Abstract
In the typical compressed signal recovery methods, the noise involved in the measurement process is assumed to be normal distributed. However, there might be impulsive noise existing in the real-world environment. Therefore, the assumption of normal distribution may lead to inaccurate recovery result. This paper proposes the Laplace density to model the measured noise of compressive sensing. A hierarchical Bayesian model is built for the model of the compressive sensing. The signal is assumed to be sparse under some transformation, and each coefficient of the transformation is supposed to be normal distributed with each precision being modeled by a gamma distribution. The zero coefficients can be automatically switched off via the proposed model setting. To estimate the parameters of the model, Variational Bayesian method is adopted to the proposed model. The proposed method is applied on the synthetic signal and the image signal; experimental results demonstrate the validity of the method.
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References
Giacobello, D., Christensen, M.G., Murthi, M.N., et al.: Sparse linear prediction and its applications to speech processing. IEEE Trans. Audio Speech Lang. Process. 20(5), 1644–1657 (2012)
He, L., Carin, L.: Exploiting structure in wavelet-based Bayesian compressive sensing. IEEE Trans. Signal Process. 57(9), 3488–3497 (2009)
Hinojosa, C., Bacca, J., Arguello, H.: Coded aperture design for compressive spectral subspace clustering. IEEE J. Sel. Top. Signal Process. 12(6), 1589–1600 (2018)
An, Y., Zhang, Y., Guo, H., Wang, J.: Compressive sensing-based three-dimensional laser imaging with dual illumination. IEEE Access 7, 25708–25717 (2019)
Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52, 1289–1306 (2006)
Mallat, S.: A Wavelet Tour of Signal Processing, 2nd edn. Academic, New York (1998)
Sakhaee, E., Entezari, A.: Joint inverse problems for signal reconstruction via dictionary splitting. IEEE Signal Process. Lett. 24(8), 1203–1207 (2017)
Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B 58, 267–288 (1996)
Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53, 4655–4666 (2007)
Needell, D., Tropp, J.A.: CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009)
Needell, D., Vershynin, R.: Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. IEEE J. Sel. Top. Signal Process. 4(2), 310–316 (2010)
Tzikas, D.G., Likas, A.C., Galatsanos, N.P.: The variational approximation for Bayesian inference. IEEE Signal Process. Mag. 25(6), 131–146 (2008)
Bishop C M: Pattern Recognition and Machine Learning. Springer, New York (2006)
Wan, H., Ma, X., Li, X.: Variational Bayesian learning for removal of sparse impulsive noise from speech signal. Digit. Signal Proc. 73, 106–116 (2018)
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Wan, H., Zhang, H. (2020). Sparse Impulsive Noise Corrupted Compressed Signal Recovery Using Laplace Noise Density. In: Kountchev, R., Patnaik, S., Shi, J., Favorskaya, M. (eds) Advances in 3D Image and Graphics Representation, Analysis, Computing and Information Technology. Smart Innovation, Systems and Technologies, vol 179. Springer, Singapore. https://doi.org/10.1007/978-981-15-3863-6_29
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DOI: https://doi.org/10.1007/978-981-15-3863-6_29
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Online ISBN: 978-981-15-3863-6
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