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Improved Measurement Matrix Construction with Pseudo-Random Sequence in Compressed Sensing

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Abstract

In compressed sensing theory, the measurement matrix improves the reconstruction performance by reducing the cross-correlation between itself and the sparse dictionary. Aiming at the difficulty of hardware implementation of random measurement matrix and the large storage cost, this paper proposes an optimized method for constructing measurement matrix based on pseudo-random sequence. This method combines the random Gaussian matrix with the pseudo-random sequence and the Hadamard matrix, adjusts the size of the measurement matrix by changing the order of the random Gaussian matrix, so that the constructed matrix not only retains the advantages of the random Gaussian matrix with few measurements and the pseudo-random sequence with high correlation, but also has good reconstruction performance. At the same time, related theorem is proposed and its rationality is verified. Finally, the one-dimensional random signal and two-dimensional images are experimentally verified on the MATLAB simulation platform. The experimental results show that, compared with the conventional matrices, the optimized matrix has better reconstruction performance, lower time computation complexity and good application value.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 61561031 and the National Natural Science Foundation of China under Grant 62061024.

Funding

This work was supported by the National Natural Science Foundation of China under Grant 61561031 and the National Natural Science Foundation of China under Grant 62061024.

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Authors and Affiliations

  1. School of computer and communication, Lanzhou University of Technology, Lanzhou, 730050, China

    Jiai He, Tong Wang, Chanfei Wang & Yanjiao Chen

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  1. Jiai He
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  2. Tong Wang
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  3. Chanfei Wang
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  4. Yanjiao Chen
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Contributions

Jiai, He determined the research direction of the paper and gave guidance. Tong, Wang developed and implemented the core concepts of the algorithm presented, finished theoretical derivation and experiment analysis in this manuscript. Chanfei, Wang conducted sufficient research. Yanjiao, Chen provided refinements and supplemental programming. All authors had significant contribution to the development of early ideas and the design of the final methods.

Corresponding author

Correspondence to Tong Wang.

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The authors declare that they have no conflict of interest.

Authors’ motivation

For the existing research work usually needs specific experimental conditions and experimental objects, which has certain limitation, it is necessary to purpose a construction algorithm that has wider applicability and better reconstruction performance.

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He, J., Wang, T., Wang, C. et al. Improved Measurement Matrix Construction with Pseudo-Random Sequence in Compressed Sensing. Wireless Pers Commun 123, 3003–3024 (2022). https://doi.org/10.1007/s11277-021-09274-6

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