Super-Resolution from Noisy Data

Emmanuel J. Candès, Carlos Fernandez-Granda

Research output: Contribution to journalArticle

Abstract

This paper studies the recovery of a superposition of point sources from noisy bandlimited data. In the fewest possible words, we only have information about the spectrum of an object in the low-frequency band [-flo,flo] and seek to obtain a higher resolution estimate by extrapolating the spectrum up to a frequency fhi>flo. We show that as long as the sources are separated by 2/flo, solving a simple convex program produces a stable estimate in the sense that the approximation error between the higher-resolution reconstruction and the truth is proportional to the noise level times the square of the super-resolution factor (SRF) fhi/flo.

Original languageEnglish (US)
Pages (from-to)1229-1254
Number of pages26
JournalJournal of Fourier Analysis and Applications
Volume19
Issue number6
DOIs
StatePublished - Dec 2013

Fingerprint

Super-resolution
Noisy Data
Frequency bands
High Resolution
Recovery
Convex Program
Approximation Error
Point Source
Estimate
Superposition
Low Frequency
Directly proportional
Truth
Object

Keywords

  • Basis mismatch
  • Deconvolution
  • Line spectra estimation
  • Sparsity
  • Stable signal recovery
  • Super-resolution factor

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Analysis

Cite this

Super-Resolution from Noisy Data. / Candès, Emmanuel J.; Fernandez-Granda, Carlos.

In: Journal of Fourier Analysis and Applications, Vol. 19, No. 6, 12.2013, p. 1229-1254.

Research output: Contribution to journalArticle

Candès, Emmanuel J. ; Fernandez-Granda, Carlos. / Super-Resolution from Noisy Data. In: Journal of Fourier Analysis and Applications. 2013 ; Vol. 19, No. 6. pp. 1229-1254.
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