Skip to main content
SpringerLink
Log in

ICRICS: iterative compensation recovery for image compressive sensing

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

Closed-loop architecture is widely utilized in automatic control systems and attains distinguished dynamic and static performance. However, classical compressive sensing systems employ an open-loop architecture with separated sampling and reconstruction units. Therefore, a method of iterative compensation recovery for image compressive sensing is proposed by introducing a closed-loop framework into traditional compressive sensing systems. The proposed method depends on any existing approaches and upgrades their reconstruction performance by adding a negative feedback structure. Theoretical analysis of the negative feedback of compressive sensing systems is performed. An approximate mathematical proof of the effectiveness of the proposed method is also provided. Simulation experiments on more than 3 image datasets show that the proposed method is superior to 10 competing approaches in reconstruction performance. The maximum increment of the average peak signal-to-noise ratio is 4.36 dB, and the maximum increment of the average structural similarity is 0.034 based on one dataset. The proposed method based on a negative feedback mechanism can efficiently correct the recovery error in the existing image compressive sensing systems.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Data availability

Not applicable.

References

  1. Yang, Y., Sun, J., Li, H.B., Xu, Z.B.: DMM-CSNet: a deep learning approach for image compressive sensing. IEEE Trans. Pattern Anal. Mach. Intell. 42(3), 521–538 (2020). https://doi.org/10.1109/TPAMI.2018.2883941

    Article  Google Scholar 

  2. Shi, W.Z., Jiang, F., Liu, S.H., Teramoto, A., Zhao, D.B.: Image compressed sensing using convolutional neural network. IEEE Trans. Image Process. 29, 375–388 (2020). https://doi.org/10.1109/TIP.2019.2928136

    Article  MathSciNet  MATH  Google Scholar 

  3. Tavares, C.A., Santos, T.M.R., Lemes, N.H.T., dos Santos, J.P.C., Ferreira, J.C., Braga, J.P.: Solving ill-posed problems faster using fractional-order Hopfield neural network. J. Comput. Appl. Math. 381, 1–14 (2021). https://doi.org/10.1016/j.cam.2020.112984

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang, Y., Hofmann, B.: On the second-order asymptotical regularization of linear ill-posed inverse problems. Appl. Anal. 99(6), 1000–1025 (2020). https://doi.org/10.1080/00036811.2018.1517412

    Article  MathSciNet  MATH  Google Scholar 

  5. Adler, J., Oktem, O.: Solving ill-posed inverse problems using iterative deep neural networks. Inverse Probl. 33(12), 1–10 (2017). https://doi.org/10.1088/1361-6420/aa9581

    Article  MathSciNet  MATH  Google Scholar 

  6. Huang, W.K., Zhou, F.B., Zou, T., Lu, P.W., Xue, Y.H., Liang, J.J., Dong, Y.K.: Alternating positive and negative feedback control model based on catastrophe theories. Mathematics 9(22), 1–19 (2021). https://doi.org/10.3390/math9222878

    Article  Google Scholar 

  7. Li, L.X., Fang, Y., Liu, L.W., Peng, H.P., Kurths, J., Yang, Y.X.: Overview of compressed sensing: sensing model, reconstruction algorithm, and its applications. Appl. Sci. Basel 10(17), 1–19 (2020). https://doi.org/10.3390/app10175909

    Article  Google Scholar 

  8. Monika, R., Samiappan, D., Kumar, R.: Adaptive block compressed sensing—a technological analysis and survey on challenges, innovation directions and applications. Multimed. Tools Appl. 80(3), 4751–5476 (2021). https://doi.org/10.1007/s11042-020-09932-0

    Article  Google Scholar 

  9. Chen, Q.P., Shah, N.J., Worthoff, W.A.: Compressed sensing in sodium magnetic resonance imaging: techniques, applications, and future prospects. J. Mag. Reson. Imaging 55(5), 1340–1356 (2022). https://doi.org/10.1002/jmri.28029

    Article  Google Scholar 

  10. Bustin, A., Fuin, N., Botnar, R.M., Prieto, C.: From compressed-sensing to artificial intelligence-based cardiac MRI reconstruction. Front. Cardiovasc. Med. 7, 1–19 (2020). https://doi.org/10.3389/fcvm.2020.00017

    Article  Google Scholar 

  11. Chul, Y.J.: Compressed sensing MRI: a review from signal processing perspective. BMC Biomed. Eng. 1(8), 1–17 (2019). https://doi.org/10.1186/s42490-019-0006-z

    Article  Google Scholar 

  12. Yang, J.G., Jin, T., Xiao, C., Huang, X.T.: Compressed sensing radar imaging: fundamentals, challenges, and advances. Sensors 19(14), 1–19 (2019). https://doi.org/10.3390/s19143100

    Article  Google Scholar 

  13. Cao, B.H., Li, S.Z., Enze, C., Fan, M.B., Gan, F.X.: Progress in terahertz imaging technology. Spectrosc. Spect. Anal. 40(9), 2686–2695 (2020). https://doi.org/10.3964/j.issn.1000-0593(2020)09-2686-10

    Article  Google Scholar 

  14. Ke, J., Zhang, L.X., Zhou, Q.: Applications of compressive sensing in optical imaging. Acta Optica Sinica 40(1), 1–10 (2020). https://doi.org/10.3788/AOS202040.0111006

    Article  Google Scholar 

  15. Hirsch, L., Gonzalez, M.G., Vega, L.R.: A comparative study of time domain compressed sensing techniques for optoacoustic imaging. IEEE Latin Am. Trans. 20(6), 1018–1024 (2022). https://doi.org/10.1109/TLA.2022.9757745

    Article  Google Scholar 

  16. Wang, J., Tong, Z.S., Hu, C.Y., Xu, M.C., Huang, Z.F.: Some mathematical problems in ghost imaging. Acta Optica Sinica 40(1), 1–10 (2020). https://doi.org/10.3788/AOS202040.0111007

    Article  Google Scholar 

  17. Yousufi, M., Amir, M., Javed, U., Tayyib, M., Abdullah, S., Ullah, H., Qureshi, I.M., Alimgeer, K.S., Akram, M.W., Khan, K.B.: Application of compressive sensing to ultrasound images: a review. Biomed. Res. Int. 2019, 1–15 (2019). https://doi.org/10.1155/2019/7861651

    Article  Google Scholar 

  18. Xie, Y.R., Castro, D.C., Rubakhin, S.S., Sweedler, J.V., Lam, F.: Enhancing the throughput of FT mass spectrometry imaging using joint compressed sensing and subspace modeling. Anal. Chem. 94(13), 5335–5343 (2022). https://doi.org/10.1021/acs.analchem.1c05279

    Article  Google Scholar 

  19. Oiknine, Y., August, I., Farber, V., Gedalin, D., Stern, A.: Compressive sensing hyperspectral imaging by spectral multiplexing with liquid crystal. J. Imaging 5(1), 1–17 (2019). https://doi.org/10.3390/jimaging5010003

    Article  Google Scholar 

  20. Calisesi, G., Ghezzi, A., Ancora, D., D’Andrea, C., Valentini, G., Farina, A., Bassi, A.: Compressed sensing in fluorescence microscopy. Prog. Biophys. Mol. Biol. 168, 66–80 (2022). https://doi.org/10.1016/j.pbiomolbio.2021.06.004

    Article  Google Scholar 

  21. Monika, R., Dhanalakshmi, S., Kumar, R., Narayanamoorthi, R., Lai, K.W.: An efficient adaptive compressive sensing technique for underwater image compression in IoUT. Wirel. Netw. Early Access (2022). https://doi.org/10.1007/s11276-022-02921-1

    Article  Google Scholar 

  22. Edgar, M.P., Gibson, G.M., Padgett, M.J.: Principles and prospects for single-pixel imaging. Nat. Photon. 13(1), 13–20 (2019). https://doi.org/10.1038/s41566-018-0300-7

    Article  Google Scholar 

  23. Xiao, X.Y., Chen, L.Y., Zhang, X.Z., Wang, C., Lan, R.J., Ren, C., Cao, D.Z.: Review on single-pixel imaging and its probability statistical analysis. Laser Optoelectron. Progress 58(10), 1–10 (2021). https://doi.org/10.3788/L0P202158.1011018

    Article  Google Scholar 

  24. Gibson, G.M., Johnson, S.D., Padgett, M.J.: Single-pixel imaging 12 years on: a review. Opt. Express 28(19), 28190–28208 (2020). https://doi.org/10.1364/OE.403195

    Article  Google Scholar 

  25. Zanotto, L., Piccoli, R., Dong, J.L., Morandotti, R., Razzari, L.: Single-pixel terahertz imaging: a review. Opto Electron. Adv. 3(9), 1–15 (2020). https://doi.org/10.29026/oea.2020.200012

    Article  Google Scholar 

  26. Liu, F., Yao, X.R., Liu, X.F., Zhai, G.J.: Single-photon time-resolved imaging spectroscopy based on compressed sensing. Laser Optoelectron. Progress 58(10), 1–10 (2021). https://doi.org/10.3788/LOP202158.1011016

    Article  Google Scholar 

  27. Zhang, M.L.: Compressive sensing acquisition with application to Marchenko imaging. Pure Appl. Geophys. Early Access (2022). https://doi.org/10.1007/s00024-022-03029-5

    Article  Google Scholar 

  28. Ravishankar, S., Ye, J.C., Fessler, J.A.: Image reconstruction: from sparsity to data-adaptive methods and machine learning. Proc. IEEE 108(1), 86–109 (2020). https://doi.org/10.1109/JPROC.2019.2936204

    Article  Google Scholar 

  29. Xie, Y.T., Li, Q.Z.: A review of deep learning methods for compressed sensing image reconstruction and its medical applications. Electronics 11(4), 586 (2022). https://doi.org/10.3390/electronics11040586

    Article  MathSciNet  Google Scholar 

  30. Saideni, W., Helbert, D., Courreges, F., Cances, J.P.: An overview on deep learning techniques for video compressive sensing. Appl. Sci. BASEL 12(5), 2734 (2022). https://doi.org/10.3390/app12052734

    Article  Google Scholar 

  31. Khosravy, M., Cabral, T.W., Luiz, M.M., Gupta, N., Crespo, R.G.: Random acquisition in compressive sensing: a comprehensive overview. Int. J. Amb. Comput. Intell. 12(3), 140–165 (2021). https://doi.org/10.4018/IJACI.2021070107

    Article  Google Scholar 

  32. Mishra, I., Jain, S.: Soft computing based compressive sensing techniques in signal processing: a comprehensive review. J. Intell. Syst. 30(1), 312–326 (2021). https://doi.org/10.1515/jisys-2019-0215

    Article  Google Scholar 

  33. Chen, Y.T., Schonlieb, C.B., Lio, P., Leiner, T., Dragotti, P.L., Wang, G., Rueckert, D., Firmin, D., Yang, G.: AI-based reconstruction for fast MRI-a systematic review and meta-analysis. Proc. IEEE 110(2), 224–245 (2022). https://doi.org/10.1109/JPROC.2022.3141367

    Article  Google Scholar 

  34. Zhang, M.L., Zhang, M.Y., Zhang, F., Chaddad, A., Evans, A.: Robust brain MR image compressive sensing via re-weighted total variation and sparse regression. Magn. Reson. Imaging 85, 271–286 (2022). https://doi.org/10.1016/j.mri.2021.10.031

    Article  Google Scholar 

  35. Zhang, J.C., Han, L.L., Sun, J.Z., Wang, Z.K., Xu, W.L., Chu, Y.H., Xia, L., Jiang, M.F.: Compressed sensing based dynamic MR image reconstruction by using 3D-total generalized variation and tensor decomposition: k-t TGV-TD. BMC Med. Imaging 22(1), 1–10 (2022). https://doi.org/10.1186/s12880-022-00826-1

    Article  Google Scholar 

  36. Yin, Z., Shi, W.Z., Wu, Z.C., Zhang, J.: Multilevel wavelet-based hierarchical networks for image compressed sensing. Pattern Recogn. 129, 1–12 (2022). https://doi.org/10.1016/j.patcog.2022.108758

    Article  Google Scholar 

  37. Yin, Z., Wu, Z.C., Zhang, J.: A deep network based on wavelet transform for image compressed sensing. Circuits Syst. Signal Process. Early Access (2022). https://doi.org/10.1007/s00034-022-02058-8

    Article  Google Scholar 

  38. Lv, M.J., Ma, L., Ma, J.C., Chen, W.F., Yang, J., Ma, X.Y., Cheng, Q.: Fast, super-resolution sparse inverse synthetic aperture radar imaging via continuous compressive sensing. IET Signal Proc. 16(3), 310–326 (2022). https://doi.org/10.1049/sil2.12092

    Article  Google Scholar 

  39. Sun, M., Tao, J.X., Ye, Z.F., Qiu, B.S., Xu, J.Z., Xi, C.F.: An algorithm combining analysis-based blind compressed sensing and nonlocal low-rank constraints for MRI reconstruction. Curr. Med. Imaging Rev. 15(3), 281–291 (2019). https://doi.org/10.2174/1573405614666180130151333

    Article  Google Scholar 

  40. Li, H.G.: Compressive domain spatial-temporal difference saliency-based realtime adaptive measurement method for video recovery. IET Image Proc. 13(11), 2008–2017 (2019). https://doi.org/10.1049/iet-ipr.2019.0116

    Article  Google Scholar 

  41. Suantai, S., Noor, M.A., Kankam, K., Cholamjiak, P.: Novel forward–backward algorithms for optimization and applications to compressive sensing and image inpainting. Adv. Differ. Equ. 2021(1), 1–22 (2021). https://doi.org/10.1186/s13662-021-03422-9

    Article  MathSciNet  MATH  Google Scholar 

  42. Mardani, M., Gong, E.H., Cheng, J.Y., Vasanawala, S.S., Zaharchuk, G., Xing, L., Pauly, J.M.: Deep generative adversarial neural networks for compressive sensing MRI. IEEE Trans. Med. Imaging 38(1), 167–179 (2019). https://doi.org/10.1109/TMI.2018.2858752

    Article  Google Scholar 

  43. Li, W.Z., Zhu, A.H., Xu, Y.G., Yin, H.S., Hua, G.: A fast multi-scale generative adversarial network for image compressed sensing. Entropy 24(6), 1–16 (2022). https://doi.org/10.3390/e24060775

    Article  Google Scholar 

  44. Zeng, G.S., Guo, Y., Zhan, J.Y., Wang, Z., Lai, Z.Y., Du, X.F., Qu, X.B., Guo, D.: A review on deep learning MRI reconstruction without fully sampled k-space. BMC Med. Imaging 21(1), 1–11 (2021). https://doi.org/10.1186/s12880-021-00727-9

    Article  Google Scholar 

  45. Han, Y., Sunwoo, L., Ye, J.C.: k-space deep learning for accelerated MRI. IEEE Trans. Med. Imaging 39(2), 377–386 (2020). https://doi.org/10.1109/TMI.2019.2927101

    Article  Google Scholar 

  46. Kravets, V., Stern, A.: Progressive compressive sensing of large images with multiscale deep learning reconstruction. Sci. Rep. 12(1), 1–10 (2022). https://doi.org/10.1038/s41598-022-11401-7

    Article  Google Scholar 

  47. Wang, Z.B., Qin, Y.L., Zheng, H., Wang, R.F.: Multiscale deep network for compressive sensing image reconstruction. J. EIectron. Imaging 31(1), 1–10 (2022). https://doi.org/10.1117/1.JEI.31.1.013025

    Article  Google Scholar 

  48. Gan, H.P., Gao, Y., Liu, C.Y., Chen, H.W., Zhang, T., Liu, F.: AutoBCS: block-based image compressive sensing with data-driven acquisition and noniterative reconstruction. IEEE Trans. Cybern. Early Access (2021). https://doi.org/10.1109/TCYB.2021.3127657

    Article  Google Scholar 

  49. You, D., Zhang, J., Xie, J.F., Chen, B., Ma, S.W.: COAST: controllable arbitrary-sampling network for compressive sensing. IEEE Trans. Image Process. 30, 6066–6080 (2021). https://doi.org/10.1109/TIP.2021.3091834

    Article  MathSciNet  Google Scholar 

  50. Song, J.C., Chen, B., Zhang, J.: Memory-augmented deep unfolding network for compressive sensing. In: Proceedings of ACM MM, Chengdu, Sichuan, China, pp. 1–10 (2021)

  51. Zhang, J., Ghanem, B.: ISTA-Net: interpretable optimization-inspired deep network for image compressive sensing. In: Proceedings of CVPR, Salt Lake City, UT, USA, pp.1828–1837 (2018)

  52. You, D., Xie, J.F., Zhang, J.: ISTA-Net++: flexible deep unfolding network for compressive sensing. In: Proceedings of ICME, Virtual, pp. 1–6 (2021)

  53. Zhang, J., Zhao, C., Gao, W.: Optimization-inspired compact deep compressive sensing. IEEE J. Select. Top. Signal Process. 14(4), 765–774 (2020). https://doi.org/10.1109/JSTSP.2020.2977507

    Article  Google Scholar 

  54. Zhang, J., Zhang, Z.Y., Xie, J.F., Zhang, Y.B.: High-throughput deep unfolding network for compressive sensing MRI. IEEE J. Select. Top. Signal Process. 16(4), 750–761 (2022). https://doi.org/10.1109/JSTSP.2022.3170227

    Article  Google Scholar 

  55. Zhang, Z.H., Liu, Y.P., Liu, J.N., Wen, F., Zhu, C.: AMP-Net: denoising-based deep unfolding for compressive image sensing. IEEE Trans. Image Process. 30, 1487–1500 (2021). https://doi.org/10.1109/TIP.2020.3044472

    Article  MathSciNet  Google Scholar 

  56. GitHub Inc.: MTC-CSNet: marrying transformer and convolution for image compressed sensing (2022). Available: https://github.com/EchoSPLab/MTC-CSNet

  57. GitHub Inc.: TCS-Net: from patch to pixel: a transformer-based hierarchical framework for compressive image sensing (2022). Available: https://github.com/CompressiveLab/TCS-Net

  58. GitHub Inc.: TransCS: a transformer-based hybrid architecture for image compressed sensing (2022). Available: https://github.com/myheuf/TransCS

  59. Harada, Y., Kanemoto, D., Inoue, T., Maida, O., Hirose, T.: Image quality improvement for capsule endoscopy based on compressed sensing with K-SVD dictionary learning. IEICE Trans. Fund. Electron. Commun. Comput. Sci. E105A(4), 743–747 (2022). https://doi.org/10.1587/transfun.2021EAL2033

    Article  Google Scholar 

  60. Ueki, W., Nishii, T., Umehara, K., Ota, J., Higuchi, S., Ohta, Y., Nagai, Y., Murakawa, K., Ishida, T., Fukuda, T.: Generative adversarial network-based post-processed image super-resolution technology for accelerating brain MRI: comparison with compressed sensing. ACTA Adiologica Early Access (2022). https://doi.org/10.1177/02841851221076330

    Article  Google Scholar 

  61. Fang, C.J., Chen, J.Y., Chen, S.L.: Image denoising algorithm of compressed sensing based on alternating direction method of multipliers. Int. J. Model. Simul. Sci. Comput. 13(01), 1–10 (2022). https://doi.org/10.1142/S179396232250009X

    Article  Google Scholar 

  62. El, M.A., Ouahabi, A., Moulay, M.S.: Image denoising using a compressive sensing approach based on regularization constraints. Sensors 22(6), 1–22 (2022). https://doi.org/10.3390/s22062199

    Article  Google Scholar 

  63. Pham, C.D.K., Yang, J., Zhou, J.J.: CSIE-M: compressive sensing image enhancement using multiple reconstructed signals for internet of things surveillance systems. IEEE Trans. Ind. Inform. 18(2), 1271–1281 (2022). https://doi.org/10.1109/TII.2021.3082498

    Article  Google Scholar 

  64. Zhang, Y., Mao, X., Wang, J., Liu, W.: DEMO: a flexible deartifacting module for compressed sensing MRI. IEEE J. Select. Top. Signal Process. 16(4), 725–736 (2022). https://doi.org/10.1109/JSTSP.2022.3158057

    Article  Google Scholar 

  65. Fornasier, M., Rauhut, H.: Iterative thresholding algorithms. Appl. Comput. Harmon. Anal. 25, 187–208 (2008). https://doi.org/10.1016/j.acha.2007.10.005

    Article  MathSciNet  MATH  Google Scholar 

  66. Upadhyaya, V., Salim, M.: Joint approach based quality assessment scheme for compressed and distorted images. Chaos Solitons Fractals 160, 112278 (2022). https://doi.org/10.1016/j.chaos.2022.112278

    Article  Google Scholar 

Download references

Acknowledgements

The authors would very much like to thank all the authors of the 10 competing approaches for selflessly releasing their source codes of image compressive sensing on the GitHub website. The open-source codes allow us to easily implement the proposed method depending on the competing approaches.

Funding

This research received no external funding.

Author information

Authors and Affiliations

  1. School of Information Engineering, Yangzhou University, Yangzhou, 225127, China

    Honggui Li

  2. LISITE Research Laboratory, Institut Supérieur d’Électronique de Paris, 75006, Paris, France

    Maria Trocan

  3. Polystim Neurotech Laboratory, Polytechnique Montreal, Montreal, H3T1J4, Canada

    Mohamad Sawan

  4. School of Engineering, Westlake University, Hangzhou, 310024, China

    Mohamad Sawan

  5. Laboratoire d’Informatique de Paris 6, Sorbonne University, 75020, Paris, France

    Dimitri Galayko

Authors
  1. Honggui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maria Trocan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohamad Sawan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dimitri Galayko
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

HL and MT conceptualized the study; HL and DG helped in methodology; HL wrote the manuscript; MS supervised the study. All authors have read and agreed to the published version of the manuscript.

Corresponding author

Correspondence to Honggui Li.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Ethical approval

Not applicable.

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

Li, H., Trocan, M., Sawan, M. et al. ICRICS: iterative compensation recovery for image compressive sensing. SIViP 17, 2953–2969 (2023). https://doi.org/10.1007/s11760-023-02516-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-023-02516-z

Keywords

Search

Navigation