RIP based condition for support recovery with A* OMP in the presence of noise

A* orthogonal matching pursuit (A* OMP) aims at combination of best-first tree search with the OMP algorithm for the compressed sensing problem. In this study, the authors present a new analysis for the A* OMP algorithm using the restricted isometry property (RIP). The results show that if the sampling matrix A satisfies the RIP with δ K ⋆ < B / ( K + B ) ( K ⋆ = max { 2 K , K + B } ), then under some constraints on SNR, A* OMP accurately recovers the support of any K-sparse signal x from the samples y = A x + e , where B is the number of child paths for each candidate in the algorithm. In addition, the proposed condition is an optimal condition that guarantees the success of A* OMP in the noise-free case.

[1]  Anamitra Makur,et al.  Signal Recovery from Random Measurements via Extended Orthogonal Matching Pursuit , 2015, IEEE Transactions on Signal Processing.

[2]  Hakan Erdogan,et al.  A* orthogonal matching pursuit: Best-first search for compressed sensing signal recovery , 2010, Digit. Signal Process..

[3]  Stephen J. Wright,et al.  Computational Methods for Sparse Solution of Linear Inverse Problems , 2010, Proceedings of the IEEE.

[4]  Mrityunjoy Chakraborty,et al.  Improving the Bound on the RIP Constant in Generalized Orthogonal Matching Pursuit , 2013, IEEE Signal Processing Letters.

[5]  Hakan Erdogan,et al.  Improving A⋆ OMP: Theoretical and empirical analyses with a novel dynamic cost model , 2013, Signal Process..

[6]  Tong Zhang,et al.  Sparse Recovery With Orthogonal Matching Pursuit Under RIP , 2010, IEEE Transactions on Information Theory.

[7]  Haifeng Li,et al.  A New Analysis for Support Recovery With Block Orthogonal Matching Pursuit , 2018, IEEE Signal Processing Letters.

[8]  Guoqi Liu,et al.  An Improved Analysis for Support Recovery With Orthogonal Matching Pursuit Under General Perturbations , 2018, IEEE Access.

[9]  Joel A. Tropp,et al.  Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit , 2007, IEEE Transactions on Information Theory.

[10]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[11]  E. Candès,et al.  Sparsity and incoherence in compressive sampling , 2006, math/0611957.

[12]  Yi Shen,et al.  Analysis of generalised orthogonal matching pursuit using restricted isometry constant , 2014 .

[13]  Entao Liu,et al.  Orthogonal Super Greedy Algorithm and Applications in Compressed Sensing ∗ , 2010 .

[14]  Jian Wang,et al.  Exact Recovery of Sparse Signals Using Orthogonal Matching Pursuit: How Many Iterations Do We Need? , 2012, IEEE Transactions on Signal Processing.

[15]  Jian Wang,et al.  A Sharp Condition for Exact Support Recovery With Orthogonal Matching Pursuit , 2017, IEEE Transactions on Signal Processing.

[16]  Haifeng Li,et al.  Improved RIP-based performance guarantee for sparse signal recovery via A*OMP , 2018 .

[17]  Michael B. Wakin,et al.  Analysis of Orthogonal Matching Pursuit Using the Restricted Isometry Property , 2009, IEEE Transactions on Information Theory.

[18]  Jian Wang,et al.  Generalized Orthogonal Matching Pursuit , 2011, IEEE Transactions on Signal Processing.

[19]  Jean-Luc Starck,et al.  Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit , 2012, IEEE Transactions on Information Theory.

[20]  Zhengchun Zhou,et al.  A Novel Sufficient Condition for Generalized Orthogonal Matching Pursuit , 2016, IEEE Communications Letters.

[21]  R. DeVore,et al.  A Simple Proof of the Restricted Isometry Property for Random Matrices , 2008 .

[22]  Jian Wang.  Support Recovery With Orthogonal Matching Pursuit in the Presence of Noise , 2015, IEEE Transactions on Signal Processing.

[23]  J. Tropp,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, Commun. ACM.

[24]  Jian Wang,et al.  Multipath Matching Pursuit , 2013, IEEE Transactions on Information Theory.

[25]  Olgica Milenkovic,et al.  Subspace Pursuit for Compressive Sensing Signal Reconstruction , 2008, IEEE Transactions on Information Theory.

[26]  Haifeng Li,et al.  Generalized covariance-assisted matching pursuit , 2019, Signal Process..

[27]  Yi Shen,et al.  Theoretical results for sparse signal recovery with noises using generalized OMP algorithm , 2015, Signal Process..

[28]  Xin Yuan,et al.  On the Fundamental Limit of Multipath Matching Pursuit , 2018, IEEE Journal of Selected Topics in Signal Processing.

[29]  Yi Shen,et al.  A Remark on the Restricted Isometry Property in Orthogonal Matching Pursuit , 2012, IEEE Transactions on Information Theory.

[30]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[31]  Haifeng Li,et al.  On the Fundamental Limit of Orthogonal Matching Pursuit for Multiple Measurement Vector , 2019, IEEE Access.

[32]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[33]  Joel A. Tropp,et al.  Greed is good: algorithmic results for sparse approximation , 2004, IEEE Transactions on Information Theory.

[34]  Jian Wang,et al.  On the Recovery Limit of Sparse Signals Using Orthogonal Matching Pursuit , 2012, IEEE Transactions on Signal Processing.