Discrete Uncertainty Principles and Sparse Signal Processing

Afonso Bandeira, Megan E. Lewis, Dustin G. Mixon

Research output: Contribution to journalArticle

Abstract

We develop new discrete uncertainty principles in terms of numerical sparsity, which is a continuous proxy for the 0-norm. Unlike traditional sparsity, the continuity of numerical sparsity naturally accommodates functions which are nearly sparse. After studying these principles and the functions that achieve exact or near equality in them, we identify certain consequences in a number of sparse signal processing applications.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalJournal of Fourier Analysis and Applications
DOIs
StateAccepted/In press - Jun 19 2017

Fingerprint

Uncertainty Principle
Sparsity
Signal Processing
Signal processing
Equality
Norm
Uncertainty

Keywords

  • Compressed sensing
  • Sparsity
  • Uncertainty principle

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Applied Mathematics

Cite this

Discrete Uncertainty Principles and Sparse Signal Processing. / Bandeira, Afonso; Lewis, Megan E.; Mixon, Dustin G.

In: Journal of Fourier Analysis and Applications, 19.06.2017, p. 1-22.

Research output: Contribution to journalArticle

Bandeira, Afonso ; Lewis, Megan E. ; Mixon, Dustin G. / Discrete Uncertainty Principles and Sparse Signal Processing. In: Journal of Fourier Analysis and Applications. 2017 ; pp. 1-22.
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