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Volumn 59, Issue 11, 2011, Pages 5369-5379

A coding theory approach to noisy compressive sensing using low density frames

Author keywords

Belief propagation; coding theory; compressive sensing; EM algorithm; Gaussian scale mixtures; low density frames; sum product algorithm

Indexed keywords

BELIEF PROPAGATION; CODING THEORY; COMPRESSIVE SENSING; EM ALGORITHMS; GAUSSIAN SCALE MIXTURES; LOW DENSITY; SUM-PRODUCT ALGORITHM;

EID: 80054073830     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2163402     Document Type: Article
Times cited : (20)

References (56)
  • 1
    • 44849094084 scopus 로고    scopus 로고
    • Aframe construction and a universal distortion bound for sparse representations
    • Jun.
    • M. Akçakaya and V. Tarokh, "Aframe construction and a universal distortion bound for sparse representations," IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2443-2550, Jun. 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.6 , pp. 2443-2550
    • Akçakaya, M.1    Tarokh, V.2
  • 2
    • 51649094858 scopus 로고    scopus 로고
    • On sparsity, redundancy and quality of frame representations
    • presented at, Nice, France, Jun.
    • M. Akçakaya and V. Tarokh, "On sparsity, redundancy and quality of frame representations," presented at the IEEE Int. Symp. Inf. Theory (ISIT), Nice, France, Jun. 2007.
    • (2007) IEEE Int. Symp. Inf. Theory (ISIT)
    • Akçakaya, M.1    Tarokh, V.2
  • 3
    • 73849138881 scopus 로고    scopus 로고
    • Shannon theoretic limits on noisy compressive sampling
    • Jan.
    • M. Akçakaya and V. Tarokh, "Shannon theoretic limits on noisy compressive sampling," IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 492-504, Jan. 2010.
    • (2010) IEEE Trans. Inf. Theory , vol.56 , Issue.1 , pp. 492-504
    • Akçakaya, M.1    Tarokh, V.2
  • 4
    • 0003071947 scopus 로고
    • Scale mixtures of normal distributions
    • D. Andrews and C. Mallows, "Scale mixtures of normal distributions," J. R. Stat. Soc., vol. 36, pp. 99-102, 1974.
    • (1974) J. R. Stat. Soc. , vol.36 , pp. 99-102
    • Andrews, D.1    Mallows, C.2
  • 5
    • 77952558371 scopus 로고    scopus 로고
    • SPARLS: A low complexity recursive L1-regularized least squares algorithm
    • Aug.
    • B. Babadi, N. Kalouptsidis, and V. Tarokh, "SPARLS: A low complexity recursive L1-regularized least squares algorithm," IEEE Trans. Signal Process., vol. 58, pp. 4013-4025, Aug. 2010.
    • (2010) IEEE Trans. Signal Process. , vol.58 , pp. 4013-4025
    • Babadi, B.1    Kalouptsidis, N.2    Tarokh, V.3
  • 7
    • 72949124697 scopus 로고    scopus 로고
    • Bayesian compressive sensing via belief propagation
    • Jan.
    • D. Baron, S. Sarvotham, and R. Baraniuk, "Bayesian compressive sensing via belief propagation," IEEE Trans. Signal Process., vol. 58, pp. 269-280, Jan. 2010.
    • (2010) IEEE Trans. Signal Process. , vol.58 , pp. 269-280
    • Baron, D.1    Sarvotham, S.2    Baraniuk, R.3
  • 9
    • 64549129145 scopus 로고    scopus 로고
    • Practical near-optimal sparse recovery in the ell-1 norm
    • presented at, Comm., Control, Comput., Monticello, IL, Sep.
    • R. Berinde, P. Indyk, and M. Ruzic, "Practical near-optimal sparse recovery in the ell-1 norm," presented at the Allerton Conf. Comm., Control, Comput., Monticello, IL, Sep. 2008.
    • (2008) Allerton Conf.
    • Berinde, R.1    Indyk, P.2    Ruzic, M.3
  • 10
    • 77949646471 scopus 로고    scopus 로고
    • Sequential sparse matching pursuit
    • presented at, Commun., Control, Comput., Monticello, IL, Sep.
    • R. Berinde and P. Indyk, "Sequential sparse matching pursuit," presented at the Allerton Conf. Commun., Control, Comput., Monticello, IL, Sep. 2009.
    • (2009) Allerton Conf.
    • Berinde, R.1    Indyk, P.2
  • 11
    • 77949641339 scopus 로고    scopus 로고
    • A low density lattice decoder via non-parametric belief propagation
    • presented at, Monticello, IL, Sep.
    • D. Bickson, A. T. Ihler, and D. Dolev, "A low density lattice decoder via non-parametric belief propagation," presented at the Allerton Conf. Commun., Control, Comput., Monticello, IL, Sep. 2009.
    • (2009) Allerton Conf. Commun., Control, Comput.
    • Bickson, D.1    Ihler, A.T.2    Dolev, D.3
  • 12
    • 33645136947 scopus 로고    scopus 로고
    • Bayesian wavelet-based image deconvolution: A GEM algorithm exploiting a class of heavy-tailed priors
    • Apr.
    • J. M. Bioucas-Dias, "Bayesian wavelet-based image deconvolution: A GEM algorithm exploiting a class of heavy-tailed priors," IEEE Trans. Image Process., vol. 15, pp. 937-951, Apr. 2006.
    • (2006) IEEE Trans. Image Process. , vol.15 , pp. 937-951
    • Bioucas-Dias, J.M.1
  • 14
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery for incomplete and inaccurate measurements
    • Aug.
    • E. J. Candès, J. Romberg, and T. Tao, "Stable signal recovery for incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol. 59, pp. 1207-1223, Aug. 2006.
    • (2006) Commun. Pure Appl. Math. , vol.59 , pp. 1207-1223
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 15
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Dec.
    • E. J. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, pp. 4203-4215, Dec. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , pp. 4203-4215
    • Candès, E.J.1    Tao, T.2
  • 16
    • 57349174008 scopus 로고    scopus 로고
    • Enhancing sparsity by reweighted l1 minimization
    • E. J. Candès, M. Wakin, and S. Boyd, "Enhancing sparsity by reweighted l1 minimization," J. Fourier Anal. Appl., vol. 14, pp. 877-905.
    • J. Fourier Anal. Appl. , vol.14 , pp. 877-905
    • Candès, E.J.1    Wakin, M.2    Boyd, S.3
  • 19
    • 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, pp. 2230-2249, May 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , pp. 2230-2249
    • Dai, W.1    Milenkovic, O.2
  • 20
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr.
    • D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, pp. 1289-1306, Apr. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , pp. 1289-1306
    • Donoho, D.L.1
  • 21
    • 73149095169 scopus 로고    scopus 로고
    • Message passing algorithms for compressed sensing
    • Nov.
    • D. L. Donoho, A. Maleki, and A. Montanari, "Message passing algorithms for compressed sensing," Proc. Natl Acad. Sci., vol. 106, pp. 18914-18919, Nov. 2009.
    • (2009) Proc. Natl Acad. Sci. , vol.106 , pp. 18914-18919
    • Donoho, D.L.1    Maleki, A.2    Montanari, A.3
  • 22
    • 0142200827 scopus 로고    scopus 로고
    • An EM algorithm for wavelet-based image restoration
    • Aug.
    • M. Figueiredo and R. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. Image Process., vol. 12, pp. 906-916, Aug. 2003.
    • (2003) IEEE Trans. Image Process. , vol.12 , pp. 906-916
    • Figueiredo, M.1    Nowak, R.2
  • 23
    • 0035442514 scopus 로고    scopus 로고
    • Wavelet-based image estimation: An empirical bayes approach using Jeffreys' noninformative prior
    • Sep.
    • M. A. T. Figueiredo and R. Nowak, "Wavelet-based image estimation: An empirical bayes approach using Jeffreys' noninformative prior," IEEE Trans. Image Process., vol. 10, pp. 1322-1331, Sep. 2001.
    • (2001) IEEE Trans. Image Process. , vol.10 , pp. 1322-1331
    • Figueiredo, M.A.T.1    Nowak, R.2
  • 24
    • 39449126969 scopus 로고    scopus 로고
    • Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
    • Dec.
    • M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Sel. Topics Signal Process., vol. 1, pp. 586-598, Dec. 2007.
    • (2007) IEEE J. Sel. Topics Signal Process. , vol.1 , pp. 586-598
    • Figueiredo, M.A.T.1    Nowak, R.D.2    Wright, S.J.3
  • 25
    • 77952733655 scopus 로고    scopus 로고
    • Sparse recovery using sparsematrices
    • Jun.
    • A. Gilbert and P. Indyk, "Sparse recovery using sparsematrices, " Proc. IEEE, vol. 98, pp. 937-947, Jun. 2010.
    • (2010) Proc. IEEE , vol.98 , pp. 937-947
    • Gilbert, A.1    Indyk, P.2
  • 26
    • 12544253129 scopus 로고    scopus 로고
    • Regular and irregular progressive edge-growth tanner graphs
    • Jan.
    • X. -Y. Hu, E. Eleftheriou, and D. M. Arnold, "Regular and irregular progressive edge-growth tanner graphs," IEEE Trans. Inf. Theory, vol. 51, pp. 386-398, Jan. 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , pp. 386-398
    • Hu, X.-Y.1    Eleftheriou, E.2    Arnold, D.M.3
  • 27
    • 57949089021 scopus 로고    scopus 로고
    • Near-optimal sparse recovery in the norm
    • presented at, Philadelphia, PA, Oct.
    • P. Indyk and M. Ruzic, "Near-optimal sparse recovery in the norm," presented at the IEEE Symp. Found. Comput. Sci., Philadelphia, PA, Oct. 2008.
    • (2008) IEEE Symp. Found. Comput. Sci.
    • Indyk, P.1    Ruzic, M.2
  • 28
    • 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, pp. 2346-2356, Jun. 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , pp. 2346-2356
    • Ji, S.1    Xue, Y.2    Carin, L.3
  • 30
    • 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, pp. 399-431, Mar. 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , pp. 399-431
    • MacKay, D.J.C.1
  • 32
    • 0010882063 scopus 로고    scopus 로고
    • Decoding low-density parity-check codes with probabilistic scheduling
    • Oct.
    • Y. Mao and A. H. Banihashemi, "Decoding low-density parity-check codes with probabilistic scheduling," IEEE Commun. Lett., vol. 5, pp. 414-416, Oct. 2001.
    • (2001) IEEE Commun. Lett. , vol.5 , pp. 414-416
    • Mao, Y.1    Banihashemi, A.H.2
  • 34
    • 0030287048 scopus 로고    scopus 로고
    • The EM algorithm in signal processing
    • Nov.
    • T. K. Moon, "The EM algorithm in signal processing," IEEE Signal Process. Mag., vol. 13, pp. 47-60, Nov. 1996.
    • (1996) IEEE Signal Process. Mag. , vol.13 , pp. 47-60
    • Moon, T.K.1
  • 35
    • 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. Comp. Harmon. Anal., vol. 26, pp. 301-321, 2008.
    • (2008) Appl. Comp. Harmon. Anal. , vol.26 , pp. 301-321
    • Needell, D.1    Tropp, J.A.2
  • 36
    • 84976657333 scopus 로고
    • LSQR: Sparse linear equations and least squares problems
    • Jun.
    • C. C. Paige and M. A. Saunders, "LSQR: Sparse linear equations and least squares problems," ACM Trans. Math. Softw. (TOMS), vol. 8, pp. 195-209, Jun. 1982.
    • (1982) ACM Trans. Math. Softw. (TOMS) , vol.8 , pp. 195-209
    • Paige, C.C.1    Saunders, M.A.2
  • 37
    • 0242636409 scopus 로고    scopus 로고
    • Image denoising using scale mixtures of Gaussians in the wavelet domain
    • Nov.
    • J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, "Image denoising using scale mixtures of Gaussians in the wavelet domain," IEEE Trans. Image Process., vol. 12, pp. 1338-1351, Nov. 2003.
    • (2003) IEEE Trans. Image Process. , vol.12 , pp. 1338-1351
    • Portilla, J.1    Strela, V.2    Wainwright, M.J.3    Simoncelli, E.P.4
  • 38
    • 78349258863 scopus 로고    scopus 로고
    • Double sparsity: Learning sparse dictionaries for sparse signal approximation
    • Mar.
    • R. Rubinstein, M. Zibulevsky, and M. Elad, "Double sparsity: Learning sparse dictionaries for sparse signal approximation," IEEE Trans. Signal Process., vol. 58, pp. 1553-1564, Mar. 2010.
    • (2010) IEEE Trans. Signal Process. , vol.58 , pp. 1553-1564
    • Rubinstein, R.1    Zibulevsky, M.2    Elad, M.3
  • 39
    • 0035246307 scopus 로고    scopus 로고
    • The capacity of low-density parity-check codes under message passing decoding
    • Feb.
    • T. J. Richardson and R. L. Urbanke, "The capacity of low-density parity-check codes under message passing decoding," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 599-618, Feb. 2001.
    • (2001) IEEE Trans. Inf. Theory , vol.47 , Issue.2 , pp. 599-618
    • Richardson, T.J.1    Urbanke, R.L.2
  • 41
    • 39049110737 scopus 로고    scopus 로고
    • Sudocodes-fast measurement and reconstruction of sparse signals
    • presented at, Seattle, WA, Jul.
    • S. Sarvotham, D. Baron, and R. Baraniuk, "Sudocodes-fast measurement and reconstruction of sparse signals," presented at the IEEE Int. Symp. Inf. Theory (ISIT), Seattle, WA, Jul. 2006.
    • (2006) IEEE Int. Symp. Inf. Theory (ISIT)
    • Sarvotham, S.1    Baron, D.2    Baraniuk, R.3
  • 42
  • 43
  • 45
    • 0019608335 scopus 로고
    • A recursive approach to low complexity codes
    • Sep.
    • R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inf. Theory, vol. 27, pp. 533-547, Sep. 1981.
    • (1981) IEEE Trans. Inf. Theory , vol.27 , pp. 533-547
    • Tanner, R.M.1
  • 46
    • 0001224048 scopus 로고    scopus 로고
    • Sparse bayesian learning and the relevance vector machine
    • M. E. Tipping, "Sparse bayesian learning and the relevance vector machine," J. Mach. Learn. Res., vol. 1, pp. 211-244, 2001.
    • (2001) J. Mach. Learn. Res. , vol.1 , pp. 211-244
    • Tipping, M.E.1
  • 47
    • 35048822888 scopus 로고    scopus 로고
    • Bayesian inference: An introduction to principles and practice in machine learning
    • New York: Springer
    • M. E. Tipping, "Bayesian inference: An introduction to principles and practice in machine learning," in Advanced Lectures on Machine Learning. New York: Springer, 2004, pp. 41-62.
    • (2004) Advanced Lectures on Machine Learning , pp. 41-62
    • Tipping, M.E.1
  • 48
    • 65649137930 scopus 로고    scopus 로고
    • Probing the pareto frontier for basis pursuit solutions
    • E. van den Berg and M. P. Friedlander, "Probing the pareto frontier for basis pursuit solutions," SIAM J. Sci. Comput., vol. 31, no. 2, pp. 890-912, 2008.
    • (2008) SIAM J. Sci. Comput. , vol.31 , Issue.2 , pp. 890-912
    • Van Den Berg, E.1    Friedlander, M.P.2
  • 49
    • 65749083666 scopus 로고    scopus 로고
    • Sharp thresholds for noisy and high-dimensional recovery of sparsity using -constrained quadratic programming
    • May
    • M. J. Wainwright, "Sharp thresholds for noisy and high-dimensional recovery of sparsity using -constrained quadratic programming," IEEE Trans. Inf. Theory, vol. 55, pp. 2183-2202, May 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , pp. 2183-2202
    • Wainwright, M.J.1
  • 50
    • 0011952756 scopus 로고    scopus 로고
    • Correctness of belief propagation in Gaussian graphical models of arbitrary topology
    • Oct.
    • Y. Weiss and W. T. Freeman, "Correctness of belief propagation in Gaussian graphical models of arbitrary topology," Neural Comput., vol. 13, no. 10, pp. 2173-2200, Oct. 2001.
    • (2001) Neural Comput. , vol.13 , Issue.10 , pp. 2173-2200
    • Weiss, Y.1    Freeman, W.T.2
  • 51
    • 77949736709 scopus 로고    scopus 로고
    • Iterative reweighted and methods for finding sparse solutions
    • Apr.
    • D. Wipf and S. Nagarajan, "Iterative reweighted and methods for finding sparse solutions," IEEE J. Sel. Topics Signal Process., vol. 4, pp. 317-329, Apr. 2010.
    • (2010) IEEE J. Sel. Topics Signal Process. , vol.4 , pp. 317-329
    • Wipf, D.1    Nagarajan, S.2
  • 52
    • 11844297352 scopus 로고    scopus 로고
    • Graph-basedmessage-passing schedules for decoding LDPC codes
    • Dec.
    • H. Xiao andA. H. Banihashemi, "Graph-basedmessage-passing schedules for decoding LDPC codes," IEEE Trans. Commun., vol. 52, pp. 2098-2105, Dec. 2004.
    • (2004) IEEE Trans. Commun. , vol.52 , pp. 2098-2105
    • Xiao, H.1    Banihashemi, A.H.2
  • 53
    • 46749155099 scopus 로고    scopus 로고
    • Efficient compressive sensing with deterministic guarantees using expander graphs
    • presented at, Lake Tahoe, CA, Sep.
    • W. Xu and B. Hassibi, "Efficient compressive sensing with deterministic guarantees using expander graphs," presented at the IEEE Inf. Theory Workshop, Lake Tahoe, CA, Sep. 2007.
    • (2007) IEEE Inf. Theory Workshop
    • Xu, W.1    Hassibi, B.2
  • 54
    • 80054060553 scopus 로고    scopus 로고
    • On the iterative decoding of high rate LDPC codes with applications in compressed sensing
    • presented at, Monticello, IL, Sep.
    • F. Zhang and H. D. Pfister, "On the iterative decoding of high rate LDPC codes with applications in compressed sensing," presented at the Allerton Conf. Commun., Control, Comput., Monticello, IL, Sep. 2008.
    • (2008) Allerton Conf. Commun., Control, Comput.
    • Zhang, F.1    Pfister, H.D.2
  • 56
    • 80054083006 scopus 로고    scopus 로고
    • LDF Website [Online]. Available
    • LDF Website [Online]. Available: http://people. fas. harvard. edu/akcakaya/ suprem. html


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