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CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. (English) Zbl 1163.94003
Summary: Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery algorithm called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix-vector multiplies with the sampling matrix. For compressible signals, the running time is just $O(N\log ^{2}N)$, where $N$ is the length of the signal.

94A12Signal theory (characterization, reconstruction, filtering, etc.)
Full Text: DOI arXiv
[1] Björck, å.: Numerical methods for least squares problems, (1996) · Zbl 0847.65023
[2] Candès, E. J.: The restricted isometry property and its implications for compressed sensing, C. R. Math. acad. Sci. Paris, ser. I 346, 589-592 (2008) · Zbl 1153.94002 · doi:10.1016/j.crma.2008.03.014
[3] Candès, E.; Romberg, J.; Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete Fourier information, IEEE trans. Inform. theory 52, No. 2, 489-509 (2006) · Zbl 1231.94017 · doi:10.1109/TIT.2005.862083
[4] Candès, E.; Romberg, J.; Tao, T.: Stable signal recovery from incomplete and inaccurate measurements, Comm. pure appl. Math. 59, No. 8, 1207-1223 (2006) · Zbl 1098.94009 · doi:10.1002/cpa.20124
[5] Candès, E. J.; Tao, T.: Decoding by linear programming, IEEE trans. Inform. theory 51, No. 12, 4203-4215 (2005) · Zbl 1264.94121
[6] Candès, E. J.; Tao, T.: Near optimal signal recovery from random projections: universal encoding strategies?, IEEE trans. Inform. theory 52, No. 12, 5406-5425 (2006) · Zbl 1309.94033
[7] A. Cohen, W. Dahmen, R. DeVore, Compressed sensing and best k-term approximation, IGPM Report, RWTH-Aachen, July 2006 · Zbl 1206.94008
[8] Cormen, T.; Lesierson, C.; Rivest, L.; Stein, C.: Introduction to algorithms, (2001)
[9] G. Cormode, S. Muthukrishnan, Combinatorial algorithms for compressed sensing, Technical report, DIMACS, 2005 · Zbl 1222.94016
[10] W. Dai, O. Milenkovic, Subspace pursuit for compressive sensing: Closing the gap between performance and complexity, available at: http://www.dsp.ece.rice.edu/cs/SubspacePursuit.pdf (preprint)
[11] Daubechies, I.; Defrise, M.; Mol, C. D.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. pure appl. Math. 57, 1413-1457 (2004) · Zbl 1077.65055 · doi:10.1002/cpa.20042
[12] Donoho, D. L.: Compressed sensing, IEEE trans. Inform. theory 52, No. 4, 1289-1306 (2006) · Zbl 1288.94016
[13] D.L. Donoho, J. Tanner, Counting faces of randomly projected polytopes when the projection radically lowers dimension, Department of Statistics Technical Report 2006-11, Stanford University, 2006 · Zbl 1206.52010
[14] D.L. Donoho, Y. Tsaig, I. Drori, J.-L. Starck, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit (StOMP), submitted for publication
[15] Figueiredo, M. A. T.; Nowak, R. D.; Wright, S. J.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems, IEEE J. Select. top. Signal process.: special issue on convex optimization methods for signal processing 1, No. 4, 586-598 (2007)
[16] Garnaev, A.; Gluskin, E.: On widths of the Euclidean ball, Sov. math. Dokl. 30, 200-204 (1984) · Zbl 0588.41022
[17] A.C. Gilbert, S. Guha, P. Indyk, Y. Kotidis, S. Muthukrishnan, M.J. Strauss, Fast, small-space algorithms for approximate histogram maintenance, in: ACM Symposium on Theoretical Computer Science, 2002 · Zbl 1192.68962
[18] A.C. Gilbert, S. Guha, P. Indyk, S. Muthukrishnan, M.J. Strauss, Near-optimal sparse Fourier representations via sampling, in: Proceedings of the 2002 ACM Symposium on Theory of Computing STOC, 2002 · Zbl 1192.94078
[19] A.C. Gilbert, M. Muthukrishnan, M.J. Strauss, Approximation of functions over redundant dictionaries using coherence, in: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, 2003 · Zbl 1094.41500
[20] A.C. Gilbert, S. Muthukrishnan, M.J. Strauss, Improved time bounds for near-optimal sparse Fourier representation via sampling, in: Proceedings of SPIE Wavelets XI, San Diego, CA, 2005
[21] A. Gilbert, M. Strauss, J. Tropp, R. Vershynin, Algorithmic linear dimension reduction in the \ell 1 norm for sparse vectors, submitted for publication
[22] A. Gilbert, M. Strauss, J. Tropp, R. Vershynin, One sketch for all: Fast algorithms for compressed sensing, in: Proceedings of the 39th ACM Symp. Theory of Computing, San Diego, 2007 · Zbl 1232.94008
[23] P. Indyk, R. Berinde, Sparse recovery using sparse matrices, CSAIL technical report, Massachusetts Institute of Technology, 2008
[24] M. Iwen, A deterministic sub-linear time sparse Fourier algorithm via non-adaptive compressed sensing methods, in: Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), 2008 · Zbl 1192.94047
[25] Kashin, B.: The widths of certain finite dimensional sets and classes of smooth functions, Izvestia 41, 334-351 (1977)
[26] Kim, S. -J.; Koh, K.; Lustig, M.; Boyd, S.; Gorinevsky, D.: A method for l1-regularized least squares, IEEE J. Select. top. Signal process. 1, No. 4, 606-617 (2007)
[27] Mallat, S.; Zhang, Z.: Matching pursuits with time -- frequency dictionaries, IEEE trans. Signal process. 41, No. 12, 3397-3415 (1993) · Zbl 0842.94004 · doi:10.1109/78.258082
[28] Miller, A. J.: Subset selection in regression, (2002) · Zbl 1051.62060
[29] D. Needell, J.A. Tropp, CoSaMP: Iterative signal recovery from incomplete and inaccurate samples, ACM Technical Report 2008-01, California Institute of Technology, Pasadena, 2008 · Zbl 1163.94003
[30] D. Needell, R. Vershynin, Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit, submitted for publication · Zbl 1183.68739
[31] D. Needell, R. Vershynin, Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit, Found. Comput. Math. (2008), in press · Zbl 1183.68739
[32] Nesterov, Y. E.; Nemirovski, A. S.: Interior point polynomial algorithms in convex programming, (1994) · Zbl 0824.90112
[33] H. Rauhut, On the impossibility of uniform sparse reconstruction using greedy methods, Sampl. Theory Signal Image Process. (2008), doi:10.1007/s10208-008-9031-3, in press · Zbl 1182.94026
[34] G. Reeves, M. Gastpar, Sampling bounds for sparse support recovery in the presence of noise, in: Proceedings of the IEEE International Symposium on Information Theory (ISIT 2008), Toronto, Canada, July 2008
[35] M. Rudelson, R. Vershynin, Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements, in: Proceedings of the 40th Annual Conference on Information Sciences and Systems, Princeton, 2006 · Zbl 1114.60009
[36] Temlyakov, V.: Nonlinear methods of approximation, Found. comput. Math. 3, No. 1, 33-107 (2003) · Zbl 1039.41012 · doi:10.1007/s102080010029
[37] Tropp, J. A.: Beyond Nyquist: efficient sampling of sparse, bandlimited signals
[38] Tropp, J. A.: Greed is good: algorithmic results for sparse approximation, IEEE trans. Inform. theory 50, No. 10, 2231-2242 (2004) · Zbl 1288.94019
[39] Tropp, J. A.; Gilbert, A. C.: Signal recovery from random measurements via orthogonal matching pursuit, IEEE trans. Inform. theory 53, No. 12, 4655-4666 (2007) · Zbl 1288.94022
[40] J.A. Tropp, A.C. Gilbert, S. Muthukrishnan, M.J. Strauss, Improved sparse approximation over quasi-incoherent dictionaries, in: Proc. 2003 IEEE International Conference on Image Processing, Barcelona, 2003