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Recovery Error Analysis of Noisy Measurement in Compressed Sensing

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Abstract

With the rapid development of compressed sensing, practical consideration such as the impact of noise in the measurement should be considered. Existing methods for establishing recovery error bound suffer from inherent drawbacks and are only valid for specific types of noise. In this paper, we establish recovery error bound for various types of noise based on restricted isometric property. Our method is constructed from probability perspective. First, we establish the recovery error bound for noiseless signal to lay the foundation for further analysis. Depending on the probabilistic characteristics of different types of noise, we then establish recovery error bound for probabilistically bounded noise as well as for probabilistically unbounded noise. To further enhance the tightness of the bound, we also establish recovery error bound based on Dantzig-selector.

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Acknowledgments

This work is supported by the China Shaanxi Natural Science foundation with the Grant Number 2014JM7273. The author would like to thank the Editor-in-Chief, Prof. M.N.S. Swamy for his very valuable help and great patience in making the presentation of this paper more readable and understandable.

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Authors and Affiliations

  1. Faculty of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, No. 5 South Jinhua Road, Xi’an, 710048, Shaanxi, China

    Bin Wang, Liaolin Hu, Jingyu An, Guangfei Liu & Jingjing Cao

  2. National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Bin Wang

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  1. Bin Wang
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  2. Liaolin Hu
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  3. Jingyu An
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Correspondence to Bin Wang.

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Wang, B., Hu, L., An, J. et al. Recovery Error Analysis of Noisy Measurement in Compressed Sensing. Circuits Syst Signal Process 36, 137–155 (2017). https://doi.org/10.1007/s00034-016-0296-5

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