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A new bound on the block restricted isometry constant in compressed sensing.

Yi Gao1, Mingde Ma2

  • 1School of Mathematics and Information Science, Beifang University of Nationalities, Wenchang Road, Yinchuan, 750021 China.

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|August 22, 2017
PubMed
Summary

This study enhances block sparse recovery using L1-minimization. It establishes a sufficient condition for exact and stable signal recovery, improving existing bounds for the block restricted isometry constant.

Keywords:
[Formula: see text]-minimizationblock restricted isometry propertyblock sparse recoverycompressed sensingnull space property

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Area of Science:

  • Signal Processing
  • Compressed Sensing
  • Mathematical Optimization

Background:

  • Block sparse recovery is crucial in signal processing.
  • L1-minimization is a common approach for sparse signal recovery.
  • Existing methods have limitations on the restricted isometry constant.

Purpose of the Study:

  • To establish a sufficient condition for block sparse recovery using L1-minimization.
  • To improve the bound on the block restricted isometry constant.
  • To analyze both noiseless and noisy measurement cases.

Main Methods:

  • Utilizing the L1-minimization algorithm.
  • Analyzing the block restricted isometry property (RIP).
  • Deriving conditions based on the block RIP constant.

Main Results:

  • A new sufficient condition for exact block sparse recovery in the noiseless case is presented.
  • Stable block sparse recovery is guaranteed in the noisy measurement case.
  • The derived bound on the block RIP constant improves upon previous results.

Conclusions:

  • The findings provide a tighter theoretical guarantee for block sparse recovery using L1-minimization.
  • This work advances the understanding of signal recovery conditions in compressed sensing.
  • The improved bounds have implications for designing more efficient recovery algorithms.