Skip to main content
SpringerLink
Log in

Sparse Signal and Image Reconstruction Algorithm for Adaptive Dual Thresholds Matching Pursuit Based on Variable-step Backtracking Strategy

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

The traditional greedy algorithm requires the signal sparsity as a known condition, and in most application scenarios, the signal sparsity is unknown, resulting in poor signal reconstruction accuracy. In order to solve such problems, this paper proposes an adaptive dual threshold matching pursuit algorithm based on a variable-step backtracking strategy (SBATMP). Firstly, the suboptimal set of atoms is selected through two adaptive thresholds. Then, through the variable-step backtracking strategy, the atoms are selected twice to obtain the optimal atomic set. The algorithm can improve the complete reconstruction rate of the signal under the condition of unknown sparsity, and the variable-step backtracking strategy can effectively reduce the complexity of the algorithm. Through the reconstruction simulation experiment, the one-dimensional signal reconstruction accuracy can reach 100\(\%\) under the condition that the ratio of the sparsity to the measured value is less than 0.25. The reconstruction speed can be improved by 0.021\(-\)0.186 s. For the two-dimensional image signal, the PSNR of the reconstructed image by the SBATMP algorithm is increased by 1.193–5.781dB, and the SSIM is increased by 0.0116\(-\)0.0645 under the compression ratio of 0.7.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Availability of data and materials

The datasets generated during and/or analyzed during the current study are available in the Baidu network disk repository, https://pan.baidu.com/s/1p3ZWZI7LBszWUdaCsTETHQ, extraction code: h9nu.

References

  1. R. Baraniuk, Compressive sensing. IEEE Signal Process. Magaz. 24, 118 (2007)

    Article  Google Scholar 

  2. T. Blumensath, M.E. Davies, On the difference between orthogonal matching pursuit and orthogonal least squares. Tech. Report. 24(2), 104–145 (2007)

    Google Scholar 

  3. W. Dai, O. Milenkovic, Subspace pursuit for compressive sensing: Closing the gap between performance and complexity (2008)

  4. D.L. Donoho, Y. Tsaig, I. Drori, J.L. Starck, Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit. IEEE Trans. Informat. Theory 58(2), 1094–1121 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Elad, M.A. Figueiredo, Y. Ma, On the role of sparse and redundant representations in image processing. PROCEED- IEEE 98(6), 972–982 (2010)

    Article  Google Scholar 

  6. Y.C. Eldar, G. Kutyniok, Compress. Sens. Theory Appl. (Compressed Sensing, Theory and Applications, 2012)

    Book  Google Scholar 

  7. S. Foucart, H. Rauhut, Restricted isometry property (Springer, New York, 2013)

    Book  Google Scholar 

  8. T. Han, K. Hao, X.-S. Tang, X. Cai, T. Wang, X. Liu, A compressed sensing network for acquiring human pressure information. IEEE Trans. Cognit. Developm. Syst. 14(2), 388–402 (2022)

    Article  Google Scholar 

  9. A. Hashemi, H. Vikalo, Sampling requirements and accelerated schemes for sparse linear regression with orthogonal least-squares (2016)

  10. A. Hashemi, H. Vikalo, Sparse linear regression via generalized orthogonal least-squares. IEEE 7, 1305–1309 (2016)

    Google Scholar 

  11. R. Hou, F. Li, Idpcnn: lterative denoising and projecting cnn for mri reconstruction. J Computat. Appl. Math. 406, 113973 (2022)

    Article  MATH  Google Scholar 

  12. W. Jian, L. Ping, Recovery of sparse signals using multiple orthogonal least squares. IEEE Trans. Signal Process. 65(8), 2049–2062 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Kim, J. Wang, L.T. Nguyen, B. Shim, Joint sparse recovery using signal space matching pursuit. IEEE Transa. Inform Theory. 99(3), 1–10 (2020)

    MathSciNet  MATH  Google Scholar 

  14. G. Li, X. Xiao, T. Jing-Tian, J. Li, Z. Hui-Jie, Z. Cong, Y. Fa-Bao, Near-source noise suppression of amt by compressive sensing and mathematical morphology filtering. Appl. Geophys. 14((004)), 581–589 (2017)

    Article  Google Scholar 

  15. M. Li, S. Zhang, F. Gao, P. Fan, O.A. Dobre, A new path division multiple access for the massive mimo-otfs networks. IEEE J. Select. Areas Commun. PP(99), 1–1 (2020)

    Google Scholar 

  16. M. Mishali, Y.C. Eldar, From theory to practice: Sub-nyquist sampling of sparse wideband analog signals. IEEE J. Select. Topic Signal Process. 4(2), 375–391 (2010)

    Article  Google Scholar 

  17. D. Needell, J.A. Tropp, Cosamp: iterative signal recovery from incomplete and inaccurate samples - sciencedirect. Appl. Computat. Harm. Analy. 26(3), 301–321 (2009)

    Article  MATH  Google Scholar 

  18. D. Needell, R. Vershynin, Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. IEEE J. Select. Topics. Signal Process. 4(2), 310–316 (2010)

    Article  Google Scholar 

  19. F. Parvaresh, H. Vikalo, S. Misra, B. Hassibi, Recovering sparse signals using sparse measurement matrices in compressed dna microarrays. IEEE J. Select. Topics Signal Process. 2(3), 275–285 (2008)

    Article  Google Scholar 

  20. M.K. Ramachandran, A. Chockalingam, Mimo-otfs in high-doppler fading channels: Signal detection and channel estimation. GLOBECOM 2018 - 2018 IEEE Global Communications Conference (2018)

  21. P. Raviteja, K.T. Phan, Y. Hong, Embedded pilot-aided channel estimation for otfs in delay-doppler channels. IEEE Trans. Vehicul. Technol. PP(99), 1–1 (2019)

    Google Scholar 

  22. S.K. Sahoo, A. Makur, Signal recovery from random measurements via extended orthogonal matching pursuit. IEEE Trans. Signal Process. 63(10), 2572–2581 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. W. Shen, L. Dai, J. An, P. Fan, Channel estimation for orthogonal time frequency space (otfs) massive mimo. IEEE Trans. Signal Process. PP(16), 1–1 (2019)

    MathSciNet  MATH  Google Scholar 

  24. Z. Yin, Z. Wu, J. Zhang, A deep network based on wavelet transform for image compressed sensing. Circuits Syst. Signal Process. 64, 1–20 (2022)

    Google Scholar 

  25. H. Zhao, J. Zhang, L. Zhang, Y. Liu, T. Zhang, Compressed sensing image restoration based on non-local low rank and weighted total variation. J. Electron. Informat. Technol. 41(8), 2025–2032 (2019)

    Google Scholar 

  26. Y. Zhu, S. WuZhen, W. Zhongcheng, Z. Jun, Multilevel wavelet-based hierarchical networks for image compressed sensing. Pattern Recognit. 129, 108758 (2022)

    Article  Google Scholar 

Download references

Acknowledgements

Acknowledgments are not compulsory. Where included they should be brief. Grant or contribution numbers may be acknowledged.

Author information

Authors and Affiliations

  1. College of Information and Communication Engineering, Harbin Engineering University, Harbin, 150001, Heilongjiang, People’s Republic of China

    Jianhong Xiang, Haoyuan Li, Liangang Qi & Hanyu Jiang

  2. Key Laboratory of Advanced Ship Communication and Information Technology, Harbin Engineering University, Harbin, People’s Republic of China

    Jianhong Xiang, Haoyuan Li, Liangang Qi & Hanyu Jiang

  3. China Electronic Technology Group(cetc-10), Chengdu, People’s Republic of China

    Yu Zhong

Authors
  1. Jianhong Xiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haoyuan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liangang Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yu Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hanyu Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liangang Qi.

Ethics declarations

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiang, J., Li, H., Qi, L. et al. Sparse Signal and Image Reconstruction Algorithm for Adaptive Dual Thresholds Matching Pursuit Based on Variable-step Backtracking Strategy. Circuits Syst Signal Process 42, 2132–2148 (2023). https://doi.org/10.1007/s00034-022-02177-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-022-02177-2

Keywords

Search

Navigation