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Sparse signals recovery from noisy measurements by orthogonal matching pursuit
1. | Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China |
2. | Department of Mathematics, Zhejiang University, Hangzhou, 310027 |
References:
[1] |
R. Baraniuk, M. Davenport, R. DeVore and M. Wakin, A simple proof of the restricted isometry property for random matrices, Constr. Approx., 28 (2008), 253-263.
doi: 10.1007/s00365-007-9003-x. |
[2] |
T. Cai, L. Wang and G. Xu, New bounds for restricted isometry constants, IEEE Trans. Inf. Theory, 56 (2010), 4388-4394.
doi: 10.1109/TIT.2010.2054730. |
[3] |
T. Cai and L. Wang, Orthogonal matching pursuit for sparse signal recovery with noise, IEEE Trans. Inf. Theory, 57 (2011), 4680-4688.
doi: 10.1109/TIT.2011.2146090. |
[4] |
T. Cai and A. Zhang, Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-rank Matrices, IEEE Trans. Inf. Theory, 60 (2014), 122-132.
doi: 10.1109/TIT.2013.2288639. |
[5] |
E. J. Candès, The restricted isometry property and its implications for compressed sensing, Comptes Rendus Mathematique, 346 (2008), 589-592.
doi: 10.1016/j.crma.2008.03.014. |
[6] |
E. J. Candès and T. Tao, Decoding by linear programming, IEEE Trans. Inf. Theory, 51 (2005), 4203-4215.
doi: 10.1109/TIT.2005.858979. |
[7] |
M. A. Davenport and M. B. Wakin, Analysis of orthogonal matching pursuit using the restricted isometry property, IEEE Trans. Inf. Theory, 56 (2010), 4395-4401.
doi: 10.1109/TIT.2010.2054653. |
[8] |
G. Davis, S. Mallat and M. Avellaneda, Adaptive greedy approximation, J. Constr. Approx., 13 (1997), 57-98.
doi: 10.1007/BF02678430. |
[9] |
D. L. Donoho and X. Huo, Uncertainty principles and ideal atomic decomposition, IEEE Trans. Inf. Theory, 47 (2001), 2845-2862.
doi: 10.1109/18.959265. |
[10] |
Z. B. Haim, Y. C. Eldar and M. Elad, Coherence-based performance guarantees for estimating a sparse vector under random noise, IEEE Trans. Signal Process., 58 (2010), 5030-5043.
doi: 10.1109/TSP.2010.2052460. |
[11] |
S. S. Huang and J. B. Zhu, Recovery of sparse signals using OMP and its variants: Convergence analysis based on RIP, Inverse Problems, 27 (2011), 035003, 14pp.
doi: 10.1088/0266-5611/27/3/035003. |
[12] |
E. T. Liu and N. Vladimir, The orthogonal super greedy algorithm and applications in compressed sensing, IEEE Trans. Inf. Theory, 58 (2012), 2040-2047.
doi: 10.1109/TIT.2011.2177632. |
[13] |
Q. Mo and Y. Shen, A remark on the restricted isometry property in orthogonal matching pursuit, IEEE Trans. Inf. Theory, 58 (2012), 3654-3656.
doi: 10.1109/TIT.2012.2185923. |
[14] |
D. Needell and J. A. Tropp, CoSaMP: Iterative signal recovery from incomplete and inaccurate samples, Appl. Comp. Harmonic Anal., 26 (2009), 301-321.
doi: 10.1016/j.acha.2008.07.002. |
[15] |
Y. C. Pati, R. Rezaiifar and P. S. Krishnaprasad, Orthogonal Matching Pursuit: Recursive function approximation with applications to wavelet decomposition, Proc. 27th Ann. Asilomar Conf. on Signals, Systems and Computers, (1993), 40-44. |
[16] |
H. Rauhut, Compressive sensing and structured random matrices, Theoretical foundations and numerical methods for sparse recovery, 9 (2010), 1-92.
doi: 10.1515/9783110226157.1. |
[17] |
W. Rui, W. Huang and D. R. Chen, The Exact Support Recovery of Sparse Signals With Noise via Orthogonal Matching Pursuit, IEEE Signal Process. Lett., 20 (2013), 403-406. |
[18] |
J. A. Tropp, Greed is good: Algorithmic results for sparse approximation, IEEE Trans. Inform. Theory, 50 (2004), 2231-2242.
doi: 10.1109/TIT.2004.834793. |
[19] |
J. A. Tropp, Computational methods for sparse solution of linear inverse Problems, Proc. IEEE, 98 (2010), 948-958. |
[20] |
M. R. Yang and F. de Hoog, Coherence and RIP Analysis for Greedy Algorithms in Compressive Sensing, preprint, 2013, arXiv:1307.1949 |
[21] |
T. Zhang, On the consistency of feature selection using greedy least squares regression, J. Machine Learning Research, 10 (2009), 555-568. |
show all references
References:
[1] |
R. Baraniuk, M. Davenport, R. DeVore and M. Wakin, A simple proof of the restricted isometry property for random matrices, Constr. Approx., 28 (2008), 253-263.
doi: 10.1007/s00365-007-9003-x. |
[2] |
T. Cai, L. Wang and G. Xu, New bounds for restricted isometry constants, IEEE Trans. Inf. Theory, 56 (2010), 4388-4394.
doi: 10.1109/TIT.2010.2054730. |
[3] |
T. Cai and L. Wang, Orthogonal matching pursuit for sparse signal recovery with noise, IEEE Trans. Inf. Theory, 57 (2011), 4680-4688.
doi: 10.1109/TIT.2011.2146090. |
[4] |
T. Cai and A. Zhang, Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-rank Matrices, IEEE Trans. Inf. Theory, 60 (2014), 122-132.
doi: 10.1109/TIT.2013.2288639. |
[5] |
E. J. Candès, The restricted isometry property and its implications for compressed sensing, Comptes Rendus Mathematique, 346 (2008), 589-592.
doi: 10.1016/j.crma.2008.03.014. |
[6] |
E. J. Candès and T. Tao, Decoding by linear programming, IEEE Trans. Inf. Theory, 51 (2005), 4203-4215.
doi: 10.1109/TIT.2005.858979. |
[7] |
M. A. Davenport and M. B. Wakin, Analysis of orthogonal matching pursuit using the restricted isometry property, IEEE Trans. Inf. Theory, 56 (2010), 4395-4401.
doi: 10.1109/TIT.2010.2054653. |
[8] |
G. Davis, S. Mallat and M. Avellaneda, Adaptive greedy approximation, J. Constr. Approx., 13 (1997), 57-98.
doi: 10.1007/BF02678430. |
[9] |
D. L. Donoho and X. Huo, Uncertainty principles and ideal atomic decomposition, IEEE Trans. Inf. Theory, 47 (2001), 2845-2862.
doi: 10.1109/18.959265. |
[10] |
Z. B. Haim, Y. C. Eldar and M. Elad, Coherence-based performance guarantees for estimating a sparse vector under random noise, IEEE Trans. Signal Process., 58 (2010), 5030-5043.
doi: 10.1109/TSP.2010.2052460. |
[11] |
S. S. Huang and J. B. Zhu, Recovery of sparse signals using OMP and its variants: Convergence analysis based on RIP, Inverse Problems, 27 (2011), 035003, 14pp.
doi: 10.1088/0266-5611/27/3/035003. |
[12] |
E. T. Liu and N. Vladimir, The orthogonal super greedy algorithm and applications in compressed sensing, IEEE Trans. Inf. Theory, 58 (2012), 2040-2047.
doi: 10.1109/TIT.2011.2177632. |
[13] |
Q. Mo and Y. Shen, A remark on the restricted isometry property in orthogonal matching pursuit, IEEE Trans. Inf. Theory, 58 (2012), 3654-3656.
doi: 10.1109/TIT.2012.2185923. |
[14] |
D. Needell and J. A. Tropp, CoSaMP: Iterative signal recovery from incomplete and inaccurate samples, Appl. Comp. Harmonic Anal., 26 (2009), 301-321.
doi: 10.1016/j.acha.2008.07.002. |
[15] |
Y. C. Pati, R. Rezaiifar and P. S. Krishnaprasad, Orthogonal Matching Pursuit: Recursive function approximation with applications to wavelet decomposition, Proc. 27th Ann. Asilomar Conf. on Signals, Systems and Computers, (1993), 40-44. |
[16] |
H. Rauhut, Compressive sensing and structured random matrices, Theoretical foundations and numerical methods for sparse recovery, 9 (2010), 1-92.
doi: 10.1515/9783110226157.1. |
[17] |
W. Rui, W. Huang and D. R. Chen, The Exact Support Recovery of Sparse Signals With Noise via Orthogonal Matching Pursuit, IEEE Signal Process. Lett., 20 (2013), 403-406. |
[18] |
J. A. Tropp, Greed is good: Algorithmic results for sparse approximation, IEEE Trans. Inform. Theory, 50 (2004), 2231-2242.
doi: 10.1109/TIT.2004.834793. |
[19] |
J. A. Tropp, Computational methods for sparse solution of linear inverse Problems, Proc. IEEE, 98 (2010), 948-958. |
[20] |
M. R. Yang and F. de Hoog, Coherence and RIP Analysis for Greedy Algorithms in Compressive Sensing, preprint, 2013, arXiv:1307.1949 |
[21] |
T. Zhang, On the consistency of feature selection using greedy least squares regression, J. Machine Learning Research, 10 (2009), 555-568. |
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