Discrete Uncertainty Principles and Sparse Signal Processing

  • Afonso S. Bandeira
  • Megan E. Lewis
  • Dustin G. Mixon
Article
  • 110 Downloads

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.

Keywords

Uncertainty principle Sparsity Compressed sensing 

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Copyright information

© Springer Science+Business Media, Inc. (outside the US) 2017

Authors and Affiliations

  • Afonso S. Bandeira
    • 1
  • Megan E. Lewis
    • 2
  • Dustin G. Mixon
    • 3
  1. 1.Department of Mathematics, Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Detachment 5, Air Force Operational Test and Evaluation CenterEdwards AFBUSA
  3. 3.Department of Mathematics and StatisticsAir Force Institute of TechnologyWright-Patterson AFBUSA

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