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Blind Spectral Signal Deconvolution with Sparsity Regularization: An Iteratively Reweighted Least-Squares Solution

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Abstract

Spectral signals often suffer from the common problems of band overlap and random Gaussian noise. To address these problems, we propose a sparsity regularization-based model that deconvolutes the degraded spectral signals. Sparsity regularization is achieved by fitting the probability density function of the gradient of the signal, and then, the iteratively reweighted least-squares method is used to solve the minimization problem. Results from experiments using real spectral signals showed that this algorithm separates the overlapping peaks and effectively suppresses the noise. The deconvoluted spectral signals will promote the practical application of infrared spectral analysis in the fields of target recognition, material identification, and chemometrics analysis.

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  1. https://www.bruker.com/products/infrared-near-infrared-and-raman-spectroscopy.html.

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Acknowledgments

The authors thank the editor and anonymous reviewers for their valuable suggestions. This research was partially funded by the National Natural Science Foundation of China under Grant (No. 61505064), the National Social Science Fund of China (14BGL131), the Project of the Program for National Key Technology Research and Development Program (2013BAH18F01, 2014BAH22F01, 2015BAK07B03), the Self-Determined Research Funds of CCNU from the Colleges’ Basic Research and Operation of MOE (CCNU15A05009, CCNU15A05010, CCNU15A05059), and the Project of the Program for National Key Technology Research and Development Program (2013BAH72B01, 2013BAH18F02, 2015BAH33F02). The authors sincerely thank Prof. Yuan Jinghe for his helpful discussions and providing the source codes of FSD and HOS methods.

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    Authors and Affiliations

    1. National Engineering Research Center for E-Learning, Central China Normal University, Wuhan, 430079, China

      Hai Liu, Tao Huang, Sanya Liu & Zhaoli Zhang

    2. School of Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

      Luxin Yan

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    1. Hai Liu
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    2. Luxin Yan
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    Correspondence to Tao Huang.

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    Hai Liu and Zhaoli Zhang have contributed equally to this work.

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    Liu, H., Yan, L., Huang, T. et al. Blind Spectral Signal Deconvolution with Sparsity Regularization: An Iteratively Reweighted Least-Squares Solution. Circuits Syst Signal Process 36, 435–446 (2017). https://doi.org/10.1007/s00034-016-0318-3

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