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Robust Sparse Bayesian Learning for Sparse Signal Recovery Under Unknown Noise Distributions

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Abstract

This paper considers the robust recovery problem of sparse signal with sparse Bayesian learning (SBL) in noisy environments. Most of the current SBL algorithms are constructed on the optimization problem using the square loss, which mainly deals with Gaussian noise. However, real measurements are often contaminated by an unknown distributed noise that is unlikely to be Gaussian. To prevent performance degradation of SBL in such cases, we propose a robust sparse Bayesian learning method with a simple but effective hierarchical noise model. Using this model, the resultant loss is made up of a weighted error measure and a priori-dependent constraint on the weight, and then provides the flexibility for resisting the outliers and adapting to the real noise. A type-II Bayesian estimate is performed to infer the related model parameter and the unknown sparse signal. The advantage of our method is demonstrated by extensive experiments on synthetic data and real radio tomographic imaging data.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Notes

  1. We use LAD as short for LAD-LASSO to save space in the figures.

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Acknowledgements

Thanks to Professor Guoli Wang and Associate Professor Xuemei Guo of Sun Yat-sen University for their support in building radio tomographic imaging systems.

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Authors and Affiliations

  1. School of Mathematics and Big Data, Foshan University, Guangdong, 528000, China

    Kaide Huang

  2. School of Software, Nanchang Hangkong University, Jiangxi, 330000, China

    Zhiyong Yang

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  1. Kaide Huang
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Correspondence to Kaide Huang.

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This work was supported by the National Natural Science Foundation of China with Grant No. 61906041 and by the Natural Science Foundation of Jiangxi Province, China with Grant No. 20181BAB202015.

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Huang, K., Yang, Z. Robust Sparse Bayesian Learning for Sparse Signal Recovery Under Unknown Noise Distributions. Circuits Syst Signal Process 40, 1365–1382 (2021). https://doi.org/10.1007/s00034-020-01529-0

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