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Error localization of best $L_{1}$ polynomial approximants

Abstract:

An important observation in compressed sensing is that the $\ell_0$ minimizer of an underdetermined linear system is equal to the $\ell_1$ minimizer when there exists a sparse solution vector and a certain restricted isometry property holds. Here, we develop a continuous analogue of this observation and show that the best $L_0$ and $L_1$ polynomial approximants of a polynomial that is corrupted on a set of small measure are nearly equal. We demonstrate an error localization property of best $...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1137/19M1242860

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Christ Church
Role:
Author
ORCID:
0000-0001-7911-1501
Publisher:
Society for Industrial and Applied Mathematics
Journal:
SIAM Journal on Numerical Analysis More from this journal
Volume:
59
Issue:
1
Pages:
314–333
Publication date:
2021-02-01
Acceptance date:
2020-11-05
DOI:
EISSN:
1095-7170
ISSN:
0036-1429
Language:
English
Keywords:
Pubs id:
1146198
Local pid:
pubs:1146198
Deposit date:
2020-11-20

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