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Deterministic Sensing Matrices Based on Multidimensional Pseudo-Random Sequences

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Abstract

An approach is proposed for producing compressed sensing (CS) matrices via multidimensional pseudo-random sequences. The columns of these matrices are binary Gold code vectors where zeros are replaced by −1. This technique is mainly applied to restore sub-Nyquist-sampled sparse signals, especially image reconstruction using block CS. First, for the specific requirements of message length and compression ratio, a set Λ which includes all preferred pairs of m-sequences is obtained by a searching algorithm. Then a sensing matrix A M×N is produced by using structured hardware circuits. In order to better characterize the correlation between any two columns of A, the average coherence is defined and the restricted isometry property (RIP) condition is described accordingly. This RIP condition has strong adaptability to different sparse signals. The experimental results show that with constant values of N and M, the sparsity bound of A is higher than that of a random matrix. Also, the recovery probability may have a maximum increase of 20 % in a noisy environment.

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Acknowledgements

The authors would like to acknowledge funding support from China state 863 Hi-tech programs under No. 2006AA12Z222 and the national Natural Science Foundation of China under No. 2008105GZ30031. The authors are also thankful to the editors and anonymous reviewers for their valuable comments.

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Authors and Affiliations

  1. Department of Geography Science, Nanjing Normal University, Nanjing, 210046, China

    Yan Tang & Guonian Lv

  2. Department of Physics and Technology, Nanjing Normal University, Nanjing, 210046, China

    Kuixi Yin

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  1. Yan Tang
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  2. Guonian Lv
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  3. Kuixi Yin
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Correspondence to Yan Tang.

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Tang, Y., Lv, G. & Yin, K. Deterministic Sensing Matrices Based on Multidimensional Pseudo-Random Sequences. Circuits Syst Signal Process 33, 1597–1610 (2014). https://doi.org/10.1007/s00034-013-9701-5

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  • DOI: https://doi.org/10.1007/s00034-013-9701-5

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