The high order block RIP condition for signal recovery

In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurement. A high order sufficient condition based on block RIP is obtained to guarantee the stable recovery of all block sparse signals in the presence of noise, and robust recovery when signals are not exactly block sparse via mixed $l_{2}/l_{1}$ minimization. Moreover, a concrete example is established to ensure the condition is sharp. The significance of the results presented in this paper lies in the fact that recovery may be possible under more general conditions by exploiting the block structure of the sparsity pattern instead of the conventional sparsity pattern.

• Publication year

  2016

• Venue

  Journal of Computational Mathematics

• Publication date

  2016-10-20

• Fields of study

  Mathematics, Computer Science, Engineering

• Identifiers
  DOI 10.4208/JCM.1710-M2017-0175arXiv 1610.06294
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Sharp Sufficient Conditions for Stable Recovery of Block Sparse Signals by Block Orthogonal Matching Pursuit

  2016cited by this paper
• Orthogonal Matching Pursuit Under the Restricted Isometry Property

  2015cited by this paper
• Block-sparse recovery via redundant block OMP

  2014cited by this paper
• Restricted p-isometry properties of nonconvex block-sparse compressed sensing

  2014cited by this paper
• Sparse Approximation and Recovery by Greedy Algorithms

  2013cited by this paper
• Compressed Sensing and Affine Rank Minimization Under Restricted Isometry

  2013cited by this paper
• Block sparse recovery via mixed l2/l1 minimization

  2013cited by this paper
• Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-Rank Matrices

  2013cited by this paper
• Sharp RIP Bound for Sparse Signal and Low-Rank Matrix Recovery

  2013cited by this paper
• Greedy Approximation in Convex Optimization

  2012cited by this paper
• Sparse Recovery Algorithms: Sufficient Conditions in Terms of RestrictedIsometry Constants

  2012cited by this paper
• Compressive Sensing with structured random matrices

  2012cited by this paper
• Adaptive Compressed Sensing Radar Oriented Toward Cognitive Detection in Dynamic Sparse Target Scene

  2012cited by this paper
• Error Estimates for Orthogonal Matching Pursuit and Random Dictionaries

  2011cited by this paper
• New bounds on the restricted isometry constant δ2k

  2011cited by this paper
• Improved stability conditions of BOGA for noisy block-sparse signals

  2011cited by this paper
• Block-Sparse Recovery via Convex Optimization

  2011cited by this paper
• Compressed sensing of color images

  2010cited by this paper
• Shifting Inequality and Recovery of Sparse Signals

  2010cited by this paper
• Orthogonal Super Greedy Algorithm and Applications in Compressed Sensing ∗

  2010cited by this paper
• Block orthogonal greedy algorithm for stable recovery of block-sparse signal representations

  2010cited by this paper
• The restricted isometry property for time–frequency structured random matrices

  2010cited by this paper
• A note on guaranteed sparse recovery via ℓ1-minimization

  2010cited by this paper
• Average Case Analysis of Multichannel Sparse Recovery Using Convex Relaxation

  2009cited by this paper
• Compressive Sensing and Structured Random Matrices

  2009cited by this paper
• The Benefit of Group Sparsity

  2009cited by this paper
• Block-Sparse Signals: Uncertainty Relations and Efficient Recovery

  2009cited by this paper
• New Bounds for Restricted Isometry Constants

  2009cited by this paper
• On the asymptotic properties of the group lasso estimator for linear models

  2008cited by this paper
• Recovering Sparse Signals Using Sparse Measurement Matrices in Compressed DNA Microarrays

  2008cited by this paper
• Robust Recovery of Signals From a Structured Union of Subspaces

  2008influential reference
• A Simple Proof of the Restricted Isometry Property for Random Matrices

  2008cited by this paper
• The group lasso for logistic regression

  2008cited by this paper
• Some theoretical results on the Grouped Variables Lasso

  2008cited by this paper
• Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors

  2008cited by this paper
• Compressed Sensing MRI

  2008cited by this paper
• Instance optimal decoding by thresholding in compressed sensing

  2008cited by this paper
• A Frame Construction and a Universal Distortion Bound for Sparse Representations

  2008cited by this paper
• Compressed sensing and best k-term approximation

  2008cited by this paper
• Consistency of the group Lasso and multiple kernel learning

  2007cited by this paper
• Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals

  2007cited by this paper
• Model selection and estimation in regression with grouped variables

  2006cited by this paper
• Stable signal recovery from incomplete and inaccurate measurements

  2005cited by this paper
• SIGNAL RECOVERY FROM PARTIAL INFORMATION VIA ORTHOGONAL MATCHING PURSUIT

  2005cited by this paper
• Decoding by linear programming

  2005cited by this paper
• Greed is good: algorithmic results for sparse approximation

  2004cited by this paper
• Sparse channel estimation via matching pursuit with application to equalization

  2002cited by this paper
• Presented by?????

  year unknowncited by this paper

• High-order block RIP for nonconvex block-sparse compressed sensing

  2024cites this paper
• Stable recovery of approximately block k-sparse signals with partial block support information via weighted ℓ2/ℓp(0<p≤1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \s

  2024cites this paper
• Block-sparse recovery and rank minimization using a weighted l p − l q

  2023cites this paper
• Convergence and stability analysis of iteratively reweighted least squares for noisy block sparse recovery

  2021cites this paper
• Recovery analysis for ℓ2/ℓ1-2 minimization via prior support information

  2021cites this paper
• The block mutual coherence property condition for signal recovery

  2020cites this paper
• The high-order block RIP for non-convex block-sparse compressed sensing

  2020cites this paper
• Weighted lp − l1 minimization methods for block sparse recovery and rank minimization

  2020cites this paper
• Coherence-Based Robust Analysis of Basis Pursuit De-Noising and Beyond

  2019cites this paper
• Sharp sufficient condition of block signal recovery via l 2/l 1-minimisation

  2019cites this paper
• Group Sparse Recovery in Impulsive Noise Via Adm

  2018cites this paper
• Coherence-Based Performance Guarantee of Regularized 𝓁1-Norm Minimization and Beyond

  2018cites this paper
• Group sparse recovery in impulsive noise via alternating direction method of multipliers

  2018influential citation
• A Note on the Block Restricted Isometry Property Condition

  2017cites this paper
• Recovery of signals by a weighted $\ell_2/\ell_1$ minimization under arbitrary prior support information

  2017cites this paper
• Tight Performance Bounds for Compressed Sensing With Conventional and Group Sparsity

  2016influential citation