Cascade neural network-based joint sampling and reconstruction for image compressed sensing


Most deep learning-based compressed sensing (DCS) algorithms adopt a single neural network for signal reconstruction and fail to jointly consider the influences of the sampling operation for reconstruction. In this paper, we propose a unified framework, which jointly considers the sampling and reconstruction process for image compressive sensing based on well-designed cascade neural networks. Two sub-networks, which are the sampling sub-network and the reconstruction sub-network, are included in the proposed framework. In the sampling sub-network, an adaptive fully connected layer instead of the traditional random matrix is used to mimic the sampling operator. In the reconstruction sub-network, a cascade network combining stacked denoising autoencoder (SDA) and convolutional neural network (CNN) is designed to reconstruct signals. The SDA is used to solve the signal mapping problem, and the signals are initially reconstructed. Furthermore, CNN is used to fully recover the structure and texture features of the image to obtain better reconstruction performance. Extensive experiments show that this framework outperforms many other state-of-the-art methods, especially at low sampling rates.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3


  1. 1.

    Gunasheela, S., Prasantha, H.: Compressed sensing for image compression: Survey of algorithms. In: Emerging Research in Computing, Information, Communication and Applications, pp. 507–517. Springer (2019)

  2. 2.

    Higham, C.F., Murray-Smith, R., Padgett, M.J., Edgar, M.P.: Deep learning for real-time single-pixel video. Sci. Rep. 8(1), 2369 (2018)

    Article  Google Scholar 

  3. 3.

    Canh, T.N., Jeon, B.: Restricted structural random matrix for compressive sensing. Sign. Process. Image Commun. 90, 116017 (2021)

    Article  Google Scholar 

  4. 4.

    Liu, J., Wu, Q., Amin, M.: Multi-task bayesian compressive sensing exploiting signal structures. Sign. Process. 178, 107804 (2021)

    Article  Google Scholar 

  5. 5.

    Gao, X., Zhang, J., Che, W., Fan, X., Zhao, D.: Block-based compressive sensing coding of natural images by local structural measurement matrix. In: 2015 Data Compression Conference, pp. 133–142 (2015)

  6. 6.

    Saha, T., Srivastava, S., Khare, S., Stanimirović, P.S., Petković, M.D.: An improved algorithm for basis pursuit problem and its applications. Appl. Math. Comput. 355, 385–398 (2019)

    MathSciNet  MATH  Google Scholar 

  7. 7.

    Li, C., Liu, X., Yu, K., Wang, X., Zhang, F.: Debiasing of seismic reflectivity inversion using basis pursuit de-noising algorithm. J. Appl. Geophys. 177, 104028 (2020)

    Article  Google Scholar 

  8. 8.

    Zhang, S., Xia, Y., Xia, Y., Wang, J.: Matrix-form neural networks for complex-variable basis pursuit problem with application to sparse signal reconstruction. IEEE Trans. Cybern. (2021)

  9. 9.

    Liu, J., Du, X.: A gradient projection method for the sparse signal reconstruction in compressive sensing. Appl. Anal. 97(12), 2122–2131 (2018)

    MathSciNet  Article  Google Scholar 

  10. 10.

    Lin, T., Ma, S., Ye, Y., Zhang, S.: An admm-based interior-point method for large-scale linear programming. Optim. Methods Softw. 1–36 (2020)

  11. 11.

    Zhang, M., Gao, Y., Sun, C., Blumenstein, M.: A robust matching pursuit algorithm using information theoretic learning. Pattern Recogn. 107, 107415 (2020)

  12. 12.

    Tirer, T., Giryes, R.: Generalizing cosamp to signals from a union of low dimensional linear subspaces. Appl. Comput. Harmon. Anal. 49(1), 99–122 (2020)

    MathSciNet  Article  Google Scholar 

  13. 13.

    Lee, J., Choi, J.W., Shim, B.: Sparse signal recovery via tree search matching pursuit. J. Commun. Netw. 18(5), 699–712 (2016)

    Article  Google Scholar 

  14. 14.

    Zarei, A., Asl, B.M.: Automatic seizure detection using orthogonal matching pursuit, discrete wavelet transform, and entropy based features of eeg signals. Comput. Biol. Med. 131, 104250 (2021)

    Article  Google Scholar 

  15. 15.

    Zhao, T., Wang, Y.: Differentiation of discrete data with unequal measurement intervals and quantification of uncertainty in differentiation using bayesian compressive sampling. Comput. Geotech. 122, 103537 (2020)

    Article  Google Scholar 

  16. 16.

    Xu, J., Wang, Y., Zhang, L.: Interpolation of extremely sparse geo-data by data fusion and collaborative bayesian compressive sampling. Comput. Geotech. 134, 104098 (2021)

    Article  Google Scholar 

  17. 17.

    Montoya-Noguera, S., Zhao, T., Hu, Y., Wang, Y., Phoon, K.K.: Simulation of non-stationary non-gaussian random fields from sparse measurements using bayesian compressive sampling and karhunen-loève expansion. Struct. Saf. 79, 66–79 (2019)

    Article  Google Scholar 

  18. 18.

    Metzler, C.A., Maleki, A., Baraniuk, R.G.: From denoising to compressed sensing. IEEE Trans. Inf. Theory 62(9), 5117–5144 (2016)

    MathSciNet  Article  Google Scholar 

  19. 19.

    Dong, W., Shi, G., Li, X., Ma, Y., Huang, F.: Compressive sensing via nonlocal low-rank regularization. IEEE Trans. Image Process. 23(8), 3618–3632 (2014)

    MathSciNet  Article  Google Scholar 

  20. 20.

    Tramel, E.W., Gabrié, M., Manoel, A., Caltagirone, F., Krzakala, F.: Deterministic and generalized framework for unsupervised learning with restricted boltzmann machines. Phys. Rev. X 8(4), 041006 (2018)

    Google Scholar 

  21. 21.

    Zhang, J., Ghanem, B.: Ista-net: Interpretable optimization-inspired deep network for image compressive sensing. In: 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 1828–1837 (2018)

  22. 22.

    Zhang, Z., Liu, Y., Liu, J., Wen, F., Zhu, C.: Amp-net: Denoising-based deep unfolding for compressive image sensing. IEEE Trans. Image Process. 30, 1487–1500 (2020)

    MathSciNet  Article  Google Scholar 

  23. 23.

    Yang, Y., Sun, J., Li, H., Xu, Z.: Admm-csnet: A deep learning approach for image compressive sensing. IEEE Trans. Pattern Anal. Mach. Intell. 42(3), 521–538 (2020)

    Article  Google Scholar 

  24. 24.

    Mousavi, A., Patel, A.B., Baraniuk, R.G.: A deep learning approach to structured signal recovery. In: 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton), pp. 1336–1343 (2015)

  25. 25.

    Mousavi, A., Baraniuk, R.G.: Learning to invert: Signal recovery via deep convolutional networks. In: 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 2272–2276 (2017)

  26. 26.

    Yao, H., Dai, F., Zhang, S., Zhang, Y., Tian, Q., Xu, C.: Dr2-net: Deep residual reconstruction network for image compressive sensing. Neurocomputing 359, 483–493 (2019)

    Article  Google Scholar 

  27. 27.

    Kulkarni, K., Lohit, S., Turaga, P., Kerviche, R., Ashok, A.: Reconnet: Non-iterative reconstruction of images from compressively sensed measurements. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 449–458 (2016)

  28. 28.

    Shi, W., Jiang, F., Liu, S., Zhao, D.: Image compressed sensing using convolutional neural network. IEEE Trans. Image Process. 29, 375–388 (2020)

    MathSciNet  Article  Google Scholar 

Download references


This work was supported by National Natural Science Foundation of China (Nos. 61901165, 61501199), Science and Technology Research Project of Hubei Education Department (No. Q20191406), Hubei Natural Science Foundation (No. 2017CFB683), Hubei Research Center for Educational Informationization Open Funding (No. HRCEI2020F0102), and Self-determined Research Funds of CCNU from the Colleges’ Basic Research and Operation of MOE (No. CCNU20ZT010).

Author information



Corresponding author

Correspondence to Zhifeng Wang.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zeng, C., Ye, J., Wang, Z. et al. Cascade neural network-based joint sampling and reconstruction for image compressed sensing. SIViP (2021).

Download citation


  • Compressed sensing
  • Deep learning
  • CNN
  • SDA
  • Image reconstruction