from a subset of the coefficients of its discrete Fourier transform. We further demonstrate that the proposed approach can easily be modified to solve the machine learning task of identifying the optimal sampling pattern in the Fourier domain for a given image and variational regularisation method, which has applications in the context of sparsity promoting reconstruction from magnetic resonance imaging data.
| Type: | Article |
|---|---|
| Title: | Trust your source: quantifying source condition elements for variational regularisation methods |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imamat/hxae008 |
| Publisher version: | https://doi.org/10.1093/imamat/hxae008 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Inverse problems, Regularisation theory, Source conditions, Range conditions, Variational regularisation, Machine learning, Optimal sampling, Compressed sensing, MRI |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10190171 |
Loading...
Loading...Loading...Loading...Archive Staff Only
 |
View Item |
