The Restricted Isometry Property for Time-Frequency Structured Random Matrices

Abstract

We establish the restricted isometry property for finite dimensional Gabor systems, that is, for families of time{frequency shifts of a randomly chosen window function. We show that the s-th order restricted isometry constant of the associated n n2 Gabor synthesis matrix is small provided s less or equal to cn2/3 / log2 n. This improves on previous estimates that exhibit quadratic scaling of n in s. Our proof develops bounds for a corresponding chaos process.

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Document Details

Document Type
Technical Report
Publication Date
Jun 16, 2011
Accession Number
ADA563016

Entities

People

  • Goetz E. Pfander
  • Holger Rauhut
  • Joel A. Tropp

Organizations

  • California Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Banach Space
  • Communication Channels
  • Compressed Sensing
  • Data Acquisition
  • Doppler Effect
  • Electronic Mail
  • Frequency
  • Frequency Shift
  • Inequalities
  • Information Theory
  • Integrals
  • Measurement
  • Probability
  • Random Variables
  • Signal Processing
  • Wireless Communications

Fields of Study

  • Mathematics

Readers

  • Image Processing and Computer Vision.
  • Linear Algebra