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Volumn 58, Issue 1, 2010, Pages 269-280

Bayesian compressive sensing via belief propagation

Author keywords

Bayesian inference; Belief propagation; Compressive sensing; Fast algorithms; Sparse matrices

Indexed keywords

ASYMPTOTICALLY OPTIMAL; BAYESIAN; BAYESIAN INFERENCE; BELIEF PROPAGATION; BELIEF PROPAGATION DECODING; DECODING ALGORITHM; ENCODING MATRIX; FAST ALGORITHMS; FAST COMPUTATION; GRAPHICAL MODEL; GREEDY ALGORITHMS; LINEAR PROJECTIONS; MIXTURE GAUSSIAN MODEL; NYQUIST; SIGNAL ACQUISITIONS; SIGNAL MODELS; SPARSE MATRICES; SPARSE SIGNALS; STATISTICAL CHARACTERIZATION; TWO-STATE;

EID: 72949124697     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2027773     Document Type: Article
Times cited : (385)

References (60)
  • 2
    • 0026727407 scopus 로고
    • Image compression through wavelet transform coding
    • Mar.
    • R. A. DeVore, B. Jawerth, and B. J. Lucier, "Image compression through wavelet transform coding," IEEE Trans. Inf. Theory, vol.38, no.2, pp. 719-746, Mar. 1992.
    • (1992) IEEE Trans. Inf. Theory , vol.38 , Issue.2 , pp. 719-746
    • DeVore, R.A.1    Jawerth, B.2    Lucier, B.J.3
  • 3
    • 0031102203 scopus 로고    scopus 로고
    • Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm
    • Mar.
    • I. F. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process., vol.45, no.3, pp. 600-616, Mar. 1997.
    • (1997) IEEE Trans. Signal Process. , vol.45 , Issue.3 , pp. 600-616
    • Gorodnitsky, I.F.1    Rao, B.D.2
  • 4
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Feb.
    • E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol.52, no.2, pp. 489-509, Feb. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 5
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr.
    • D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol.52, no.4, pp. 1289-1306, Apr. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 6
    • 85032751965 scopus 로고    scopus 로고
    • A lecture on compressive sensing
    • R. G. Baraniuk, "A lecture on compressive sensing," IEEE Signal Process. Mag., vol.24, no.4, pp. 118-121, 2007.
    • (2007) IEEE Signal Process. Mag. , vol.24 , Issue.4 , pp. 118-121
    • Baraniuk, R.G.1
  • 8
    • 0032131292 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • S. Chen, D. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol.20, no.1, pp. 33-61, 1998.
    • (1998) SIAM J. Sci. Comput. , vol.20 , Issue.1 , pp. 33-61
    • Chen, S.1    Donoho, D.2    Saunders, M.3
  • 9
    • 22144471532 scopus 로고    scopus 로고
    • Neighborliness of randomly projected simplices in high dimensions
    • D. Donoho and J. Tanner, "Neighborliness of randomly projected simplices in high dimensions," Proc. Nat. Acad. Sci., vol.102, no.27, pp. 9452-9457, 2005.
    • (2005) Proc. Nat. Acad. Sci. , vol.102 , Issue.27 , pp. 9452-9457
    • Donoho, D.1    Tanner, J.2
  • 10
    • 33646479497 scopus 로고    scopus 로고
    • High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension
    • Mar.
    • D. Donoho, "High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension," Discrete Comput. Geomet., vol.35, no.4, pp. 617-652, Mar. 2006.
    • (2006) Discrete Comput. Geomet. , vol.35 , Issue.4 , pp. 617-652
    • Donoho, D.1
  • 11
    • 0023604331 scopus 로고
    • An algorithm for linear programming which requires O(((m+n)n2+(m+n)1.5n) L) arithmetic operations
    • New York
    • P. M. Vaidya, "An algorithm for linear programming which requires O(((m+n)n2+(m+n)1.5n)L) arithmetic operations," in Proc. 19th ACM Symp. Theory Computing (STOC), New York, 1987, pp. 29-38.
    • (1987) Proc. 19th ACM Symp. Theory Computing (STOC) , pp. 29-38
    • Vaidya, P.M.1
  • 12
    • 64649083745 scopus 로고    scopus 로고
    • Signal recovery from random measurements via orthogonal matching pursuit
    • Dec.
    • J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, vol.53, no.12, pp. 4655-4666, Dec. 2007.
    • (2007) IEEE Trans. Inf. Theory , vol.53 , Issue.12 , pp. 4655-4666
    • Tropp, J.A.1    Gilbert, A.C.2
  • 13
    • 85006516756 scopus 로고    scopus 로고
    • Near optimal approximation of arbitrary vectors from highly incomplete measurements
    • Aachen, Germany, Preprint
    • A. Cohen, W. Dahmen, and R. A. DeVore, "Near optimal approximation of arbitrary vectors from highly incomplete measurements," Institut für Geometrie und Praktische Mathematik, Aachen, Germany, 2007, Preprint.
    • (2007) Institut für Geometrie und Praktische Mathematik
    • Cohen, A.1    Dahmen, W.2    DeVore, R.A.3
  • 14
    • 54049123649 scopus 로고    scopus 로고
    • Fast reconstruction of piecewise smooth signals from random projections
    • presented at the, Rennes, France, Nov.
    • M. F. Duarte, M. B. Wakin, and R. G. Baraniuk, "Fast reconstruction of piecewise smooth signals from random projections," presented at the SPARS, Rennes, France, Nov. 2005.
    • (2005) SPARS
    • Duarte, M.F.1    Wakin, M.B.2    Baraniuk, R.G.3
  • 16
    • 62749175137 scopus 로고    scopus 로고
    • CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
    • D. Needell and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Appl. Comput. Harmon. Anal., vol.26, no.3, pp. 301-321, 2008.
    • (2008) Appl. Comput. Harmon. Anal. , vol.26 , Issue.3 , pp. 301-321
    • Needell, D.1    Tropp, J.A.2
  • 17
    • 72949089365 scopus 로고    scopus 로고
    • Iterative hard thresholding for compressed sensing
    • to be published
    • T. Blumensath and M. E. Davies, "Iterative hard thresholding for compressed sensing," Appl. Comput. Harmon. Anal., 2008, to be published.
    • (2008) Appl. Comput. Harmon. Anal.
    • Blumensath, T.1    Davies, M.E.2
  • 18
    • 65749110333 scopus 로고    scopus 로고
    • Subspace pursuit for compressive sensing: Closing the gap between performance and complexity
    • May
    • W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing: Closing the gap between performance and complexity," IEEE Trans. Inf. Theory, vol.55, no.5, pp. 2230-2249, May 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.5 , pp. 2230-2249
    • Dai, W.1    Milenkovic, O.2
  • 20
    • 39449126969 scopus 로고    scopus 로고
    • Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
    • Dec.
    • M. Figueiredo, R. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Sel. Topics Signal Process., no.4, pp. 586-597, Dec. 2007.
    • (2007) IEEE J. Sel. Topics Signal Process. , Issue.4 , pp. 586-597
    • Figueiredo, M.1    Nowak, R.2    Wright, S.J.3
  • 25
    • 44849087307 scopus 로고    scopus 로고
    • Bayesian compressive sensing
    • Jun.
    • S. Ji, Y. Xue, and L. Carin, "Bayesian compressive sensing," IEEE Trans. Signal Process., vol.56, no.6, pp. 2346-2356, Jun. 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.6 , pp. 2346-2356
    • Ji, S.1    Xue, Y.2    Carin, L.3
  • 29
    • 42149091048 scopus 로고    scopus 로고
    • Multiuser detection of sparsely spread CDMA
    • G. Guo and C.-C. Wang, "Multiuser detection of sparsely spread CDMA," IEEE J. Sel. Areas Commun., vol.26, no.3, pp. 421-431, 2008.
    • (2008) IEEE J. Sel. Areas Commun. , vol.26 , Issue.3 , pp. 421-431
    • Guo, G.1    Wang, C.-C.2
  • 33
    • 0004031805 scopus 로고    scopus 로고
    • Understanding belief propagation and its generalizations
    • Tech. Rep. TR2001-022, Jan.
    • J. S. Yedidia, W. T. Freeman, and Y. Weiss, "Understanding belief propagation and its generalizations," Mitsubishi Electric Res. Labs., Tech. Rep. TR2001-022, Jan. 2002.
    • (2002) Mitsubishi Electric Res. Labs.
    • Yedidia, J.S.1    Freeman, W.T.2    Weiss, Y.3
  • 37
    • 84925405668 scopus 로고
    • Low-density parity-check codes
    • Jan.
    • R. G. Gallager, "Low-density parity-check codes," IEEE Trans. Inf. Theory, vol.8, no.1, pp. 21-28, Jan. 1962.
    • (1962) IEEE Trans. Inf. Theory , vol.8 , Issue.1 , pp. 21-28
    • Gallager, R.G.1
  • 38
    • 0035246127 scopus 로고    scopus 로고
    • Design of capacity-approaching irregular low-density parity-check codes
    • Feb.
    • T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inf. Theory, vol.47, pp. 619-637, Feb. 2001.
    • (2001) IEEE Trans. Inf. Theory , vol.47 , pp. 619-637
    • Richardson, T.J.1    Shokrollahi, M.A.2    Urbanke, R.L.3
  • 39
    • 39049110737 scopus 로고    scopus 로고
    • Sudocodes-Fast measurement and reconstruction of sparse signals
    • presented at the, Seattle, WA, Jul.
    • S. Sarvotham, D. Baron, and R. G. Baraniuk, "Sudocodes-Fast measurement and reconstruction of sparse signals," presented at the Int. Symp. Inf. Theory (ISIT), Seattle, WA, Jul. 2006.
    • (2006) Int. Symp. Inf. Theory (ISIT)
    • Sarvotham, S.1    Baron, D.2    Baraniuk, R.G.3
  • 43
    • 33747727601 scopus 로고    scopus 로고
    • Wavelet-based signal processing using hidden Markov models
    • Apr.
    • M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, "Wavelet-based signal processing using hidden Markov models," IEEE Trans. Signal Process., vol.46, no.4, pp. 886-902, Apr. 1998.
    • (1998) IEEE Trans. Signal Process. , vol.46 , Issue.4 , pp. 886-902
    • Crouse, M.S.1    Nowak, R.D.2    Baraniuk, R.G.3
  • 44
    • 84893179575 scopus 로고
    • Variable selection via Gibbs sampling
    • E. I. George and R. E. McCulloch, "Variable selection via Gibbs sampling," J. Amer. Statist. Assoc., vol.88, pp. 881-889, 1993.
    • (1993) J. Amer. Statist. Assoc. , vol.88 , pp. 881-889
    • George, E.I.1    McCulloch, R.E.2
  • 45
    • 0000647838 scopus 로고    scopus 로고
    • Variable selection and model comparison in regression
    • J. Geweke, "Variable selection and model comparison in regression," in Bayesian Statist. 5, 1996, pp. 609-620.
    • (1996) Bayesian Statist. , vol.5 , pp. 609-620
    • Geweke, J.1
  • 46
    • 69349089478 scopus 로고    scopus 로고
    • Exploiting structure in wavelet-based Bayesian compressive sensing
    • Sep.
    • L. He and L. Carin, "Exploiting structure in wavelet-based Bayesian compressive sensing," IEEE Trans. Signal Process., vol.57, no.9, pp. 3488-3497, Sep. 2008.
    • (2008) IEEE Trans. Signal Process. , vol.57 , Issue.9 , pp. 3488-3497
    • He, L.1    Carin, L.2
  • 47
    • 0000007140 scopus 로고
    • Recursive Bayesian estimation using Gaussian sums
    • H. W. Sorenson and D. L. Alspach, "Recursive Bayesian estimation using Gaussian sums," Automatica, vol.7, pp. 465-479, 1971.
    • (1971) Automatica , vol.7 , pp. 465-479
    • Sorenson, H.W.1    Alspach, D.L.2
  • 48
    • 5444237123 scopus 로고    scopus 로고
    • Greed is good: Algorithmic results for sparse approximation
    • Oct.
    • J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol.50, no.10, pp. 2231-2242, Oct. 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.10 , pp. 2231-2242
    • Tropp, J.A.1
  • 50
    • 0025401005 scopus 로고
    • The computational complexity of probabilistic inference using Bayesian belief networks
    • G. Cooper, "The computational complexity of probabilistic inference using Bayesian belief networks," Artif. Intell., vol.42, pp. 393-405, 1990.
    • (1990) Artif. Intell. , vol.42 , pp. 393-405
    • Cooper, G.1
  • 51
    • 0035246564 scopus 로고    scopus 로고
    • Factor graphs and the sum-product algorithm
    • Feb.
    • F. R. Kschischang, B. J. Frey, and H.-A. Loeliger, "Factor graphs and the sum-product algorithm," IEEE Trans. Inf. Theory, vol.47, no.2, pp. 498-519, Feb. 2001.
    • (2001) IEEE Trans. Inf. Theory , vol.47 , Issue.2 , pp. 498-519
    • Kschischang, F.R.1    Frey, B.J.2    Loeliger, H.-A.3
  • 53
    • 84898964205 scopus 로고    scopus 로고
    • A revolution: Belief propagation in graphs with cycles
    • M. Jordan, M. S. Kearns, and S. A. Solla, Eds.
    • B. J. Frey and D. J. C. MacKay, "A revolution: Belief propagation in graphs with cycles," in Adv. Neural Inf. Process. Syst., M. Jordan, M. S. Kearns, and S. A. Solla, Eds., 1998, vol. 10.
    • (1998) Adv. Neural Inf. Process. Syst. , vol.10
    • Frey, B.J.1    MacKay, D.J.C.2
  • 54
    • 21844467514 scopus 로고    scopus 로고
    • Loopy belief propagation: Convergence and effects of message errors
    • May
    • A. Ihler, J. Fisher, and A. S.Willsky, "Loopy belief propagation: Convergence and effects of message errors," J. Mach. Learn. Res., vol.6, pp. 905-936, May 2005.
    • (2005) J. Mach. Learn. Res. , vol.6 , pp. 905-936
    • Ihler, A.1    Fisher, J.2    Willsky, A.S.3
  • 55
    • 29044446846 scopus 로고    scopus 로고
    • A message-passing algorithm with damping
    • Nov.
    • M. Pretti, "A message-passing algorithm with damping," J. Stat. Mech., Nov. 2005.
    • (2005) J. Stat. Mech.
    • Pretti, M.1
  • 56
    • 0033099611 scopus 로고    scopus 로고
    • Good error-correcting codes based on very sparse matrices
    • Mar.
    • D. J. C. MacKay, "Good error-correcting codes based on very sparse matrices," IEEE Trans. Inf. Theory, vol.45, no.11, pp. 399-431, Mar. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.45 , Issue.11 , pp. 399-431
    • MacKay, D.J.C.1
  • 57
    • 0035419513 scopus 로고    scopus 로고
    • From kernels to mixtures
    • Aug.
    • D. W. Scott and W. F. Szewczyk, "From kernels to mixtures," Technometrics, vol.43, pp. 323-335, Aug. 2001.
    • (2001) Technometrics , vol.43 , pp. 323-335
    • Scott, D.W.1    Szewczyk, W.F.2
  • 59
    • 0036800732 scopus 로고    scopus 로고
    • A digital fountain approach to asynchronous reliable multicast
    • Oct.
    • J. W. Byers, M. Luby, and M. Mitzenmacher, "A digital fountain approach to asynchronous reliable multicast," IEEE J. Sel. Areas Commun., vol.20, no.8, pp. 1528-1540, Oct. 2002.
    • (2002) IEEE J. Sel. Areas Commun. , vol.20 , Issue.8 , pp. 1528-1540
    • Byers, J.W.1    Luby, M.2    Mitzenmacher, M.3


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