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Deterministic Construction of Toeplitzed Structurally Chaotic Matrix for Compressed Sensing

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Abstract

The construction of sensing matrix is a fundamental issue in compressed sensing (CS). This paper introduces a new deterministic construction, referred to as Toeplitzed structurally chaotic matrix (TSCM), which possesses the advantages of both random and structural sensing matrices. We derive the matrix by first multiplying an orthonormal matrix with a chaotic-based Toeplitz matrix, and then subsampling the resultant matrix to obtain the structural one. Theoretically, we show that the entries of the TSCM are asymptotically normally distributed with that of arbitrary sparsifying matrices, yielding low mutual coherence that guarantees faithful recovery. Moreover, the proposed scheme is implementation friendly and hardware efficient, since its entries have almost no randomness and are easy to generate. Extensive numerical results via Matlab suggest that the TSCM outperforms the state-of-the-art matrix schemes and demonstrate its promising potentials.

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Acknowledgments

This work is supported by National Natural Science Foundation, China (61072042), Natural Science Foundation of Jiangsu Province, China (BK2012510), and Pre-research Foundations of PLA University of Science and Technology (20110211). The authors would like to thank the anonymous reviewers for their constructive comments and questions which greatly improve the paper.

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Authors and Affiliations

  1. College of Command Information Systems, PLA University of Science and Technology, Nanjing, China

    Li Zeng, Xiongwei Zhang, Tieyong Cao & Jibin Yang

  2. College of Communications Engineering, PLA University of Science and Technology, Nanjing, China

    Liang Chen

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  1. Li Zeng
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  2. Xiongwei Zhang
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  3. Liang Chen
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  4. Tieyong Cao
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Correspondence to Li Zeng.

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Zeng, L., Zhang, X., Chen, L. et al. Deterministic Construction of Toeplitzed Structurally Chaotic Matrix for Compressed Sensing. Circuits Syst Signal Process 34, 797–813 (2015). https://doi.org/10.1007/s00034-014-9873-7

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  • DOI: https://doi.org/10.1007/s00034-014-9873-7

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