Spike detection from inaccurate samplings

Jean Marc Azaïs; Yohann De Castro; Fabrice Gamboa

doi:10.1016/j.acha.2014.03.004

Spike detection from inaccurate samplings

Jean Marc Azaïs
, Yohann De Castro
, Fabrice Gamboa

Université de Toulouse
Laboratoire de Mathématiques d'Orsay

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

Abstract

This article investigates the support detection problem using the LASSO estimator in the space of measures. More precisely, we study the recovery of a discrete measure (spike train) from few noisy observations (Fourier samples, moments, etc.) using an ^ℓ1-regularization procedure. In particular, we provide an explicit quantitative localization of the spikes.

Original language	English
Pages (from-to)	177-195
Number of pages	19
Journal	Applied and Computational Harmonic Analysis
Volume	38
Issue number	2
DOIs	https://doi.org/10.1016/j.acha.2014.03.004
Publication status	Published - 1 Mar 2015
Externally published	Yes

Keywords

Compressed sensing
LASSO
Semidefinite programming
Signed measure
Super-resolution

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10.1016/j.acha.2014.03.004

Cite this

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title = "Spike detection from inaccurate samplings",

abstract = "This article investigates the support detection problem using the LASSO estimator in the space of measures. More precisely, we study the recovery of a discrete measure (spike train) from few noisy observations (Fourier samples, moments, etc.) using an ℓ1-regularization procedure. In particular, we provide an explicit quantitative localization of the spikes.",

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AU - Azaïs, Jean Marc

AU - De Castro, Yohann

AU - Gamboa, Fabrice

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N2 - This article investigates the support detection problem using the LASSO estimator in the space of measures. More precisely, we study the recovery of a discrete measure (spike train) from few noisy observations (Fourier samples, moments, etc.) using an ℓ1-regularization procedure. In particular, we provide an explicit quantitative localization of the spikes.

AB - This article investigates the support detection problem using the LASSO estimator in the space of measures. More precisely, we study the recovery of a discrete measure (spike train) from few noisy observations (Fourier samples, moments, etc.) using an ℓ1-regularization procedure. In particular, we provide an explicit quantitative localization of the spikes.

KW - Compressed sensing

KW - LASSO

KW - Semidefinite programming

KW - Signed measure

KW - Super-resolution

UR - https://www.scopus.com/pages/publications/84921877977

U2 - 10.1016/j.acha.2014.03.004

DO - 10.1016/j.acha.2014.03.004

M3 - Article

AN - SCOPUS:84921877977

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SP - 177

EP - 195

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

IS - 2

ER -

Spike detection from inaccurate samplings

Abstract

Keywords

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