Abstract
In this paper, we study how to achieve sparse sampling and high-quality reconstruction of natural images, and propose an interpretable deep network based on proximal gradient descent (PGD), dubbed AICS-Net, while performing joint constraint optimization of adaptive sparse sampling and reconstruction of images. AICS-Net consists of a sampling sub-network, an initialization sub-network and a recovery sub-network. The sampling sub-network achieves adaptive sampling of images, and the initialization sub-network uses the transpose of the measurement matrix to achieve initialized reconstruction of images. Integrating the gradient estimation strategy into the gradient descent step of the PGD algorithm in the recovery sub-network, then an optimization-based staged network structure is constructed. Moreover, to increase the hardware reputability of AICS-Net, binary constraint and orthogonal constraint are added to the measurement matrix. To improve the quality and visual effect of reconstructed images, a loss function is created to account for the color and texture differences between images. Experimental results show that the proposed AICS-Net can achieve better image reconstruction while maintaining reconstruction speed compared to existing state-of-the-art network-based CS algorithms, especially at low CS ratios. When the CS ratio is 1%, for Set11, PNSR and SSIM can be improved by at least 6.63% and 7.57%, respectively.
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References
Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006). https://doi.org/10.1109/TIT.2006.871582
Candès, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006). https://doi.org/10.1109/TIT.2005.862083
Liutkus, A., Martina, D., Popoff, S., Chardon, G., Katz, O., Lerosey, G., Gigan, S., Daudet, L., Carron, I.: Imaging with nature: compressive imaging using a multiply scattering medium. Sci. Rep. 4(4), 5552 (2014). https://doi.org/10.1038/srep05552
Sekar, K., Devi, K.S., Srinivasan, P.: Compressed tensor completion: a robust technique for fast and efficient data reconstruction in wireless sensor networks. IEEE Sens. J. 22(11), 10794–10807 (2022). https://doi.org/10.1109/JSEN.2022.3169226
Roohi, S.F., Zonoobi, D., Kassim, A.A., Jaremko, J.L.: Multi-dimensional low rank plus sparse decomposition for reconstruction of under-sampled dynamic mri. Pattern Recognit. 63, 667–679 (2016). https://doi.org/10.1016/j.patcog.2016.09.040
Rani, M., Dhok, S.B., Deshmukh, R.B.: A systematic review of compressive sensing: concepts implementations and applications. IEEE Access 6, 4875–4894 (2018). https://doi.org/10.1109/ACCESS.2018.2793851
Wu, Z., Zhang, L., Liu, H., Kou, N.: Enhancing microwave metamaterial aperture radar imaging performance with rotation synthesis. IEEE Sens. J. 16(22), 8035–8043 (2016). https://doi.org/10.1109/JSEN.2016.2609200
Jiang, W., Tong, F., Zheng, S., Cao, X.: Estimation of underwater acoustic channel with hybrid sparsity via static-dynamic discriminative compressed sensing. IEEE Sens. J. 20(23), 14548–14558 (2020). https://doi.org/10.1109/JSEN.2020.3008163
Nath, S., Mala, C.: Thermal image processing-based intelligent technique for object detection. Signal Image Video Process. 16(6), 1631–1639 (2022). https://doi.org/10.1007/s11760-021-02118-7
Lu, Z., Chen, Y.: Single image super-resolution based on a modified u-net with mixed gradient loss. Signal Image Video Process. 16(5), 1143–1151 (2022). https://doi.org/10.1007/s11760-021-02063-5
Lee, D.-H., Chen, K.-L., Liou, K.-H., Liu, C.-L., Liu, J.-L.: Deep learning and control algorithms of direct perception for autonomous driving. Appl. Intell. 51, 237–247 (2021). https://doi.org/10.1007/s10489-020-01827-9
Lyu, P., Wei, M., Wu, Y.: High-precision and real-time visual tracking algorithm based on the siamese network for autonomous driving. Signal Image Video Process. 17(4), 1235–1243 (2022). https://doi.org/10.1007/s11760-022-02331-y
Shi, Y., Feng, D., Cheng, Y., Boswas, S.: A natural language-inspired multilabel video streaming source identification method based on deep neural networks. Signal Image Video Process. 15(6), 1161–1168 (2021). https://doi.org/10.1007/s11760-020-01844-8
Lata, K., Singh, P., Dutta, K.: Mention detection in coreference resolution: survey. Appl. Intell. 52, 9816–9860 (2022). https://doi.org/10.1007/s10489-021-02878-2
Lata, K., Singh, P., Dutta, K.: Mention detection in coreference resolution: survey. Appl. Intell. 52, 9816–9860 (2022). https://doi.org/10.1007/s10489-021-02878-2
Zhang, J., Ghanem, B.: ISTA-Net: Interpretable optimization-inspired deep network for image compressive sensing. In: Paper presented at 2018 IEEE/CVF conference on computer vision and pattern recognition, Salt Lake City, UT, USA, 18–23 June 2018 (2018)
Yao, H., Dai, F., Zhang, D., Ma, Y., Zhang, S., Zhang, Y., Tian, Q.: DR2-Net: deep residual reconstruction network for image compressive sensing. Neurocomputing 359, 483–493 (2019). https://doi.org/10.1016/j.neucom.2019.05.006
Kulkarni, K., Lohit, S., Turaga, P., Kerviche, R., Ashok, A.: ReconNet: Non-iterative reconstruction of images from compressively sensed measurements. In: Paper presented at 2016 IEEE/CVF conference on computer vision and pattern recognition, Las Vegas, NV, USA, 27–30 June 2016 (2016)
Canh, T.N., Jeon, B.: Multi-scale deep compressive imaging. IEEE Trans. Comput. Imaging 7, 86–97 (2021). https://doi.org/10.1109/TCI.2020.3034433
Joseph, G., Kafle, S., Varshney, P.K.: One-bit compressed sensing using generative models. In: Paper presented at 2020 IEEE international conference on acoustics, speech and signal processing, Barcelona, Spain, 04–08 May 2020 (2020)
Chen, Y., Tan, B., Wu, J., Zhang, Z., Ren, H.: A deep image coding scheme with generative network to learn from correlated images. IEEE Trans. Multimed. 23, 2235–2244 (2021). https://doi.org/10.1109/TMM.2021.3087011
Zheng, B., Zhang, J., Sun, G., Ren, X.: EnGe-CSNet: A trainable image compressed sensing model based on variational encoder and generative networks. Electron. 10(9), 1089–2002 (2021). https://doi.org/10.3390/electronics10091089
Bora, A., Jalal, A., Price, E., Dimakis, A.G.: Compressed sensing using generative models. arxiv:1703.03208v1 (2017)
Zhang, J., Zhao, C., Gao, W.: Optimization-inspired compact deep compressive sensing. IEEE J. Sel. Top. Signal Process. 14(4), 765–774 (2020). https://doi.org/10.1109/JSTSP.2020.2977507
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 (2021). https://doi.org/10.1109/TIP.2020.3044472
Sun, Y., Chen, J., Liu, Q., Liu, B., Guo, G.: Dual-path attention network for compressed sensing image reconstruction. IEEE Trans. Image Process. 29, 9482–9495 (2020). https://doi.org/10.1109/TIP.2020.3023629
Shi, W., Jiang, F., Liu, S., Zhao, D.: Image compressed sensing using convolutional neural network. IEEE Trans. Image Process. 29, 375–388 (2020). https://doi.org/10.1109/TIP.2019.2928136
Shi, W., Caballero, J., Huszár, F., Totz, J., Aitken, A.P., Bishop, R., Rueckert, D., Wang, Z.: Real-time single image and video super-resolution using an efficient sub-pixel convolutional neural network. In: Paper presented at 2016 IEEE/CVF conference on computer vision and pattern recognition, Las Vegas, NV, USA, 27–30 June 2016 (2016)
Parikh, N., Boyd, S.: Proximal algorithms. Found. Trends Optim. 1(3), 127–239 (2014). https://doi.org/10.1561/2400000003
Candès, E.J., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005). https://doi.org/10.1109/TIT.2005.858979
Candès, E.J.: The restricted isometry property and its implications for compressed sensing. C. R. Math. 346(9), 589–592 (2008). https://doi.org/10.1016/j.crma.2008.03.014
Mallat, S.G., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Process. 41(12), 3397–3415 (1993). https://doi.org/10.1109/78.258082
Needell, D., Tropp, J.A.: CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26(3), 301–321 (2009). https://doi.org/10.1016/j.acha.2008.07.002
Dai, W., Milenkovic, O.: Subspace pursuit for compressive sensing signal reconstruction. IEEE Trans. Inf. Theory 55(5), 2230–2249 (2009). https://doi.org/10.1109/TIT.2009.2016006
Donoho, D.L.: De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41(3), 613–627 (1995). https://doi.org/10.1109/18.382009
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183–202 (2009). https://doi.org/10.1137/080716542
Blumensath, T., Davies, M.E.: Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27(3), 265–274 (2009). https://doi.org/10.1016/j.acha.2009.04.002
Afonso, M.V., Bioucas-Dias, J.M., Figueiredo, M.A.T.: An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Trans. Image Process. 20(3), 681–695 (2011). https://doi.org/10.1109/TIP.2010.2076294
Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001). https://doi.org/10.1137/S003614450037906X
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). https://doi.org/10.1109/TPAMI.2018.2883941
Hu, J., Shen, L., Albanie, S., Sun, G., Wu, E.: Squeeze-and-excitation networks. IEEE Trans. Pattern Anal. Mach. Intell. 42(8), 2011–2023 (2020). https://doi.org/10.1109/TPAMI.2019.2913372
Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Paper presented at IEEE international conference on computer vision, Vancouver, BC, Canada, 07–14 July 2001 (2001)
Huang, J.-B., Singh, A., Ahuja, N.: Single image super-resolution from transformed self-exemplars. In: Paper presented at 2015 IEEE conference on computer vision and pattern recognition, Boston, MA, USA, 07–12 June 2015 (2015)
Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 898–916 (2011). https://doi.org/10.1109/TPAMI.2010.161
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004). https://doi.org/10.1109/TIP.2003.819861
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The authors would like to thank Tianjin Key Laboratory of Optoelectronic Sensor and Sensor Network Technology for providing working conditions.
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This work was supported by Natural Science Foundation of Tianjin City (No.21JCZDJC00340) and National Natural Science Foundation of China (No.61901233).
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Material preparation, data collection and analysis were performed by RN, BZ and LW. The first draft of the manuscript was written by RN, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Nan, R., Sun, G., Zheng, B. et al. Adaptive deep learning network for image reconstruction of compressed sensing. SIViP 18, 1463–1475 (2024). https://doi.org/10.1007/s11760-023-02879-3
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DOI: https://doi.org/10.1007/s11760-023-02879-3