Compressive sensing: From theory to applications, a survey

Journal of Communications and Networks

Volumn 15, Issue 5, 2013, Pages 443-456

  Qaisar, Saad ^a   Bilal, Rana Muhammad ^a   Iqbal, Wafa ^b   Naureen, Muqaddas ^c   Lee, Sungyoung ^d  

^a NATIONAL UNIVERSITY OF SCIENCES AND TECHNOLOGY   (Pakistan)

^b SAN JOSE STATE UNIVERSITY   (United States)

^c National Research Centre   (Pakistan)

^d Kyung Hee University   (South Korea)

Author keywords

Compressive imaging; Compressive sensing (CS); Incoherence; Sparsity; Wireless sensor networks (WSNs)

Indexed keywords

SURVEYS; WIRELESS SENSOR NETWORKS;

COMPRESSIVE IMAGING; COMPRESSIVE SENSING; INCOHERENCE; INHERENT CHARACTERISTICS; ITS APPLICATIONS; MATHEMATICAL FOUNDATIONS; NYQUIST SAMPLING THEOREM; SPARSITY; WIRELESS SENSOR NETWORK;

COMPRESSED SENSING;

EID: 84889657929     PISSN: 12292370     EISSN: None     Source Type: Journal    
DOI: 10.1109/JCN.2013.000083     Document Type: Review

References (112)

1. J. Claerbout and F. Muir, "Robust modeling with erratic data: Geo-physics," Geophysics, Vol. 38, no. 5, pp. 826-844, Oct. 1973.
2. B. Kashin, "The widths of certain finite dimensional sets and classes of smooth functions," Math. USSR Izv., Vol. 41, no. 2, pp. 334-351, 1977.
3. E. Gluskin, "Norms of random matrices and widths of finite-dimensional sets," Math. USSR-Sbornik, Vol. 48, p. 173, 1984.
4. F. Santosa and W. Symes, "Linear inversion of band-limited reflection seis-mograms," SIAM J. Scientific Statistical Comput., Vol. 7, p. 1307, 1986.
5. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D: Nonlinear Phenomena, Vol. 60, no. 1-4, pp. 259-268, 1992.
6. S. Mallat, A Wavelet Tour of Signal Processing. Academic Pr., 1999.
7. M. Rudelson, "Random vectors in the isotropic position," Arxiv preprint math/9608208, 1996.
8. P. Schmieder, A. Stern, G. Wagner, and J. Hoch, "Application of nonlinear sampling schemes to COSY-type spectra," J. Biomolecular NMR, Vol. 3, no. 5, pp. 569-576, 1993.
9. M. Unser, "Sampling-50 years after Shannon," Proc. IEEE, Vol. 88, no. 4, pp. 569-587, 2000.
10. E. Novak, "Optimal recovery and n-widths for convex classes of functions," J. Approximation Theory, Vol. 80, no. 3, pp. 390-408, 1995.
11. S. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process., Vol. 41, no. 12, pp. 3397-3415, 1993.
12. D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, Vol. 52, no. 4, pp. 1289-1306, 2006.
13. E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Applied Math., Vol. 59, no. 8, pp. 1207-1223, 2006.
14. E. Candès and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse Problems, Vol. 23, p. 969, 2007.
15. M. Wakin, "An introduction to compressive sampling," IEEE Signal Process. Mag., 2008.
16. E. Candes, "The restricted isometry property and its implications for compressed sensing," Comptes Rendus Mathematique, Vol. 346, no. 9-10, pp. 589-592, 2008.
17. 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, p. 489, 2006.
18. Z. Chen and J. Dongarra, "Condition numbers of Gaussian random matrices," SIAM J. Matrix Analysis Appl, Vol. 27, no. 3, pp. 603-620, 2006.
19. E. Candes and T. Tao, "Near-optimal signal recovery from random projections: Universal encoding strategies?," IEEE Trans. Inf. Theory, Vol. 52, no. 12, pp. 5406-5425, 2006.
20. E. Candes, M. Wakin, and S. Boyd, "Enhancing sparsity by reweighted 1 1 minimization," J. Fourier Analysis Appl, Vol. 14, no. 5, pp. 877-905, 2008.
21. E. Candes and J. Romberg, "Practical signal recovery from random projections," IEEE Trans. Signal Process., 2005.
22. Y. Sharon, J. Wright, and Y. Ma, "Computation and relaxation of conditions for equivalence between 11 and 10 minimization," CSL Tech. Rep. UILU-ENG-07-2208, Univ. of Illinois, Urbana-Champaign, 2007.
23. D. Donoho and J. Tanner, "Sparse nonnegative solution of underde-termined linear equations by linear programming," Proc. Nat. Academy Sci. United States of America, Vol. 102, no. 27, p. 9446, 2005.
24. J. Tropp and A. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Trans. Inf. Theory, Vol. 53, no. 12, p. 4655, 2007.
25. T. Blumensath and M. Davies, "Iterative hard thresholding for compressed sensing," Applied and Computational Harmonic Analysis, Vol. 27, no. 3, pp. 265-274, 2009.
26. D. Donoho, A. Maleki, and A. Montanari, "Message-passing algorithms for compressed sensing," Proc. Nat. Academy Sci., Vol. 106, no. 45, p. 18914, 2009.
27. E. Candes and B. Recht, "Exact matrix completion via convex optimization," Foundations Computational Math., Vol. 9, no. 6, pp. 717-772, 2009.
28. S. Chen, D. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SIAM Rev., Vol. 43, no. 1, pp. 129-159, 2001.
29. W. Lu and N. Vaswani, "Modified basis pursuit denoising (modified BPDN) for noisy compressive sensing with partially known support," in Proc. ICASSP, 2010, pp. 3926-3929.
30. R. Tibshirani, "Regression shrinkage and selection via the lasso," J. Royal Statistical Society. Series B (Methodological), pp. 267-288, 1996.
31. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, "Least angle regression," Annals of statistics, Vol. 32, no. 2, pp. 407-451, 2004.
32. B. Recht, M. Fazel, and P. Parrilo, "Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization," SIAM Rev., Vol. 52, no. 3, pp. 471-501, Aug. 2010.
33. D. Needell and R. Vershynin, "Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit," Foundations computational math., Vol. 9, no. 3, pp. 317-334, 2009.
34. D. Donoho, Y. Tsaig, I. Drori, and J. Starck, "Sparse solution of underde-termined linear equations by stagewise orthogonal matching pursuit," 2006.
35. D. Needell and J. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Applied Comput. Harmonic Analysis, Vol. 26, no. 3, pp. 301-321, 2009.
36. W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Trans. Inf. Theory, Vol. 55, no. 5, pp. 2230-2249, 2009.
37. M. Figueiredo, R. Nowak, and S. Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE J. Sel. Topics Signal Process., Vol. 1, no. 4, pp. 586-597, 2008.
38. E. Liu and V. Temlyakov, "Orthogonal super greedy algorithm and applications in compressed sensing," IEEE Trans. Inf. Theory, Vol. 58, no. 4, pp. 2040-2047, Apr. 2012.
39. D. Donoho, "De-noising by Soft-thresholding," IEEE Trans. Inf. Theory, Vol. 41, no. 3, pp. 613-627, 2002.
40. P. Indyk and M. Ruzic, "Near-optimal sparse recovery in the 11 norm," in Proc. IEEE FOCS, 2008, pp. 199-207.
41. R. Berinde, P. Indyk, and M. Ruzic, "Practical near-optimal sparse recovery in the 11 norm," in Proc. Allerton Conf. Commun., Control, Comput., 2009, pp. 198-205.
42. R. Berinde and P. Indyk, "Sequential sparse matching pursuit," in Proc. Allerton Conf. Commun., Control, Comput., 2010, pp. 36-43.
43. D. Baron, S. Sarvotham, and R. Baraniuk, "Bayesian compressive sensing via belief propagation," IEEE Trans. Signal Process., Vol. 58, no. 1, pp. 269-280, 2009.
44. A. Gilbert, S. Muthukrishnan, and M. Strauss, "Improved time bounds for near-optimal sparse Fourier representations," in Proc. SPIE, Vol. 5914, p. 59141A, 2005.
45. A. Gilbert, M. Strauss, J. Tropp, and R. Vershynin, "Algorithmic linear dimension reduction in the 11 norm for sparse vectors," Arxiv preprint cs/0608079, 2006.
46. A. Gilbert, M. Strauss, J. Tropp, and R. Vershynin, "One sketch for all: Fast algorithms for compressed sensing," in Proc. ACM Symp. Theory Cornput., 2007, pp. 237-246.
47. R. Chartrand, "Exact reconstruction of sparse signals via nonconvex minimization," IEEE Signal Process. Lett., Vol. 14, no. 10, pp. 707-710, 2007.
48. J. Murray and K. Kreutz-Delgado, "An improved FOCUSS-based learning algorithm for solving sparse linear inverse problems," in Proc. Asilomar Conf. Signals, Syst., Comput., Vol. 1, 2001, pp. 347-354.
49. R. Chartrand and W. Yin, "Iteratively reweighted algorithms for compressive sensing," in Proc. IEEE ICASSP, 2008.
50. D. Wipf and B. Rao, "Sparse Bayesian learning for basis selection," IEEE Trans. Signal Process., Vol. 52, no. 8, pp. 2153-2164, 2004.
51. S. Godsill, A. Cemgil, C. Fvotte, and P. Wolfe, "Bayesian computational methods for sparse audio and music processing," in Proc. EURASIP Conf. Signal Process., 2007.
52. W. Tin, S. Osher, D. Goldfarb, and J. Darbon, "Bregman iterative algorithms for 11-minimization with applications to compressed sensing," SIAM J. Imaging Sci., Vol. 1, no. 1, pp. 143-168, 2008.
53. M. Duarte, M. Davenport, D. Takhar, J. Laska, T. Sun, K. Kelly, and R. Baraniuk, "Single-pixel imaging via compressive sampling," IEEE Signal Process. Mag., Vol. 25, no. 2, pp. 83-91, 2008.
54. M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. Kelly, and R. Baraniuk, "An architecture for compressive imaging," in Proc. IEEE Int. Conf. Image Process., 2006, pp. 1273-1276.
55. D. Takhar, J. Laska, M. Wakin, M. Duarte, D. Baron, S. Sarvotham, K. Kelly, and R. Baraniuk, "A new compressive imaging camera architecture using optical-domain compression," IS&T/SP1E Computational Imaging IV, Vol. 6065, 2006.
56. P. Nagesh et al., "Compressive imaging of color images," in Proc. IEEE ICASSP, 2009, pp. 1261-1264.
57. A. Elgammal, D. Harwood, and L. Davis, "Non-parametric model for background subtraction," Comput. Vision-ECCV, pp. 751-767, 2000.
58. M. Piccardi, "Background subtraction techniques: A review," in Proc. IEEE Int. Conf. Syst., Man, Cybernetics, Vol. 4, 2004, pp. 3099-3104.
59. V. Cevher, A. Sankaranarayanan, M. Duarte, D. Reddy, R. Baraniuk, and R. Chellappa, "Compressive sensing for background subtraction," Comput. Vision-ECCV 2008, pp. 155-168, 2008.
60. W. Chan, K. Charan, D. Takhar, K. Kelly, R. Baraniuk, and D. Mittleman, "A single-pixel terahertz imaging system based on compressed sensing," Appl. Phys. Lett., Vol. 93, p. 121105, 2008.
61. M. Lustig, D. Donoho, J. Santos, and J. Pauly, "Compressed sensing MRI," IEEE Signal Process. Mag., Vol. 25, no. 2, pp. 72-82, 2008.
62. U. Gamper, P. Boesiger, and S. Kozerke, "Compressed sensing in dynamic MRI," Magnetic Resonance Medicine, Vol. 59, no. 2, pp. 365-373, 2008.
63. M. Lustig, D. Donoho, and J. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magnetic Resonance Medicine, Vol. 58, no. 6, pp. 1182-1195, 2007.
64. H. Jung, K. Sung, K. Nayak, E. Kim, and J. Ye, "kt FOCUSS: a general compressed sensing framework for high resolution dynamic MRI," Magnetic Resonance Medicine, Vol. 61, no. 1, pp. 103-116, 2009.
65. F. Herrmann and G. Hennenfent, "Non-parametric seismic data recovery with curvelet frames," Geophysical J. Int., Vol. 173, no. 1, pp. 233-248, 2008.
66. G. Hennenfent and F. J. Herrmann, "Simply denoise: Wavefield reconstruction via jittered undersampling," Geophysics, pp. 19-28, 2008.
67. N. Shental, A. Amir, and O. Zuk, "Rare-Allele detection using compressed Se(que)nsing," Arxiv preprint arXiv:0909.0400, 2009.
68. D. Du and F. Hwang, Combinatorial Group Testing and Its Applications. World Scientific Pub. Co. Inc., 2000.
69. M. Mohtashemi, H. Smith, D. Walburger, F. Sutton, and J. Diggans, "Sparse sensing DNA microarray-based biosensor: Is it feasible?," in Proc. SAS, 2010, pp. 127-130.
70. F. Parvaresh, H. Vikalo, S. Misra, and B. Hassibi, "Recovering sparse signals using sparse measurement matrices in compressed DNA mi-croarrays," IEEE J. Sel. Topics Signal Process., Vol. 2, no. 3, pp. 275-285, 2008.
71. R. Baraniuk and P. Steeghs, "Compressive radar imaging," in Proc. IEEE Radar Conf, 2007, pp. 128-133.
72. M. Herman and T. Strohmer, "High-resolution radar via compressed sensing," IEEE Trans. Signal Process., Vol. 57, no. 6, pp. 2275-2284, 2009.
73. X. Xia, "Discrete chirp-Fourier transform and its application to chirp rate estimation," IEEE Trans. Signal Process., Vol. 48, no. 11, pp. 3122-3133, 2000.
74. R. Moses, L. Potter, and M. Cetin, "Wide angle SAR imaging," in Proc. SPIE, Vol. 5427, 2004, pp. 164-175.
75. A. Gurbuz, J. McClellan, and W. Scott, "A compressive sensing data acquisition and imaging method for stepped frequency GPRs," IEEE Trans. Signal Process., Vol. 57, no. 7, 2009.
76. L. Qu and T. Yang, "Investigation of air/ground reflection and antenna beamwidth for compressive sensing SFCW GPR migration imaging," IEEE Trans. Geosci. Remote Sens., 2012.
77. M. A. C. Tuncer and A. C. Gurbuz, "Ground reflection removal in compressive sensing ground penetrating radars," IEEE Geosci. Remote Sens. Lett., Vol. 9, no. 1, 2011.
78. F. Ahmad, "Through-the-wall human motion indication using sparsity-sriven change detection," IEEE Trans. Geosci. Remote Sens., pp. 881-890, 2013.
79. R. Walden, "Analog-to-digital converter survey and analysis," IEEE J. Sel. Areas Commun., Vol. 17, no. 4, pp. 539-550, 1999.
80. S. Kirolos, J. Laska, M. Wakin, M. Duarte, D. Baron, T. Ragheb, Y. Mas-soud, and R. Baraniuk, "Analog-to-information conversion via random demodulation," in Proc. IEEE Dallas/CAS Workshop DCAS, 2006, pp. 71-74.
81. J. Laska, S. Kirolos, M. Duarte, T. Ragheb, R. Baraniuk, and Y. Massoud, "Theory and implementation of an analog-to-information converter using random demodulation," in Proc. IEEE ISCAS, 2007, pp. 1959-1962.
82. J. Tropp, M. Wakin, M. Duarte, D. Baron, and R. Baraniuk, "Random filters for compressive sampling and reconstruction," in Proc. ICSAAP, Vol. 3, 2006.
83. M. Mishali and Y. Eldar, "From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals," IEEE J. Sel. Topics Signal Process., 2009.
84. W. Bajwa, J. Haupt, A. Sayeed, and R. Nowak, "Compressed channel sensing: A new approach to estimating sparse multipath channels," Proc. IEEE, Vol. 98, no. 6, pp. 1058-1076, 2010.
85. C. Berger, S. Zhou, J. Preisig, and P. Willett, "Sparse channel estimation for multicarrier underwater acoustic communication: From subspace methods to compressed sensing," IEEE Trans. Signal Process., Vol. 58, no. 3, pp. 1708-1721, 2010.
86. G. Taubock, F. Hlawatsch, D. Eiwen, and H. Rauhut, "Compressive estimation of doubly selective channels in multicarrier systems: Leakage effects and sparsity-enhancing processing," IEEE J. Sel. Topics Signal Process., Vol. 4, no. 2, pp. 255-271, 2010.
87. Y. Tachwali, W. Barnes, F. Basma, and H. Refai, "The Feasibility of a fast Fourier sampling technique for wireless microphone detection in IEEE 802.22 air interface," in Proc. IEEE INFOCOM, 2010, pp. 1-5.
88. Y. Wang, A. Pandharipande, Y. Polo, and G. Leus, "Distributed compressive wide-band spectrum sensing," IEEE Proc. Inf. Theory Appl., pp. 1-4, 2009.
89. Z. Yu, S. Hoyos, and B. Sadler, "Mixed-signal parallel compressed sensing and reception for cognitive radio," in Proc. IEEE ICASSP, 2008, pp. 3861-3864.
90. Z. Tian, Y. Tafesse, and B. M. Sadler, "Cyclic feature detection with sub-Nyquist sampling for wideband spectrum sensing," IEEE J. Sel. Topics Signal Process., Vol. 6, no. 1, Feb. 2012.
91. C.-C. Huang and L.-C. Wang, "Dynamic sampling rate adjustment for compressive spectrum sensing over cognitive radio network," IEEE Wireless Commun. Lett., 2012.
92. P. Zhang, Z. Hu, R. Qiu, and B. Sadler, "A compressed sensing based ultra-wideband communication system," in Proc. IEEE ICC, 2009, pp. 1-5.
93. C. Luo, F. Wu, J. Sun, and C. Chen, "Compressive data gathering for large-scale wireless sensor networks," in Proc. ACM MOBICOM, 2009, pp. 145-156.
94. Q. Ling and Z. Tian, "Decentralized sparse signal recovery for compressive sleeping wireless sensor networks," IEEE Trans. Signal Process., Vol. 58, no. 7, pp. 3816-3827, 2010.
95. S. Fu, X. Kuai, R. Zheng, G. Yang, and Z. Hou, "Compressive sensing approach based mapping and localization for mobile robot in an indoor wireless sensor network," in Proc. 1CNSC, 2010, pp. 122-127.
96. Z. Charbiwala, S. Chakraborty, S. Zahedi, Y. Kim, M. Srivastava, T. He, and C. Bisdikian, "Compressive oversampling for robust data transmission in sensor networks," in Proc. IEEE INFOCOM, 2010, pp. 1-9.
97. Y. Zhang, M. Roughan, W. Willinger, and L. Qiu, "Spatio-temporal compressive sensing and internet traffic matrices," ACM SIGCOMM Comput. Commun. Rev., Vol. 39, no. 4, pp. 267-278, 2009.
98. Z. Dong, S. Anand, and R. Chandramouli, "Estimation of missing RTTs in computer networks: Matrix completion vs compressed sensing," Elsevier Comput. Net., Vol. 55, issue 15, Oct. 2011.
99. S. Pudlewski and T. Melodia, "On the performance of compressive video streaming for wireless multimedia sensor networks," in Proc. IEEE ICC, 2010, pp. 1-5.
100. A. HesamMohseni, M. Babaie-Zadeh, and C. Jutten, "Inflating compressed samples: A joint source-channel coding approach for noise-resistant compressed sensing," in Proc. IEEE ICASSP, 2009, pp. 2957-2960.
101. C. Deng, W. Lin, B. Lee, and C. Lau, "Robust image compression based on compressive sensing," in Proc. IEEEICME, 2010, pp. 462-467.
102. Y. Tsaig and D. Donoho, "Extensions of compressed sensing," Signal Process., Vol. 86, no. 3, pp. 549-571, 2006.
103. M. Cossalter, G. Valenzise, M. Tagliasacchi, and S. Tubaro, "Joint compressive video coding and analysis," IEEE Trans. Multimedia, Vol. 12, no. 3, pp. 168-183, 2010.
104. C. Feng, W. S. Anthea, S. Valaee, and Z. Tan, "Compressive sensing based positioning using RSS of WLAN access points," in Proc. IEEE INFOCOM, 2010, pp. 1-9.
105. A. Tabibiazar and O. Basir, "Compressive sensing indoor localization,", in Proc. IEEE SMC, 2011.
106. L. Tong, F. Dai, Y Zhang, J. Li, and D. Zhang, "Compressive sensing based video scrambling for privacy protection," in Proc. IEEE VCIP, 2011.
107. Y. Zhang, M. Roughan, W. Willinger, and L. Qiu, "Spatio-temporal compressive sensing and Internet traffic matrices," in Proc. ACM SIGCOMM, 2009.
108. M. Mardani, G. Mateos, and G. B. Giannakis, "Dynamic anomalography: Tracking network anomalies via sparsity and low rank," IEEE J. Sel. Topics Signal Process., Vol. 7, no. 1, Feb 2013.
109. S. Budhaditya, P. Duc-Son, M. Lazarescu, and S. Venkatesh, "Effective anomaly detection in sensor networks data streams," in Proc. IEEE ICDM, 2009.
110. M. Sartipi, "Low-complexity distributed compression in wireless sensor networks," in Proc. IEEE DCC, 2012, pp. 227-236.
111. C.-M. Yu, C.-S. Lu, and S.-Y. Kuo, "CSI: Compressed sensing-based clone identification in sensor networks,", in IEEE Int. Conf. Pervasive Comput. Commun., 2012.
112. Wireless Integrated Circuits and Systems (WICS) Group at University of Michigan. [Online]. Available: http://www.eecs.umich.edu/wics/