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.
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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)
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)
Canh, T.N., Jeon, B.: Restricted structural random matrix for compressive sensing. Sign. Process. Image Commun. 90, 116017 (2021)
Liu, J., Wu, Q., Amin, M.: Multi-task bayesian compressive sensing exploiting signal structures. Sign. Process. 178, 107804 (2021)
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)
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)
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)
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)
Liu, J., Du, X.: A gradient projection method for the sparse signal reconstruction in compressive sensing. Appl. Anal. 97(12), 2122–2131 (2018)
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)
Zhang, M., Gao, Y., Sun, C., Blumenstein, M.: A robust matching pursuit algorithm using information theoretic learning. Pattern Recogn. 107, 107415 (2020)
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)
Lee, J., Choi, J.W., Shim, B.: Sparse signal recovery via tree search matching pursuit. J. Commun. Netw. 18(5), 699–712 (2016)
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)
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)
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)
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)
Metzler, C.A., Maleki, A., Baraniuk, R.G.: From denoising to compressed sensing. IEEE Trans. Inf. Theory 62(9), 5117–5144 (2016)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Shi, W., Jiang, F., Liu, S., Zhao, D.: Image compressed sensing using convolutional neural network. IEEE Trans. Image Process. 29, 375–388 (2020)
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).
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Zeng, C., Ye, J., Wang, Z. et al. Cascade neural network-based joint sampling and reconstruction for image compressed sensing. SIViP (2021). https://doi.org/10.1007/s11760-021-01955-w
- Compressed sensing
- Deep learning
- Image reconstruction