NOISES IN RANDOMLY SAMPLED SPARSE SIGNALS
Abstract
Sparse signals can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Two main reconstruction directions are in the sparse transformation domain analysis of signals and the gradient based algorithms. In the transformation domain analysis, that will be considered here, the estimation of nonzero signal coefficients is based on the signal transform calculated using available samples only. The missing samples manifest themselves as a noise. This kind of noise is analyzed in the case of random sampling, when the sampling instants do not coincide with the sampling theorem instants. Analysis of the external noise influence to the results, with randomly sampled sparse signals, is done as well. Theory is illustrated and checked on statistical examples.
Full Text:
PDFReferences
D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006.
E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489–509, 2006.
L. Stanković, I. Orović, S. Stanković, and M. G. Amin, “Robust Time-Frequency Analysis based on the L-estimation and Compressive Sensing,” IEEE Signal Processing Letters, May 2013, pp. 499–502.
R. E. Carrillo, K. E. Barner, and T. C. Aysal, “Robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise,” IEEE Journal of Selected Topics in Signal Processing, 2010, 4(2), pp. 392–408.
L. Stanković, M. Daković, and T. Thayaparan, Time–Frequency Signal Analysis with Application, Artech House, 2013.
L. Stanković, S. Stanković, I. Orović, and M. G. Amin, “Compressive Sensing Based Separation of Non-Stationary and Stationary Signals Overlapping in Time-Frequency, ”IEEE Transactions on Signal Processing, vol. 61, no. 18, pp. 4562–4572, Sept. 2013
M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,”IEEE Journal of Selected Topics in Signal Processing,, vol. 1, no. 4, pp. 586–597, 2007.
D. Donoho, M. Elad, and V. Temlyakov, “Stable recovery of sparse overcomplete representations in the presence of noise,” IEEE Transactions on Information Theory, vol. 52, pp. 6–18, 2006.
B. Turlach, “On algorithms for solving least squares problems under an L1 penalty or an L1 constraint,” Proc. of the American Statistical Association; Statistical Computing Section, pp. 2572–2577, Alexandria, VA, 2005.
R. Baraniuk, “Compressive sensing,” IEEE Signal Processing Magazine, vol. 24, no. 4, 2007, pp. 118–121.
P. Flandrin and P. Borgnat, “Time-Frequency Energy Distributions Meet Compressed Sensing,” IEEE Transactions on Signal Processing, vol. 58, no. 6, 2010, pp. 2974–2982.
Y. D. Zhang and M. G. Amin, “Compressive sensing in nonstationary array processing using bilinear transforms," in Proc. IEEE Sensor Array and Multichannel Signal Processing Workshop, Hoboken, NJ, June 2012.
L. Stanković, S. Stanković, and M. G. Amin, “Missing Samples Analysis in Signals for Applications to L-Estimation and Compressive Sensing”, Signal Processing, Elsevier, Volume 94, Jan. 2014, Pages 401–408.
S. Aviyente, “Compressed Sensing Framework for EEG Compression”, in Proc. Stat. Sig. Processing, 2007, Aug. 2007.
L. Stanković, “A measure of some time–frequency distributions concentration,” Signal Processing, vol. 81, pp. 621–631, 2001
N.B. Karahanoglu and H. Erdogan, ” Compressed sensing signal recovery via forward–backward pursuit”, Digital Signal Processing, Vol.23, Issue 5, Sept. 2013, Pages 1539–1548.
S. Stanković, I. Orović, and E. Sejdić, Multimedia signals and Systems, Springer, 2012.
E. Sejdić, A. Cam, L. F. Chaparro, C. M. Steele, and T. Chau, “Compressive sampling of swallowing accelerometry signals using TF dictionaries based on modulated discrete prolate spheroidal sequences,” EURASIP Journal on Advances in Signal Processing, 2012:101 doi:10.1186/1687–6180–2012–101.
S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Transactions on Signal Processing, vol. 41, no. 12, pp. 3397–3415, 1993.
I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Communications on pure and applied mathematics, vol. 57, no. 11, pp. 1413–1457, 2004.
L. Stanković, M. Daković, and S. Vujović, “Adaptive Variable Step Algorithm for Missing Samples Recovery in Sparse Signals,”IET Signal Processing, in print, 2014 (first version available on arxiv.org/abs/1309.5749).
L. Stanković, M. Daković, and S. Vujović, “Concentration Measures with an Adaptive Algorithm for Processing Sparse Signals,” in Proceedings of ISPA 2013, Sept. 4–6, 2013, Trieste, Italy, pp. 418–423.
L. Stanković, M. Daković, and S. Vujović, “Reconstruction of Sparse Signals in Impulsive Noise", IEEE Transactions on Signal Processing, submitted (first version available on arxiv.org)
S. Stanković, I. Orović, and L. Stanković, "An Automated Signal Reconstruction Method based on Analysis of Compressive Sensed Signals in Noisy Environment", Signal Processing, Elsevier, Volume 94, in print.
E. Margolis and Y.C. Eldar, "Nonuniform Sampling of Periodic Bandlimited Signals," IEEE Transactions on Signal Processing, vol.56, no.7, pp.2728,2745, July 2008.
Refbacks
- There are currently no refbacks.
ISSN: 0353-3670 (Print)
ISSN: 2217-5997 (Online)
COBISS.SR-ID 12826626