The theory of compressed sensing and reconstruction algorithm

Tien Tzu Hsueh Pao/Acta Electronica Sinica

Volumn 39, Issue 1, 2011, Pages 142-148

  Yang, Hai Rong ^a,b   Zhang, Cheng ^a   Ding, Da Wei ^a   Wei, Sui ^a  

^a ANHUI UNIVERSITY   (China)

^b HEFEI NORMAL UNIVERSITY   (China)

Author keywords

Analog to information conversion; Compressive sensing; Signal recovery; Sparse representation; Wireless sensor networks

Indexed keywords

ADAPTIVE MEASUREMENTS; BASIC THEORY; COMPRESSED SENSING; COMPRESSIVE SENSING; HIGH PROBABILITY; INFORMATION CONVERSION; ITERATIVE ALGORITHM; NYQUIST FREQUENCY; OPTIMIZATION METHOD; RECONSTRUCTION ALGORITHMS; SIGNAL RECOVERY; SPARSE REPRESENTATION;

AIRCRAFT PROPULSION; ALGORITHMS; COMPUTER SYSTEM RECOVERY; SENSORS; SIGNAL PROCESSING; SIGNAL RECONSTRUCTION;

WIRELESS SENSOR NETWORKS;

EID: 79953224066     PISSN: 03722112     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. D Donoho. Compressed sensing[J]. IEEE Trans Inform Theory, 2006, 52(4): 1289-1306.
2. M A T Figueiredo, R D Nowak, S J Wright. Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems[J]. IEEE J Selected Topics in Signal Processing: Special Issue on Convex Optimization Methods for Signal Processing, 2007, 1(4): 586-598.
3. 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.
4. T Blumensath, M Davies. Iterative hard thresholding for compressed sensing[J]. Appl Comput Harmon Anal, 2009, 27(3): 265-274.
5. A C Gilbert, S Guha, P Indyk, S Muthukrishnan, M J Strauss. Near-optimal sparse Fourier representations via sampling[A]. Proc. of the 2002 ACM Symposium on Theory of Computing STOC[C]. Montreal, Quebec, Canada, 2002. 152-161.
6. E Candès, J Romberg, T Tao. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Trans Inform Theory, 2006, 52(2): 489-509.
7. Fang Hong, Zhang Quanbing, Wei Sui. A method of image reconstruction based on sub-Gaussian random projection[J]. Journal of Computer Research and Development, 2008, 45(8): 1402-1407. (in Chinese)
8. E Candes, T Tao. Error correction via linear programming[A]. Proc. of 46th Annual IEEE Symposium on Foundations of Computer Science FOCS[C]. Pittsburgh, Pennsylvania, USA, 2005. 295-308.
9. S Mallat, Z Zhang. Matching pursuit in a time-frequency dictionary[J]. IEEE Trans Singal Processing, 1993, 41(12): 3397-3415.
10. E J Candès, T Tao. Decoding by linear programming[J]. IEEE Trans Inform Theory, 2005, 51(12): 4203-4215.
11. 1-regularized least-squares problems with applications in signal processing and statistics[J]. Journal of Machine Learning Research, 2007, 7(8): 1519-1555.
12. W Yin, S Osher, D Goldfarb, J Darbon. Bregman iterative algorithms for compressed sensing and related problems[J]. SIAMJ Imaging Sciences, 2008, 1(1): 143-168.
13. J Tropp, A Gilbert. Signal recovery from ran dom measurement s via ort hogonal matching pursuit[J]. IEEE Trans. Inform. Theory, 2007, 53(12): 4655-4666.
14. Fang Hong, Zhang Quanbing, Wei Sui. Image reconstruction based on improved backward optimized orthogonal matching pursuit algorithm[J]. Journal of South China University of Technology, 2008, 36(8): 23-27. (in Chinese)
15. D Needell, Vershynin R. Uniform uncertainty principle and signal recovery via regularized ort hogonal matching pursuit[J]. Found. Comput Math, 2009, 9(3): 317-334.
16. D L Donoho, I Drori, Y Tsaig, J L Starck. Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit[R]. Stanford University, 2006.
17. D Needell, J A Tropp. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples[J]. Appl And Comp Harm. Anal, 2009, 26(3): 301-321.
18. W Dai, O Milenkovic. Subspace pursuit for compressive sensing signal reconstruction[J]. IEEE Trans Inform Theory, 2009, 5, 55(5): 2230-2249.
19. 1 norm for sparse vectors[A]. Proc. 44th Annual Allerton Conf Communication, Contron, and Computing[C]. Allerton, USA, 2006, 9.
20. A Gilbert, M Strauss, J Tropp, R Vershynin. One sketch for all: Fast algorithms for compressed sensing[A]. Proc. 39th ACM Symp. Theory of Computing[C]. San Diego, USA, 2007. 7. 237-246.
21. M Iwen. A deterministic sub-linear time sparse Fourier algorithm via non-adaptive compressed sensing methods[DB/OL]. http://dsp.rice.edu/cs, 2007.
22. Joel A Tropp, Marco F Duarte, Justin K Romberg, Richard G Baraniuk. Beyond nyquist: Efficient sampling of sparse bandlimited signals[J]. IEEE Transactions on Information Theory, 2010, 56(1): 520-544.
23. W U Bajwa, J Haupt, A M Sayeed, R Nowak. Compressive wireless sensing[A]. Proc. IPSN'06[C]. Nashville, TN, USA, 2006. 4. 134-142.
24. M Rabbat, J Haupt, A Singh, R Nowak. Decentralized compression and predistribution via randomized gossiping[A]. Proc. IPSN'06[C]. Nashville, TN, USA, 2006. 4. 51-59.
25. W U Bajwa, J Haupt, A M Sayeed, R Nowak. A universal matched source-channel communication scheme for wireless sensor ensembles[A]. Proc. ICASSP'06[C]. Toulouse, France, 2006. 5. 1153-1156.
26. Waheed U Bajwa, Jarvis D Haupt, Akbar M Sayeed, Robert D Nowak. Joint source-channel communication for distributed estimation in sensor networks[J]. IEEE Trans Inform Theory, 2007, 53(10): 3629-3653.
27. Jarvis Haupt, Waheed U Bajwa, Michael Rabbat, Robert Nowak. Compressed sensing for networkedData[J]. IEEE Signal Processing Magazine, 2008, 25(2): 92-101.
28. Bing Du, Liang Liu, Jun Zhang. Multisensor Information Compression and Reconstruction[DB/OL]. http://dsp.rice.edu/cs, 2009.
29. Di Guo, Xiaobo Qu, Mingbo Xiao, Yan Yao. Comparative analysis on transform and reconstruction of compressed sensingin sensor networks[A]. CMC'09. WRI International Conference[C]. IEEE Computer Society Washington, DC, USA, 2009. 441-445.
30. Shi Guangming, Liu Danhua, Gao Dahua, Liu Zhe, Lin jie, Wang Liangjun. Advance in theory and application of compressed sensing[J]. Acta Electronica Sinica, 2009, 37(5): 1070-1081. (in Chinese)
31. Li Shutao, Wei Dan. A survey on compressive sensing[J]. Acta Automatica Sinica, 2009, 35(11): 1-7. (in Chinese)