Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. (English) Zbl 1231.94017


94A12 Signal theory (characterization, reconstruction, filtering, etc.)
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
94A13 Detection theory in information and communication theory
94A20 Sampling theory in information and communication theory
Full Text: DOI arXiv


[1] Candès E J. Compressive sampling. In: Proceedings of International Congress of Mathematics. 2006. 1433-1452 · Zbl 1130.94013
[2] Candès E J, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inform Theory, 2006, 52: 489-509 · Zbl 1231.94017
[3] Candès E J, Romberg J. Quantitative robust uncertainty principles and optimally sparse decompositions. Found Comput Math, 2006, 6: 227-254 · Zbl 1102.94020
[4] Donoho D L. Compressed sensing. IEEE Trans Inform Theory, 2006, 52: 1289-1306 · Zbl 1288.94016
[5] Candès E J, Romberg J. Practical signal recovery from random projections. Wavelet Appl Sig Image Proc XI, 2005, 5914: 1029228
[6] Donoho D L, Tsaig Y. Extensions of compressed sensing. Signal Process, 2006, 86: 533-548 · Zbl 1163.94398
[7] Goyal V K. Multiple description coding: compression meets the network. IEEE Signal Proc Mag, 2001, 18: 74-93
[8] Carrillo R E, Barner K E, Aysal T C. Robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise. IEEE J Sel Topic Signal Proc, 2010, 4: 132-408
[9] Shi G M, Chen X Y, Song X X, et al. Signal matching wavelet for ultrasonic flaw detection in high background noise. IEEE Trans Ultrason Ferr, 2011, 58: 776-787
[10] Marcia R F, Willett R M, Harmany Z T. Compressive optical imaging: architectures and algorithms. In: Optical and Digital Image Processing: Fundamentals and Applications. 2011
[11] Suzen M, Giannoula A, Durduran T. Compressed sensing in diffuse optical tomograph. Opt Express, 2010, 18: 23676-23690
[12] Lustig M, Donoho D, Pauly J M. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn Reson Med, 2007, 58: 1182-1195
[13] Chartrand R. Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data. In: IEEE International Symposium on Biomedical Imaging (ISBI). 2009. 262-265
[14] Herman M, Strohmer T. High-resolution radar via compressed sensing. IEEE Trans Signal Process, 2009, 57: 2275-2284 · Zbl 1391.94236
[15] Easley P V M, Healy G R, Chellappa D M R. Compressed synthetic aperture radar. IEEE J Sel Top Signal Proc, 2010, 4: 244-254
[16] Tibshirani R. Regression shrinkage and selection via the lasso. J Roy Stat Soc B, 1996, 58: 267-288 · Zbl 0850.62538
[17] Chen S, Donoho D, Saunders M. Atomic decomposition by basis pursuit. SIAM J Sci Comput, 1998, 20: 33-61 · Zbl 0919.94002
[18] Figueiredo M A T, Nowak R D, Wright S J. Gradient projection for sparse reconstruction: application to compresed sensing and other inverse problems. IEEE J Sel Top Signal Proc, 2007, 1: 586-597
[19] Candes E, Wakin M, Boyd S. Enhancing sparsity by reweighted l1 minimizaion. J Fourier Anal Appl, 2008, 14: 877-905 · Zbl 1176.94014
[20] Chartrand R, Yin W. Iteratively reweighted algorithms for compressive sensing. In: Proceedings of International Conference on Accoustics, Speech, and Signal Processing. 2008. 3869-3872
[21] Chartrand R. Exact reconstruction of sparse signal via nonconvex minimization. IEEE Signal Proc Lett, 2007, 14: 707-710
[22] Rao B D, Kreutz-Delgado K. An affine scaling methodology for best basis selection. IEEE Trans Signal Process, 1999, 47: 187-200 · Zbl 0984.94010
[23] Rao B D, Engan K, Cotter S F, et al. Subset selection in noise based on diversity measure minimization. IEEE Trans Signal Process, 2003, 51: 760-770
[24] Gorodntisky I F, Rao B D. Sparse singal reconstruction from limited data using FOUSS: a reweighted minimim norm algorithm. IEEE Trans Signal Process, 1997, 45: 600-616
[25] Hager W W, Park S. The gradient projection method with exact line search. J Global Optim, 2004, 30: 103-118 · Zbl 1136.90513
[26] Liu D H, Shi G M, Zhou J S, et al. New metod of multiple description coding for image based on compressed sensing. J Infrared Millim Wave, 2009, 28: 298-302
[27] Donoho D L,
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