Discrete Uncertainty Principles and Sparse Signal Processing

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

Research output: Contribution to journalArticlepeer-review


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)935-956
Number of pages22
JournalJournal of Fourier Analysis and Applications
Issue number4
StatePublished - Aug 1 2018


  • Compressed sensing
  • Sparsity
  • Uncertainty principle

ASJC Scopus subject areas

  • Analysis
  • General Mathematics
  • Applied Mathematics


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