A sampling theorem for deconvolution of point sources

Brett Bernstein; Carlos Fernandez-Granda

doi:10.1109/SAMPTA.2017.8024426

A sampling theorem for deconvolution of point sources

Brett Bernstein, Carlos Fernandez-Granda

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We study the problem of recovering point sources from samples of their convolution with a Gaussian kernel, showing that a convex program achieves exact deconvolution as long as the sources are not too clustered together and there are at least two samples close to the location of each source. The result is established using a novel dual-certificate construction.

Original language	English (US)
Title of host publication	2017 12th International Conference on Sampling Theory and Applications, SampTA 2017
Editors	Gholamreza Anbarjafari, Andi Kivinukk, Gert Tamberg
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	60-63
Number of pages	4
ISBN (Electronic)	9781538615652
DOIs	https://doi.org/10.1109/SAMPTA.2017.8024426
State	Published - Sep 1 2017
Event	12th International Conference on Sampling Theory and Applications, SampTA 2017 - Tallinn, Estonia Duration: Jul 3 2017 → Jul 7 2017

Publication series

Name	2017 12th International Conference on Sampling Theory and Applications, SampTA 2017

Other

Other	12th International Conference on Sampling Theory and Applications, SampTA 2017
Country/Territory	Estonia
City	Tallinn
Period	7/3/17 → 7/7/17

ASJC Scopus subject areas

Signal Processing
Statistics, Probability and Uncertainty
Analysis
Statistics and Probability
Applied Mathematics

Access to Document

10.1109/SAMPTA.2017.8024426

Cite this

Bernstein, B., & Fernandez-Granda, C. (2017). A sampling theorem for deconvolution of point sources. In G. Anbarjafari, A. Kivinukk, & G. Tamberg (Eds.), 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017 (pp. 60-63). Article 8024426 (2017 12th International Conference on Sampling Theory and Applications, SampTA 2017). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SAMPTA.2017.8024426

A sampling theorem for deconvolution of point sources. / Bernstein, Brett; Fernandez-Granda, Carlos.
2017 12th International Conference on Sampling Theory and Applications, SampTA 2017. ed. / Gholamreza Anbarjafari; Andi Kivinukk; Gert Tamberg. Institute of Electrical and Electronics Engineers Inc., 2017. p. 60-63 8024426 (2017 12th International Conference on Sampling Theory and Applications, SampTA 2017).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Bernstein, B & Fernandez-Granda, C 2017, A sampling theorem for deconvolution of point sources. in G Anbarjafari, A Kivinukk & G Tamberg (eds), 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017., 8024426, 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017, Institute of Electrical and Electronics Engineers Inc., pp. 60-63, 12th International Conference on Sampling Theory and Applications, SampTA 2017, Tallinn, Estonia, 7/3/17. https://doi.org/10.1109/SAMPTA.2017.8024426

Bernstein B, Fernandez-Granda C. A sampling theorem for deconvolution of point sources. In Anbarjafari G, Kivinukk A, Tamberg G, editors, 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017. Institute of Electrical and Electronics Engineers Inc. 2017. p. 60-63. 8024426. (2017 12th International Conference on Sampling Theory and Applications, SampTA 2017). doi: 10.1109/SAMPTA.2017.8024426

Bernstein, Brett ; Fernandez-Granda, Carlos. / A sampling theorem for deconvolution of point sources. 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017. editor / Gholamreza Anbarjafari ; Andi Kivinukk ; Gert Tamberg. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 60-63 (2017 12th International Conference on Sampling Theory and Applications, SampTA 2017).

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A sampling theorem for deconvolution of point sources

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