Kereta, Ž;
Maly, J;
Naumova, V;
(2021)
Computational approaches to non-convex, sparsity-inducing multi-penalty regularization.
Inverse Problems
, 37
(5)
, Article 055008. 10.1088/1361-6420/abdd46.
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Abstract
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction to an augmented single-penalty formulation, to the non-convex setting and discuss its computational intractability in large-scale applications. To circumvent this limitation, we propose an alternative single-penalty reduction based on infimal convolution that shares the benefits of the augmented approach but is computationally less dependent on the problem size. We provide linear convergence rates for both approaches, and their dependence on design parameters. Numerical experiments substantiate our theoretical findings.
| Type: | Article |
|---|---|
| Title: | Computational approaches to non-convex, sparsity-inducing multi-penalty regularization |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1361-6420/abdd46 |
| Publisher version: | https://doi.org/10.1088/1361-6420/abdd46 |
| Language: | English |
| Additional information: | Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence (https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
| 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/10128616 |
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