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

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

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Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	251-278
Número de páginas	28
Publicación	Applied and Computational Harmonic Analysis
Volumen	52
DOI	https://doi.org/10.1016/j.acha.2020.02.001
Estado	Publicada - may. 2021
Publicado de forma externa	Sí

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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",

author = "Hern{\'a}n Garc{\'i}a and Camilo Hern{\'a}ndez and Mauricio Junca and Mauricio Velasco",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

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doi = "10.1016/j.acha.2020.02.001",

language = "Ingl{\'e}s",

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T1 - Approximate super-resolution of positive measures in all dimensions

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

UR - https://www.scopus.com/pages/publications/85079515993

U2 - 10.1016/j.acha.2020.02.001

DO - 10.1016/j.acha.2020.02.001

M3 - Artículo

AN - SCOPUS:85079515993

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

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