Bayesian Hypothesis Testing for One Bit Compressed Sensing with Sensing Matrix Perturbation

Document Type : Research Note

Authors

1 Department of Electrical and Computer engineering, Qom university of technology, Qom, Iran.

2 School of Software and Electrical Engineering, Swinburne University of Technology, Hawthorn, 3122 Australia

3 Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran

Abstract

This paper proposes a low-computational Bayesian algorithm for noisy sparse recovery in the context of one bit compressed sensing with sensing matrix perturbation. The proposed algorithm which is called BHT-MLE comprises a sparse support detector and an amplitude estimator. The support detector utilizes Bayesian hypothesis test, while the amplitude estimator uses an ML estimator which is obtained by solving a convex optimization problem. Simulation results show that Bayesian hypothesis testing in combination with the ML estimator has more reconstruction accuracy than that of only an ML estimator and also has less computational complexity.

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Main Subjects


References
1. Zymnis, A., Boyd, S., and Candes, E. Compressed
sensing with quantized measurements", IEEE Signal
Processing Letters, 17(2), pp. 149-152 (2010).
2. BouFounos, P. and Baraniuk, R. 1-bit compressive
sensing", Proceeding 42nd Annu. Conf. Inf. Sci. Sys.
(2008).
3. BouFounos, P. Greedy sparse signal reconstruction
from sign measurements", Proceeding 43rd Asilomar.
Conf. Signals, Syst., Comput. (Asilomar'09) (2009).
4. Laska, J.N., Wen, Z., Yin, W., and Baraniuk, R.
Trust, but verify: fast and accurate signal recovery
from 1-bit compressive measurements", IEEE Trans
Signal Processing, 59(11), pp. 5289-5301 (2011).
5. Jacques, L., Laska, J., Boufounos, P., and Baraniuk,
R. Robust 1-bit compressive sensing via binary stable
embeddings of sparse vectors", IEEE Trans Inf. Theory,
59(4), pp. 2082-2102 (2013).
6. Yan, M., Yang, Y., and Osher, S. Robust 1-bit
compressive sensing using adaptive outlier pursuit",
IEEE Trans Signal Processing, 60(7), pp. 3868-3875
(2012).
7. Movahed, A., Panahi, A. and Durisi, G. A robust
RFPI-based 1-bit compressive sensing reconstruction
algorithm", Proceeding IEEE ITW (2012).
8. Plan, Y. and Vershynin, R. Robust 1-bit compressed
sensing and sparse logistic regression: A convex programming
approach", IEEE Trans Inf. Theory, 59(1),
pp. 482-494 (2013).
9. Zayyani, H., Korki, M., and Marvasti, F. Dictionary
learning for blind one bit compressed sensing", IEEE
Signal Processing Letters, 23(2), pp. 187-191 (2016).
10. Zayyani, H., Haddadi, F., and Korki, M. Double
detector for sparse signal detection from one-bit compressed
sensing measurements", IEEE Signal Processing
Letters, 23(11), pp. 1637-1641 (2016).
11. Zayyani, H., Korki, M., and Marvasti, F. A distributed
1-bit compressed sensing algorithm robust
to impulsive noise", IEEE Communications Letters,
20(6), pp. 1132-1135 (2016).
12. Candes, E.J. and Tao, T. Near-optimal signal recovery
from random projections: universal encoding
strategies?", IEEE Trans Inf. Theory, 52(12), pp.
5406-5425 (2006).
13. Donoho, D.L. Compressed sensing", IEEE Trans Inf.
Theory, 52(4), pp. 1289-1306 (2006).
14. Li, F., Fang, J., Li, H., and Huang, L. Robust onebit
Bayesian compressed sensing with sign-
ip errors",
IEEE Signal Processing Letters, 22(7), pp. 857-861
(2015).
15. Dong, X. and Zhang, Y. A MAP approach for 1-bit
compressive sensing in synthetic aperture radar imaging",
IEEE Geoscience and Remote Sensing Letters,
12(6), pp. 1237-1241 (2015).
16. Zhu, J., Wang, X., Lin, X., and Ju, Y. Maximum likelihood
estimation from sign measurements with sensing
matrix perturbation", IEEE Trans Signal Processing,
62(15), pp. 3741-3753 (2014).
17. Zayyani, H., Babaie-zadeh, M., and Jutten, C. An
iterative Bayesian algorithm for sparse component
analysis (SCA) in presence of noise", IEEE Trans
Signal Processing, 57(11), pp. 4378-4390 (2009).
18. Zayyani, H., Babaie-zadeh, M., and Jutten, C.
Bayesian pursuit algorithm for sparse representation",
Proceeding ICASSP2009 (2009).
19. Zayyani, H. and Babaie-zadeh, M. Thresholded
smoothed L0 (SL0) dictionary learning for sparse
representations", Proceeding ICASSP2009 (2009).
Volume 25, Issue 6
Transactions on Computer Science & Engineering and Electrical Engineering (D)
November and December 2018
Pages 3628-3633