Work

Convergence rates in $\ell^1$-regularization when the basis is not smooth enough

Year: 2013

Type: preprint

Abstract: Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation with respect to a fixed basis. We drop this sparsity assumption and provide error estimates for non-sparse solutions. After discussing a result in this direction published earlier by one of the authors and coauthors we prove a similar error estimate under weaker assumptions. Two examples illustrate that this set of weaker assumptions indeed covers additional situations which appear in applications.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1311.1923

Authors: Flemming, Jens, Hegland, Markus

Institutions: Australian National University, Chemnitz University of Technology

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Technische Universität Chemnitz, Deutsche Forschungsgemeinschaft, Technische Universität München

Award: G6537443

OpenAlex ID: W2952501717

Cites: 13

Cited by: 1

Related to: 10