Discrete Uncertainty Principles and Sparse Signal Processing

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

doi:10.1007/s00041-017-9550-x

Discrete Uncertainty Principles and Sparse Signal Processing

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	935-956
Number of pages	22
Journal	Journal of Fourier Analysis and Applications
Volume	24
Issue number	4
DOIs	https://doi.org/10.1007/s00041-017-9550-x
State	Published - Aug 1 2018

Keywords

Compressed sensing
Sparsity
Uncertainty principle

ASJC Scopus subject areas

Analysis
General Mathematics
Applied Mathematics

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10.1007/s00041-017-9550-x

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Discrete Uncertainty Principles and Sparse Signal Processing

Abstract

Keywords

ASJC Scopus subject areas

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