Advances in theory and application of compressed sensing

Tien Tzu Hsueh Pao/Acta Electronica Sinica

Volumn 37, Issue 5, 2009, Pages 1070-1081

  Shi, Guang Ming ^a   Liu, Dan Hua ^a   Gao, Da Hua ^a,b   Liu, Zhe ^c   Lin, Jie ^a   Wang, Liang Jun ^a  

^a XIDIAN UNIVERSITY   (China)

^b AIR FORCE ENGINEERING UNIVERSITY   (China)

^c NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

Author keywords

Compressed sensing; Information sampling; Measurement matrix; Sparse representation

Indexed keywords

APPLICATION FIELDS; COMPRESSED SENSING; DIGITAL SIGNALS; ELECTRONIC INFORMATION; EXISTING SYSTEMS; HIGH SPEED SAMPLING; INFORMATION SAMPLING; LATEST DEVELOPMENT; MEASUREMENT MATRIX; OPEN PROBLEMS; RECONSTRUCTION ALGORITHMS; SOURCE SIGNALS; SPARSE REPRESENTATION; TECHNICAL PROBLEM; THEORETICAL FRAMEWORK; URGENT PROBLEMS; VOLUME DATA;

SIGNAL RECONSTRUCTION;

PROBLEM SOLVING;

EID: 66449118784     PISSN: 03722112     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (83)

1. E Candès. Compressive sampling [A]. Proceedings of the International Congress of Mathematicians [C]. Madrid, Spain, 2006, 3: 1433-1452.
2. E Candès, J Romberg, Terence Tao. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information [J]. IEEE Trans. on Information Theory, 2006, 52 (2): 489-509.
3. E Candès and J Romberg. Quantitative robust uncertainty principles and optimally sparse decompositions [J]. Foundations of Comput Math, 2006, 6 (2): 227-254.
4. D L Donoho. Compressed sensing [J]. IEEE Trans. on Information Theory. 2006, 52 (4): 1289-1306.
5. E J Candès, J Romberg. Practical signal recovery from random projections [OL]. http://www.acm.caltech.edu/-emmanuel/papers/PracticalRecovery.pdf.
6. D L Donoho, Y Tsaig. Extensions of compressed sensing [J]. Signal Processing. 2006, 86 (3): 533-548.
7. B Kashin. The widths of certain finite dimensional sets and classes of smooth functions [J]. Izv Akad Nauk SSSR. 1977, 41 (2): 334-351.
8. E J Candès and T Tao. Near optimal signal recovery from random projections: Universal encoding strategies [J]. IEEE Trans. Info. Theory. 2006, 52 (12): 5406-5425.
9. Jiao Li-cheng, Tan Shan. Development and prospect of image multiscale geometric analysis [J]. Acta Sinica Electronica, 2003, 31 (12A): 1975-1981. (in Chinese)
10. R Baraniuk. A lecture on compressive sensing [J]. IEEE Signal Processing Magazine, 2007, 24 (4): 118-121.
11. Guangming Shi, Jie Lin, Xuyang Chen, Fei Qi, Danhua Liu and Li Zhang. UWB echo signal detection with ultra-low rate sampling based on compressed sensing [J]. IEEE Trans. On Circuits and Systems-II: Express Briefs, 2008, 55 (4): 379-383.
12. Cand, S E J. Ridgelets: Theory and applications [D]. Stanford: Stanford University. 1998.
13. E Candès, D L Donoho. Curvelets [R]. USA: Department of Statistics, Stanford University. 1999.
14. E L Pennec, S Mallat. Image compression with geometrical wavelets [A]. Proc. of IEEE International Conference on Image Processing, ICIP'2000 [C]. Vancouver, BC: IEEE Computer Society, 2000. 1: 661-664.
15. Do, Minh N, Vetterli, Martin. Contourlets: A new directional multiresolution image representation [A]. Conference Record of the Asilomar Conference on Signals, Systems and Computers [C]. Pacific Groove, CA, United States: IEEE Computer Society. 2002. 1: 497-501.
16. G Peyré. Best Basis compressed sensing [J]. Lecture Notes in Computer Science, 2007, 4485: 80-91.
17. Zhang Chunmei, Yin Zhongke, Chen Xiangdong, Xiao Mingxia. Signal overcomplete representation and sparse decomposition based on redundant dictionaries [J]. Chinese Science Bulletin. 2005, 50 (23): 2672-2677.
18. V Temlyakov. Nonlinear Methods of Approximation [R]. IMI Research Reports, Dept of Mathematics, University of South Carolina. 2001. 01-09.
19. S Mallat, Z Zhang. Matching pursuits with time-frequency dictionaries [J]. IEEE Trans Signal Process, 1993, 41 (12): 3397-3415.
20. D L Donoho, X Huo. Uncertainty principles and ideal atomic decompositions [J]. IEEE Trans Inform Theory, 2001, 47 (7): 2845-2862.
21. M Elad, A M Bruckstein. A generalized uncertainty principle and sparse representation in pairs of bases [J]. IEEE Trans Inform Theory. 2002, 48 (9): 2558-2567.
22. A Feuer, A Nemirovsky. On sparse representation in pairs of bases [J]. IEEE Trans Inform Theory, 2003, 49 (6): 1579-1581.
23. J A Tropp. Greed Is Good: Algorithmic Results for Sparse Approximation [J]. IEEE Transactions on Information Theory, 2004, 50 (10): 2231-2242.
24. R Gribonval, M Nielsen. Sparse decompositions in unions of bases [J]. IEEE Transactions on Information Theory, 2003, 49 (12): 3320-3325.
25. Liu Danhua, Shi Guangming, Zhou Jiashe. New method for signal sparse decomposition over a redundant dictionary [J]. Journal of Xidian University, 2008, 35 (2): 228-232. (in Chinese)
26. R Neff, A Zakhor. Very low bit rate video coding based on matching pursuits [J]. IEEE Transactions on Circuits and Systems for Video Technology, 1997, 7 (1): 158-171.
27. S S Chen, D L Donoho, and M A Saunders. Atomic decomposition by basis pursuit [J]. SIAM Review, 2001, 43 (1): 129-159.
28. J A Tropp and A C Gilbert. Signal Recovery from Partial Information by Orthogonal Matching Pursuit [OL]. April 2005, www-personal.umich.edu/-jtropp/papers/TG05-Signal-Recovery.pdf.
29. C La, M N Do. Signal reconstruction using sparse tree representation [A]. Proceedings of SPIE [C]. San Diego, CA, United States: International Society for Optical Engineering. 2005. 5914: 1-11.
30. D L Donoho, Y Tsaig, I Drori etc. Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit [R]. Technical Report, 2006.
31. E Candès. The restricted isometry property and its implications for compressed sensing [J]. Acadèmie des sciences, 2006, 346 (I): 598-592.
32. R G Baraniuk, M Davenport, R DeVore etc. The Johnson-Lindenstrauss lemma meets compressed sensing [OL]. http://dsp.rice.edu/cs/jlcs-v03.pdf.
33. S Sarvotham, D Baron, R G Baraniuk. Measurements vs. bits: Compressed sensing meets information theory [A]. In Proc. Allerton Conference on Communication, Control and Computing [C]. Monticello, IL, 2006. 1419-1423.
34. L M Bregman. The method of successive projection for finding a common point of convex sets [J]. Doklady Mathematics, 1965, (6): 688-692.
35. E T Hale, W T Yin, Y Zhang. A Fixed-point continuation method for L1-regularization with application to compressed sensing [R]. Rice University CAAM Technical Report, TR07, 2007.
36. G Cormode and S Muthukrishnan. Towards an algorithmic theory of compressed sensing [R]. DIMACS Tech. Report 2005-25, September 2005.
37. A C Gilbert, M J Strauss, J A Tropp, etc. Algorithmic linear dimension reduction in the norm for sparse vectors [OL]. http://www.math.ucdavis.edu/-vershynin/papers/ algorithmic-dim-reduction.pdf
38. D Needell, J A Tropp. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples [J]. Appl Comp Harmonic Anal, 2009, 26 (3): 301-321.
39. D Needell, R Vershynin. Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit [OL]. http://www.math.ucdavis.edu/%7Evershynin/papers/ROMP-stability.pdf.
40. D Needell, R Vershynin. Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit [OL]. http://www.math.ucdavis.edu/-vershynin/papers/ROMP.pdf.
41. S J Kim, K Koh, M Lustig, etc. Gorinevsky. A method for large-scale-regularized least-squares [J]. IEEE Journal on Selected Topics in Signal Processing, 2007, 4 (1): 606-617.
42. M A T Figueiredo, R D Nowak, S J Wright. Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems [J]. Journal of Selected Topics in Signal Processing: Special Issue on Convex Optimization Methods for Signal Processing, 2007, 1 (4): 586-598.
43. I Daubechies, M Defrise, C De Mol. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint [J]. Comm. Pure Appl. Math., 2004, 57 (11): 1413-1457.
44. A C Gilbert, S Guha, P Indyk, etc. Near-optimal sparse Fourier representations via sampling [A]. Proceedings of the Annual ACM Symposium on Theory of Computing [C]. Montreal, Que, Canada: Association for Computing Machinery. 2002. 152-161.
45. A C Gilbert, S Muthukrishnan, M J Strauss. Improved time bounds for near-optimal sparse Fourier representation [A]. Proceedings of SPIE, Wavelets XI [C]. Bellingham WA: International Society for Optical Engineering. 2005, 5914: 1-15.
46. A C Gilbert, M J Strauss, J A Tropp, et al. One sketch for all: Fast algorithms for compressed sensing [A]. Proceedings of the 39th Annual ACM Symposium on Theory of Computing [C]. New York: Association for Computing Machiner. 2007. 237-246.
47. H Rauhut, K Schass, P Vandergheynst. Compressed sensing and redundant dictionaries [J]. IEEE Transactions on Information Theory, 2008, 54 (5): 2210-2219.
48. S Sarvotham, D Baron, and R G. Baraniuk. Compressed sensing reconstruction via belief propagation [R]. Technical report ECE-06-01, Department of Electrical and Computer Engineering, Rice University, Jul. 2006.
49. S Kirolos, J Laska, M. Wakin etc. Analog-to-information conversion via random demodulation [A]. Proceedings of the IEEE Dallas Circuits and Systems Workshop (DCAS) [C]. Dallas, Texas. 2006.
50. J Laska, S Kirolos, Y Massoud etc. Random sampling for analog-to-information conversion of wideband signals [A]. Proceedings of the IEEE Dallas Circuits and Systems Workshop (DCAS'06) [C]. Dallas, Texas, 2006.
51. J Laska, S Kirolos, M Duarte etc. Theory and implementation of an analog-to-information converter using random demodulation [A]. Proceedings of the IEEE Int. Symp. on Circuits and Systems (ISCAS) [C]. Piscataway: Institute of Electrical and Electronics Engineers Inc. 2007. 1959-1962.
52. S Bhattacharya, T Blumensath, B Mulgrew etc. Fast encoding of synthetic aperture radar raw data using compressed sensing [A]. IEEE Workshop on Statistical Signal Processing [C]. Madison, Wisconsin, 2007. 448-452.
53. D Baron, M B Wakin, M Duarte, etc. Distributed compressed sensing [OL]. http://www.dsp.rice.edu/-drorb/pdf/DCS112005.pdf.
54. W Bajwa, J Haupt, A Sayeed, etc. Compressive wireless sensing [A]. Proceedings of the fifth International Conference on Information Processing in Sensor Networks, IPSN'06 [C]. New York: Association for Computing Machinery. 2006. 134-142.
55. D Takhar, J Laska, M Wakin, etc. A new compressive imaging camera architecture using optical-domain compression [A]. Proceedings of SPIE [C]. Bellingham WA: International Society for Optical Engineering. 2006, 6065.
56. M Lustig, D L Donoho, J M Pauly. Rapid MR Imaging with Compressed Sensing and Randomly Under-Sampled 3DFT Trajectories [A]. Proceedings of the 14th. Annual Meeting of ISMRM [C]. Seattle, WA. 2006.
57. Mona Sheikh, Olgica Milenkovic, Richard Baraniuk. Compressed sensing DNA microarrays [OL]. http://www.dsp.ece.rice.edu/cs/CSMProbeDesign02.pdf.
58. P Borgnat, P Flandrin. Time-frequency localization from sparsity constraints [A]. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP) [C]. Piscataway: Institute of Electrical and Electronics Engineers Inc., 2008. 3785-3788.
59. R Willett, M Gehm, D Brady. Multiscale reconstruction for computational spectral imaging [A]. Proceedings of SPIE-IS and T Electronic Imaging-Computational Imaging V [C]. Bellingham: SPIE, 2007. 64980L.
60. J W Ma, F X L Dimet. Deblurring from highly incomplete measurements for remote sensing [OL]. To appear in IEEE Trans. Geoscience and Remote Sensing. http://www.dsp.ece.rice.edu/cs/CS-Deblurring.pdf.
61. F J Herrmann, G Hennenfent. Non-parametric seismic data recovery with curvelet frames [R]. UBC Earth & Ocean Sciences Department Technical Report TR-2007-1, 2007.
62. F J Herrmann, D Wang, G Hennenfent etc. Curvelet-based seismic data processing: A multiscale and nonlinear approa-ch [J]. Geophysic. 2008, 73 (1): A1-A5.
63. D Takhar, V Bansal, M Wakin, etc. A compressed sensing camera: New theory and an implementation using digital micromirrors [A]. SPIE Electronic Imaging: Computational Imaging [C]. San Jose. 2006.
64. H Jung, J C Ye, E Y Kim. Improved k-t Blask and k-t Sense using Focuss [J]. Physics in Medicine and Biology. 2007, 52: 3201-3226.
65. M Lustig, J M Santos, D L Donoho, etc. K-t SPARSE: High frame rate dynamic MRI exploiting spatio-temporal sparsity [A]. Proceedings of the 14th Annual Meeting of ISMRM [C]. Seattle, Washington. 2006. 2420-2443.
66. M A Sheikh, O Milenkovic, R G Baraniuk. Compressed sensing DNA microarrays [R]. Rice ECE Department Technical Report TREE 0706, May 2007.
67. Liangjun Wang, Xiaolin Wu, Guangming Shi. A compressive sensing approach of multiple descriptions for network multimedia communication [A]. IEEE 10th Workshop on Multimedia Signal Processing [C]. IEEE Press, 2008, 445-449.
68. R Chartrand. Nonconvex compressed sensing and error correction [A]. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP'07 [C]. Piscataway: Institute of Electrical and Electronics Engineers Inc. 2007, 3: 889-892.
69. R Chartrand. Exact Reconstruction of Sparse Signals via Nonconvex Minimization [J]. IEEE Signal Processing Letters. 2007, 14 (10): 707-710.
70. R Tibshirani. Regression shrinkage and selection via the lasso [J]. The Journal of the Royal Statistical Society, Series B, 1996, 58 (1): 267-288.
71. E van den Berg, M P Friedlander. In pursuit of a root [OL]. http://www.optimizationonline.org/DB-FILE/2007/06/1708.pdf.
72. I F Gorodnitsky, B D Rao. Sparse signal reconstruction from limited data using FOCUSS: A re-weighted norm minimization algorithm [J]. IEEE Transactions on Signal Processing, 1997, 45 (3): 600-616.
73. B D Rao, K Engan, S F Cotter, etc. Subset selection in noise based on diversity measure minimization [J]. IEEE Transactions on Signal Processing, 2003, 51 (3): 760-770.
74. J A Tropp and A C Gilbert. Signal recovery from random measurements via orthogonal matching pursuit [J]. IEEE Transactions on Information Theory, 2007, 53 (12): 4655-4666.
75. S Kunis, H Rauhut. Random sampling of sparse trigonometric polynomials II-Orthogonal matching pursuit versus basis pursuit [OL]. http://homepage.univie.ac.at/holger.rauhut/KunisRauhutOMP.pdf.
76. E J Candes, J Romberg. Sparsity and incoherence in compressive sampling [J]. Inverse Problems. 2007, 23 (3): 969-985.
77. J A Tropp, M B Wakin, M F Duarte, etc. Random filters for compressive sampling and reconstruction [A]. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) [C]. Piscataway: Institute of Electrical and Electronics Engineers Inc. 2006. 3: 872-875.
78. T T Do, T D. Tran, L Gan. Fast compressive sampling with structurally random matrces [OL]. http://www.dsp.ece.rice.edu/cs/FastCS14.pdf.
79. S Ji, Y Xue, L Carin. Bayesian compressive sensing [J]. IEEE Transactions Signal Processing, 2008, 56 (6): 2346-2356.
80. J Haupt, R Nowak. Signal reconstruction from noisy random projections [J]. IEEE Transactions Information Theory, 2006, 52 (9): 4036-4048.
81. W Wang, M Garofalakis, K Ramchandran. Distributed sparse random projections for refinable approximation [A]. Proceedings of the Sixth International Symposium on Information Processing in Sensor Networks, (IPSN2007) [C]. New York: Association for Computing Machinery, 2007. 331-339.
82. J Wright, A Yang, A Ganesh, etc. Robust face recognition viasparse representation [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31 (2): 201-227.