Super-resolution of point sources via convex programming

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recent work has shown that convex programming allows to recover a superposition of point sources exactly from low-resolution data as long as the sources are separated by 2/fc, where fc is the cut-off frequency of the sensing process. The proof relies on the construction of a certificate whose existence implies exact recovery. This certificate has since been used to establish that the approach is robust to noise and to analyze related problems such as compressed sensing off the grid and the super-resolution of splines from moment measurements. In this work we construct a new certificate that allows to extend all these results to signals with minimum separations above 1.26/fc. This is close to 1/fc, the threshold at which the problem becomes inherently ill posed, in the sense that signals with a smaller minimum separation may have low-pass projections with negligible energy.

Original languageEnglish (US)
Title of host publication2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages41-44
Number of pages4
ISBN (Electronic)9781479919635
DOIs
StatePublished - 2015
Event6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015 - Cancun, Mexico
Duration: Dec 13 2015Dec 16 2015

Publication series

Name2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015

Other

Other6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
CountryMexico
CityCancun
Period12/13/1512/16/15

ASJC Scopus subject areas

  • Signal Processing
  • Computational Mathematics

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