A survey on compressive sensing

Zidonghua Xuebao/ Acta Automatica Sinica

Volumn 35, Issue 11, 2009, Pages 1369-1377

  Li, Shu Tao ^a   Wei, Dan ^a  

^a HUNAN UNIVERSITY   (China)

Author keywords

Compressive; Compressive sensing; Restricted isometry property; Signal reconstruction; Sparse representation

Indexed keywords

BIOSENSING; BROAD APPLICATION; COMPRESSIVE IMAGING; COMPRESSIVE SENSING; DATA STORAGE; IMAGE AND VIDEO PROCESSING; INFORMATION CONVERSION; LINEAR PROJECTIONS; NEW THEORY; NYQUIST RATE; OPTIMIZATION PROCESS; SAMPLING FREQUENCIES; SAMPLING RATES; SHANNON THEOREM; SIGNAL ACQUISITIONS; SIGNAL SAMPLING; SPARSE REPRESENTATION; TRANSMISSION COSTS;

REPAIR; SIGNAL ANALYSIS; SIGNAL RECONSTRUCTION; SURVEYS;

SIGNAL PROCESSING;

EID: 71949107686     PISSN: 02544156     EISSN: None     Source Type: Journal    
DOI: 10.3724/SP.J.1004.2009.01369     Document Type: Review

References (61)

1. Donoho D L. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306
2. Candès E, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 2006, 52(2): 489-509
3. Candès E. Compressive sampling. In: Proceedings of International Congress of Mathematicians. Madrid, Spain: European Mathematical Society Publishing House, 2006. 1433-1452
4. Baraniuk R G. Compressive sensing. IEEE Signal Processing Magazine, 2007, 24(4): 118-121
5. Olshausen B A, Field D J. Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 1996, 381(6583): 607-609
6. Mallat S. A Wavelet Tour of Signal Processing. San Diego: Academic Press, 1996
7. Candès E, Donoho D L. Curvelets-A Surprisingly Effective Nonadaptive Representation for Objects with Edges, Technical Report 1999-28, Department of Statistics, Stanford University, USA, 1999
8. Sun Yu-Bao, Xiao Liang, Wei Zhi-Hui, Shao Wen-Ze. Sparse representations of images by a multi-component Gabor perception dictionary. Acta Automatica Sinica, 2008, 34(11): 1379-1387
9. Aharon M, Elad M, Bruckstein A M. The K-SVD: an algorithm for designing of over complete dictionaries for sparse representations. IEEE Transactions on Image Processing, 2006, 54(11): 4311-4322
10. Rauhut H, Schnass K, Vandergheynst P. Compressed sensing and redundant dictionaries. IEEE Transactions on Information Theory, 2008, 54(5): 2210-2219
11. Candès E, Romberg J. Sparsity and incoherence in compressive sampling. Inverse Problems, 2007, 23(3): 969-985
12. Candès E, Braun N, Wakin M B. Sparse signal and image recovery from compressive samples. In: Proceedings of the 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro. Washington D. C., USA: IEEE, 2007. 976-979
13. Tropp J A, Gilbert A C. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory, 2007, 53(12): 4655-4666
14. Blumensath T, Davies M E. Iterative thresholding for sparse approximations. Journal of Fourier Analysis and Applications, 2008, 14(5-6): 629-654
15. Candès E, Tao T. Near optimal signal recovery from random projections: Universal encoding strategies? IEEE Transactions on Information Theory, 2006, 52(12): 5406-5425
16. Candès E, Tao T. Decoding by linear programming. IEEE Transactions on Information Theory, 2005, 51(12): 4203-4215
17. Candès E, Romberg J, Tao T. Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure and Applied Mathematics, 2006, 59(8): 1207-1223
18. 1-norm solution is also the sparsest solution. Communications on Pure and Applied Mathematics, 2006, 59(6): 797-829
19. 1-norm near-solution approximates the sparsest near-solution. Communications on Pure and Applied Mathematics, 2006, 59(7): 907-934
20. Fang Hong, Zhang Quan-Bing, Wei Shui. A method of image reconstruction based on sub-Gaussian random projection. Journal of Computer Research and Development, 2008, 45(8): 1402-1407
21. Gilbert A C, Guha S, Indyk P, Muthukrishnan S, Strauss M. Near-optimal sparse Fourier representations via sampling. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing. Quebec, Canada: ACM, 2006. 152-161
22. Tsaig Y, Donoho D L. Extensions of compressed sensing. Signal Processing, 2006, 86(3): 549-571
23. Pinkus A. N-Widths in Approximation Theory. New York: Springer-Verlag, 1985
24. Bajwa W U, Haupt J D, Raz G M, Wright S J, Nowak R D. Toeplitz-structured compressed sensing matrices. In: Proceedings of the IEEE Workshop on Statistical Signal Processing. Washington D. C., USA: IEEE, 2007. 294-298
25. Sebert F, Zou Y M, Ying L. Toeplitz block matrices in compressed sensing and their applications in imaging. In: Proceedings of International Conference on Technology and Applications in Biomedicine. Washington D. C., USA: IEEE, 2008. 47-50
26. Do T T, Trany T D, Gan L. Fast compressive sampling with structurally random matrices. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing. Washington D. C., USA: IEEE, 2008. 3369-3372
27. 1-norm solution is also the sparsest solution. Communications on Pure and Applied Mathematics, 2006, 59(6): 797-829
28. Chen S B, Donoho D L, Saunders M A. Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 1998, 20(1): 33-61
29. Donoho D L, Elad M, Temlyakov V N. Stable recovery of sparse over complete representations in the presence of noise. IEEE Transactions on Information Theory, 2006, 52(1): 6-18
30. 1 regularized least squares. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4): 606-617
31. Fiqueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4): 586-597
32. 1-Norm Minimization Problems When the Solution May Be Sparse, Technical Report, Department of Statistics, Stanford University, USA, 2008
33. Needell D, Vershynin R. Greedy signal recovery and uncertainty principles. In: Proceedings of the Conference on Computational Imaging. San Jose, USA: SPIE, 2008. 1-12
34. Needell D, Tropp J A. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Applied and Computational Harmonic Analysis, 2008, 26(3): 301-321
35. Lobo M S, Vandenberghe L, Boyd S, Lebret H. Applications of second-order cone programming. Linear Algebra and Its Applications, 1998, 284(1-3): 193-228
36. Kingsbury N. Complex wavelets for shift invariant analysis and filtering of complex wavelets for shift invariant analysis and filtering of signals. Applied and Computational Harmonic Analysis, 2001, 10(3): 234-253
37. Herrity K K, Gilbert A C, Tropp J A. Sparse approximation via iterative thresholding. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing. Washington D. C., USA: IEEE, 2006. 624-627
38. Duarte M F, Davenport M A, Takhar D, Sun T, Kelly K F, Baraniuk R G. Single-pixel imaging via compressive sampling. IEEE Signal Processing Magazine, 2008, 25(2): 83-91
39. Baraniuk R, Steeghs P. Compressive radar imaging. In: Proceedings of the Radar Conference. Washington D. C., USA: IEEE, 2007. 128-133
40. Bhattacharya S, Blumensath T, Mulgrew B, Davies M. Fast encoding of synthetic aperture radar raw data using compressed sensing. In: Proceedings of the 14th Workshop on Statistical Signal Processing. Washington D. C., USA: IEEE, 2007. 448-452
41. Lustig M, Donoho D L, Pauly J M. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine, 2007, 58(6): 1182-1195
42. Hu S, Lustig M, Chen A P, Crane J, Kerr A, Kelley D A C. Compressed sensing for resolution enhancement of hyper-polarized 13C fly back 3D-MRSI. Journal of Magnetic Resonance, 2008, 192(2): 258-264
43. Haupt J, Nowak R. Compressive sampling vs. conventional imaging. In: Proceedings of the IEEE International Conference on Image Processing. Washington D. C., USA: IEEE, 2006. 1269-1272
44. Wakin M B, Laska J N, Duarte M F, Baron D, Sarvotham S, Takhar D. An architecture for compressive imaging. In: Proceedings of IEEE International Conference on Image Processing. Washington D. C., USA: IEEE, 2006. 1273-1276
45. Stankovic V, Stankovic L, Cheng S. Compressive video sampling. In: Proceedings of the European Signal Processing Conference. Lausanne, Switzerland: Elsevier, 2008. 1-5
46. Marcia R F, Willett R M. Compressive coded aperture video reconstruction. In: Proceedings of the European Signal Processing Conference. Lausanne, Switzerland: 2008. 6-10
47. Gan L. Block compressed sensing of natural images. In: Proceedings of the 15th International Conference on Digital Signal Processing. Washington D. C., USA: IEEE, 2007. 403-406
48. Cevher V, Sankaranarayanan A, Duarte M F, Reddy D, Baraniuk R G, Chellappa R. Compressive sensing for back-ground subtraction. In: Proceedings of the 10th European Conference on Computer Vision. Marseille, France: Springer, 2008. 155-168
49. Kirolos S, Laska J, Wakin M, Duarte M F, Baron D, Ragheb T. Analog-to-information conversion via random demodulation. In: Proceedings of the IEEE Dallas Circuits and Systems Workshop. Richardson, USA: IEEE, 2006. 71-74
50. Ragheb T, Kirolos S, Laska J, Gilbert A, Strauss M, Baraniuk R. Implementation models for analog-to-information conversion via random sampling. In: Proceedings of the 50th Midwest Symposium on Circuits and Systems. Washington D. C., USA: IEEE, 2007. 325-328
51. Laska J, Kirolos S, Massoud Y, Baraniuk R, Gilbert A, Iwen M. Random sampling for analog-to-information conversion of wideband signals. In: Proceedings of the IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software. Washington D. C., USA: IEEE, 2006. 119-122
52. Sheikh M A, Milenkovic O, Baraniuk R G. Designing compressive sensing DNA microarrays. In: Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing. Washington D. C., USA: IEEE, 2007. 141-144
53. Sheikh M A, Sarvotham S, Milenkovic O, Baraniuk R G. DNA array decoding from nonlinear measurements by belief propagation. In: Proceedings of the 14th Workshop on Statistical Signal Processing. Washington D. C., USA: IEEE, 2007. 215-219
54. Haupt J, Nowak R. Compressive sampling for signal detection. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing. Washington D. C., USA: IEEE, 2007. 1509-1512
55. Davenport M A, Wakin M B, Baraniuk R G. Detection and Estimation with Compressive Measurements, Technical Report TREE 0610, Department of Electrical Engineering, Rice University, USA, 2006
56. Haupt J, Castro R, Nowak R, Fudge G, Yeh A. Compressive sampling for signal classification. In: Proceedings of the Fortieth Asilomar Conference on the Signals, Systems and Computers. Washington D. C., USA: IEEE, 2006. 1430-1434
57. Bajwa W, Haupt J, Sayeed A, Nowak R. Compressive wire-less sensing. In: Proceedings of the International Conference on Information Processing in Sensor Networks. Nashville, USA: ACM, 2006. 134-142
58. Taubock G, Hlawatsch F. A compressed sensing technique for OFDM channel estimation in mobile environments: exploiting channel sparsity for reducing pilots. In: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing. Las Vegas, USA: IEEE, 2008. 2885-2888
59. Bajwa WU, Haupt J, Raz G, Nowak R. Compressed channel sensing. In: Proceedings of the 42nd Annual Conference on Information Sciences and Systems. Washington D. C., USA: IEEE, 2008. 5-10
60. Hennenfent G, Herrmann F J. Simply denoise: wave field re-construction via jittered under sampling. Geophysics, 2008, 73(3): 19-28
61. Gehm M E, John R, Brady D J, Willett R M, Schulz T J. Single-shot compressive spectral imaging with dual-disperser architecture. Optics Express, 2007, 15(21): 14013-14027