Approximate super-resolution of positive measures in all dimensions

Hernán García; Camilo Hernández; Mauricio Junca; Mauricio Velasco

doi:10.1016/j.acha.2020.02.001

Approximate super-resolution of positive measures in all dimensions

Hernán García, Camilo Hernández, Mauricio Junca, Mauricio Velasco

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study the problem of reconstructing a positive discrete measure on a compact set K⊆Rⁿ from a finite set of moments (possibly known only approximately) via convex optimization. We give new uniqueness results, new quantitative estimates for approximate recovery and a new sum-of-squares based hierarchy for approximate super-resolution on compact semi-algebraic sets.

Original language	English
Pages (from-to)	251-278
Number of pages	28
Journal	Applied and Computational Harmonic Analysis
Volume	52
DOIs	https://doi.org/10.1016/j.acha.2020.02.001
State	Published - May 2021
Externally published	Yes

Keywords

Compressed sensing
Super-resolution
Truncated moment problems

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10.1016/j.acha.2020.02.001

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title = "Approximate super-resolution of positive measures in all dimensions",

abstract = "We study the problem of reconstructing a positive discrete measure on a compact set K⊆Rn from a finite set of moments (possibly known only approximately) via convex optimization. We give new uniqueness results, new quantitative estimates for approximate recovery and a new sum-of-squares based hierarchy for approximate super-resolution on compact semi-algebraic sets.",

keywords = "Compressed sensing, Super-resolution, Truncated moment problems",

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AU - García, Hernán

AU - Hernández, Camilo

AU - Junca, Mauricio

AU - Velasco, Mauricio

PY - 2021/5

Y1 - 2021/5

N2 - We study the problem of reconstructing a positive discrete measure on a compact set K⊆Rn from a finite set of moments (possibly known only approximately) via convex optimization. We give new uniqueness results, new quantitative estimates for approximate recovery and a new sum-of-squares based hierarchy for approximate super-resolution on compact semi-algebraic sets.

AB - We study the problem of reconstructing a positive discrete measure on a compact set K⊆Rn from a finite set of moments (possibly known only approximately) via convex optimization. We give new uniqueness results, new quantitative estimates for approximate recovery and a new sum-of-squares based hierarchy for approximate super-resolution on compact semi-algebraic sets.

KW - Compressed sensing

KW - Super-resolution

KW - Truncated moment problems

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DO - 10.1016/j.acha.2020.02.001

M3 - Artículo

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SN - 1063-5203

VL - 52

SP - 251

EP - 278

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

ER -

Approximate super-resolution of positive measures in all dimensions

Abstract

Keywords

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