Journal title
SIAM Journal on Numerical Analysis
DOI
10.1137/19M1242860
Issue
1
Volume
59
Last updated
2024-04-08T18:17:19.01+01:00
Page
314-333
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 $L_1$ polynomial approximants and use our observations to develop an improved algorithm for computing best $L_1$ polynomial approximants to continuous functions.
Symplectic ID
1146198
Submitted to ORA
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Publication type
Journal Article
Publication date
01 Feb 2021