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Improved adaptive forward-backward matching pursuit algorithm to compressed sensing signal recovery

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Abstract

As a novel two-stage greedy approximation algorithm, Forward-Backward Pursuit (FBP) algorithm attracts wide attention because of its high reconstruction accuracy and no need for sparsity as a priori information. However, the FBP algorithm has to spend much more time to get a higher accuracy. In view of this, an Improved Adaptive Forward-Backward Matching Pursuit (IAFBP) algorithm is proposed in this paper. In the forward stage, the IAFBP algorithm uses an adaptive threshold to select the appropriate number of atoms into support set, so that the number of selected atoms is more random. In the backward stage, the projection coefficient of the atoms is taken as the basis of rejection, and the deletion threshold is introduced to reject the atoms adaptively, so that more right atoms are retained in each iteration and the reconstruction speed can be accelerated. At the same time, it overcomes the excessive backtracking phenomenon existing in the adaptive process and improves the accuracy of the algorithm. The simulation results of one-dimensional sparse signals and two-dimensional images show that the IAFBP algorithm has more advantages than the FBP algorithm in reconstruction performance and computational time.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (No. 51575472), by the Natural Science Foundation of Hebei Province of China (No.E2019203448), the scientific research program of Hebei Education Department (No. ZD2015049) and the scientific research program for Talents Returning from Overseas of Hebei Province (No. C2015005020).

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Authors and Affiliations

  1. Key Lab of measurement technology and Instrumentation of Hebei Province, Yanshan University, Qinhuangdao, 066004, People’s Republic of China

    Zong Meng, Zuozhou Pan, Ying Shi & Zijun Chen

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  1. Zong Meng
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  2. Zuozhou Pan
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  3. Ying Shi
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  4. Zijun Chen
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Correspondence to Zong Meng.

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Meng, Z., Pan, Z., Shi, Y. et al. Improved adaptive forward-backward matching pursuit algorithm to compressed sensing signal recovery. Multimed Tools Appl 78, 33969–33984 (2019). https://doi.org/10.1007/s11042-019-08161-4

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  • DOI: https://doi.org/10.1007/s11042-019-08161-4

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