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Compressed sensing with coherent tight frames via $l_q$-minimization for $0 < q \leq 1$
1. | Department of Mathematics, Zhejiang University, Hangzhou, 310027, China, China |
References:
[1] |
R. Baraniuk, E. J. Candès, R. Nowak and M. Vetterli, Sensing, Sampling, and Compression,, IEEE Signal Proc. Mag., 25 (2008). Google Scholar |
[2] |
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.
doi: 10.1007/s00365-007-9003-x. |
[3] |
E. J. Candès., The restricted isometry property and its implications for compressed sensing,, C. R. Math. Acad. Sci. Paris, 346 (2008), 589.
doi: 10.1016/j.crma.2008.03.014. |
[4] |
E. J. Candès, Y. C. Eldar and D. Needell, Compressed Sensing with Coherent and Redundant Dictionaries,, Appl. Comput. Harmon. Anal., 31 (2011), 59.
doi: 10.1016/j.acha.2010.10.002. |
[5] |
E. J. Candès, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,, IEEE Trans. Inform. Theory, 52 (2006), 489.
doi: 10.1109/TIT.2005.862083. |
[6] |
E. J. Candès, J. Romberg and T. Tao, Stable signal recovery from incomplete and inaccurate measurements,, Comm. Pure Appl. Math., 59 (2006), 1207.
doi: 10.1002/cpa.20124. |
[7] |
E. J. Candès and T. Tao, Decoding by linear programming,, IEEE Trans. Inform. Theory, 51 (2005), 4203.
doi: 10.1109/TIT.2005.858979. |
[8] |
T. Cai, L. Wang and J. Zhang, Shifting inequality and recovery of sparse signals,, IEEE Trans. Inform. Theory, 58 (2010), 1300.
doi: 10.1109/TSP.2009.2034936. |
[9] |
T. Cai, L. Wang and G. Xu, New bounds for restricted isometry constants,, IEEE Trans. Inform. Theory, 56 (2010), 4388.
doi: 10.1109/TIT.2010.2054730. |
[10] |
R. Chartrand, Exact reconstructions of sparse signals via nonconvex minimization,, IEEE Signal Process. Lett., 14 (2007), 707.
doi: 10.1109/LSP.2007.898300. |
[11] |
R. Chartrand and V. Staneva, Restricted isometry properties and nonconvex compressive sensing,, Inverse Problems, 24 (2008), 1.
doi: 10.1088/0266-5611/24/3/035020. |
[12] |
D. Donoho, Compressed sensing,, IEEE Trans. Inform. Theory, 52 (2006), 1289.
doi: 10.1109/TIT.2006.871582. |
[13] |
I. Daubechies, R. Devore, M. Fornasier and S. Gunturk, Iteratively reweighted least squares minimization for sparse recovery,, Comm. Pure. Appl. Math., 63 (2010), 1.
doi: 10.1002/cpa.20303. |
[14] |
M. E. Davies and R. Gribonval, Restricted isometry properties where $l_p$ sparse recovery can fail for $0 < p \leq 1$,, IEEE Trans. Inform. Theory, 55 (2009), 2203.
doi: 10.1109/TIT.2009.2016030. |
[15] |
S. Foucart and M. J. Lai, Sparsest solutions of underdetermined linear systems via $l_q$ minimization for $0 < q \leq1$,, Appl. Comput. Harmon. Anal., 26 (2009), 395.
doi: 10.1016/j.acha.2008.09.001. |
[16] |
D. D. Ge, X. Y. Jiang and Y. Y. Ye, A note on complexity of $l_p$ minimization,, Mathematical Programming, 129 (2011), 285.
doi: 10.1007/s10107-011-0470-2. |
[17] |
M. J. Lai and L. Y. Liu, A new estimate of restricted isometry constants for sparse solutions,, manuscript., (). Google Scholar |
[18] |
Q. Mo and S. Li, New bounds on the restricted isometry constant $\delta_{2k}$,, Appl. Comput. Harmon. Anal., 31 (2011), 460.
doi: 10.1016/j.acha.2011.04.005. |
[19] |
S. G. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries,, IEEE Trans. Signal Process., 41 (1993), 3397.
doi: 10.1109/78.258082. |
[20] |
B. K. Natarajan, Sparse approximate solutions to linear systems,, SIAM J. Comput., 24 (1995), 227.
doi: 10.1137/S0097539792240406. |
[21] |
D. Needell and J. A. Tropp, CoSaMP: Iterative signal recovery from noisy samples,, Appl. Comput. Harmon. Anal., 26 (2009), 301.
doi: 10.1016/j.acha.2008.07.002. |
[22] |
H. Rauhut, K. Schnass and P. Vandergheynst, Compressed sensing and redundant dictionaries,, IEEE Trans. Inform. Theory, 54 (2008), 2210.
doi: 10.1109/TIT.2008.920190. |
[23] |
M. Rudelson and R. Vershynin, On sparse reconstruction from Fourier and Gaussian measurements,, Comm. Pure Appl. Math., 61 (2008), 1025.
doi: 10.1002/cpa.20227. |
[24] |
R. Saab, R. Chartrand and O. Yilmaz, Stable sparse approximations via nonconvex optimization,, Proceedings of the 33rd IEEE International Conference on Acoustics, (2008), 3885.
doi: 10.1109/ICASSP.2008.4518502. |
[25] |
Q. Sun, Recovery of sparsest signals via $l_q$-minimization,, Appl. Comput. Harmon. Anal., 32 (2012), 329.
doi: 10.1016/j.acha.2011.07.001. |
[26] |
J. A. Tropp, Greed is good: Algorithmic results for sparse approximation,, IEEE Trans. Info. Theory, 50 (2004), 2231.
doi: 10.1109/TIT.2004.834793. |
[27] |
A. M. Zoubir and D. R. Iskander, Bootstrap Methods in Signal Processing,, IEEE Signal Proc. Mag., 24 (2007). Google Scholar |
show all references
References:
[1] |
R. Baraniuk, E. J. Candès, R. Nowak and M. Vetterli, Sensing, Sampling, and Compression,, IEEE Signal Proc. Mag., 25 (2008). Google Scholar |
[2] |
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.
doi: 10.1007/s00365-007-9003-x. |
[3] |
E. J. Candès., The restricted isometry property and its implications for compressed sensing,, C. R. Math. Acad. Sci. Paris, 346 (2008), 589.
doi: 10.1016/j.crma.2008.03.014. |
[4] |
E. J. Candès, Y. C. Eldar and D. Needell, Compressed Sensing with Coherent and Redundant Dictionaries,, Appl. Comput. Harmon. Anal., 31 (2011), 59.
doi: 10.1016/j.acha.2010.10.002. |
[5] |
E. J. Candès, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,, IEEE Trans. Inform. Theory, 52 (2006), 489.
doi: 10.1109/TIT.2005.862083. |
[6] |
E. J. Candès, J. Romberg and T. Tao, Stable signal recovery from incomplete and inaccurate measurements,, Comm. Pure Appl. Math., 59 (2006), 1207.
doi: 10.1002/cpa.20124. |
[7] |
E. J. Candès and T. Tao, Decoding by linear programming,, IEEE Trans. Inform. Theory, 51 (2005), 4203.
doi: 10.1109/TIT.2005.858979. |
[8] |
T. Cai, L. Wang and J. Zhang, Shifting inequality and recovery of sparse signals,, IEEE Trans. Inform. Theory, 58 (2010), 1300.
doi: 10.1109/TSP.2009.2034936. |
[9] |
T. Cai, L. Wang and G. Xu, New bounds for restricted isometry constants,, IEEE Trans. Inform. Theory, 56 (2010), 4388.
doi: 10.1109/TIT.2010.2054730. |
[10] |
R. Chartrand, Exact reconstructions of sparse signals via nonconvex minimization,, IEEE Signal Process. Lett., 14 (2007), 707.
doi: 10.1109/LSP.2007.898300. |
[11] |
R. Chartrand and V. Staneva, Restricted isometry properties and nonconvex compressive sensing,, Inverse Problems, 24 (2008), 1.
doi: 10.1088/0266-5611/24/3/035020. |
[12] |
D. Donoho, Compressed sensing,, IEEE Trans. Inform. Theory, 52 (2006), 1289.
doi: 10.1109/TIT.2006.871582. |
[13] |
I. Daubechies, R. Devore, M. Fornasier and S. Gunturk, Iteratively reweighted least squares minimization for sparse recovery,, Comm. Pure. Appl. Math., 63 (2010), 1.
doi: 10.1002/cpa.20303. |
[14] |
M. E. Davies and R. Gribonval, Restricted isometry properties where $l_p$ sparse recovery can fail for $0 < p \leq 1$,, IEEE Trans. Inform. Theory, 55 (2009), 2203.
doi: 10.1109/TIT.2009.2016030. |
[15] |
S. Foucart and M. J. Lai, Sparsest solutions of underdetermined linear systems via $l_q$ minimization for $0 < q \leq1$,, Appl. Comput. Harmon. Anal., 26 (2009), 395.
doi: 10.1016/j.acha.2008.09.001. |
[16] |
D. D. Ge, X. Y. Jiang and Y. Y. Ye, A note on complexity of $l_p$ minimization,, Mathematical Programming, 129 (2011), 285.
doi: 10.1007/s10107-011-0470-2. |
[17] |
M. J. Lai and L. Y. Liu, A new estimate of restricted isometry constants for sparse solutions,, manuscript., (). Google Scholar |
[18] |
Q. Mo and S. Li, New bounds on the restricted isometry constant $\delta_{2k}$,, Appl. Comput. Harmon. Anal., 31 (2011), 460.
doi: 10.1016/j.acha.2011.04.005. |
[19] |
S. G. Mallat and Z. Zhang, Matching pursuits with time-frequency dictionaries,, IEEE Trans. Signal Process., 41 (1993), 3397.
doi: 10.1109/78.258082. |
[20] |
B. K. Natarajan, Sparse approximate solutions to linear systems,, SIAM J. Comput., 24 (1995), 227.
doi: 10.1137/S0097539792240406. |
[21] |
D. Needell and J. A. Tropp, CoSaMP: Iterative signal recovery from noisy samples,, Appl. Comput. Harmon. Anal., 26 (2009), 301.
doi: 10.1016/j.acha.2008.07.002. |
[22] |
H. Rauhut, K. Schnass and P. Vandergheynst, Compressed sensing and redundant dictionaries,, IEEE Trans. Inform. Theory, 54 (2008), 2210.
doi: 10.1109/TIT.2008.920190. |
[23] |
M. Rudelson and R. Vershynin, On sparse reconstruction from Fourier and Gaussian measurements,, Comm. Pure Appl. Math., 61 (2008), 1025.
doi: 10.1002/cpa.20227. |
[24] |
R. Saab, R. Chartrand and O. Yilmaz, Stable sparse approximations via nonconvex optimization,, Proceedings of the 33rd IEEE International Conference on Acoustics, (2008), 3885.
doi: 10.1109/ICASSP.2008.4518502. |
[25] |
Q. Sun, Recovery of sparsest signals via $l_q$-minimization,, Appl. Comput. Harmon. Anal., 32 (2012), 329.
doi: 10.1016/j.acha.2011.07.001. |
[26] |
J. A. Tropp, Greed is good: Algorithmic results for sparse approximation,, IEEE Trans. Info. Theory, 50 (2004), 2231.
doi: 10.1109/TIT.2004.834793. |
[27] |
A. M. Zoubir and D. R. Iskander, Bootstrap Methods in Signal Processing,, IEEE Signal Proc. Mag., 24 (2007). Google Scholar |
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