Abstract
In recent years, Deep Neural Networks (DNN) have empowered Compressed Sensing (CS) substantially and have achieved high reconstruction quality and speed far exceeding traditional CS methods. However, there are still lots of issues to be further explored before it can be practical enough. There are mainly two challenging problems in CS, one is to achieve efficient data sampling, and the other is to reconstruct images with high-quality. To address the two challenges, this paper proposes a novel Runge-Kutta Convolutional Compressed Sensing Network (RK-CCSNet). In the sensing stage, RK-CCSNet applies Sequential Convolutional Module (SCM) to gradually compact measurements through a series of convolution filters. In the reconstruction stage, RK-CCSNet establishes a novel Learned Runge-Kutta Block (LRKB) based on the famous Runge-Kutta methods, reformulating the process of image reconstruction as a discrete dynamical system. Finally, the implementation of RK-CCSNet achieves state-of-the-art performance on influential benchmarks with respect to prestigious baselines, and all the codes are available at https://github.com/rkteddy/RK-CCSNet.
This research is supported by National Natural Science Foundation of China grant No. 61772232.
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http://vllab.ucmerced.edu/wlai24/LapSRN/.
References
Arbelaez, P., Maire, M., Fowlkes, C.C., Malik, J.: Contour detection and hierarchical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 33(5), 898–916 (2011)
August, Y., Vachman, C., Rivenson, Y., Stern, A.: Compressive hyperspectral imaging by random separable projections in both the spatial and the spectral domains. Appl. Opt. 52(10), D46–D54 (2013)
Candès, E.J.: The restricted isometry property and its implications for compressed sensing. C.R. Math. 346(9–10), 589–592 (2008)
Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001)
Donoho, D.L., et al.: Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)
Du, J., Xie, X., Wang, C., Shi, G., Xu, X., Wang, Y.: Fully convolutional measurement network for compressive sensing image reconstruction. Neurocomputing 328, 105–112 (2019)
Duarte, M.F., et al.: Single-pixel imaging via compressive sampling. IEEE Signal Process. Mag. 25(2), 83–91 (2008)
Weinan, E.: A proposal on machine learning via dynamical systems. Commun. Math. Stat. 5(1), 1–11 (2017). https://doi.org/10.1007/s40304-017-0103-z
Gehm, M., John, R., Brady, D., Willett, R., Schulz, T.: Single-shot compressive spectral imaging with a dual-disperser architecture. Opt. Express 15(21), 14013–14027 (2007)
He, K., Zhang, X., Ren, S., Sun, J.: Delving deep into rectifiers: surpassing human-level performance on ImageNet classification. In: 2015 IEEE International Conference on Computer Vision, ICCV 2015, Santiago, Chile, 7–13 December 2015, pp. 1026–1034. IEEE Computer Society (2015)
He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: 2016 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016, Las Vegas, NV, USA, 27–30 June 2016, pp. 770–778. IEEE Computer Society (2016)
He, K., Zhang, X., Ren, S., Sun, J.: Identity mappings in deep residual networks. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9908, pp. 630–645. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46493-0_38
Hitomi, Y., Gu, J., Gupta, M., Mitsunaga, T., Nayar, S.K.: Video from a single coded exposure photograph using a learned over-complete dictionary. In: Metaxas, D.N., Quan, L., Sanfeliu, A., Gool, L.V. (eds.) IEEE International Conference on Computer Vision, ICCV 2011, Barcelona, Spain, 6–13 November 2011, pp. 287–294. IEEE Computer Society (2011)
Horé, A., Ziou, D.: Image quality metrics: PSNR vs. SSIM. In: 20th International Conference on Pattern Recognition, ICPR 2010, Istanbul, Turkey, 23–26 August 2010, pp. 2366–2369 (2010)
Huang, G., Liu, Z., van der Maaten, L., Weinberger, K.Q.: Densely connected convolutional networks. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, 21–26 July 2017, pp. 2261–2269. IEEE Computer Society (2017)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. In: 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, 7–9 May 2015, Conference Track Proceedings (2015)
Kulkarni, K., Lohit, S., Turaga, P.K., 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 2016, Las Vegas, NV, USA, 27–30 June 2016, pp. 449–458. IEEE Computer Society (2016)
Lambert, J.D.: Numerical Methods for Ordinary Differential Systems: The Initial Value Problem. Wiley, New York (1991)
Li, C.: An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing. Master’s thesis, Rice University (2010)
Lu, Y., Zhong, A., Li, Q., Dong, B.: Beyond finite layer neural networks: bridging deep architectures and numerical differential equations. In: Dy, J.G., Krause, A. (eds.) Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholmsmässan, Stockholm, Sweden, 10–15 July 2018. Proceedings of Machine Learning Research, vol. 80, pp. 3282–3291. PMLR (2018)
Lustig, M., Donoho, D.L., Santos, J.M., Pauly, J.M.: Compressed sensing MRI. IEEE Signal Process. Mag. 25(2), 72 (2008)
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 2017, New Orleans, LA, USA, 5–9 March 2017, pp. 2272–2276. IEEE (2017)
Mousavi, A., Dasarathy, G., Baraniuk, R.G.: A data-driven and distributed approach to sparse signal representation and recovery. In: International Conference on Learning Representations (2018)
Mousavi, A., Patel, A.B., Baraniuk, R.G.: A deep learning approach to structured signal recovery. In: 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015, Allerton Park & Retreat Center, Monticello, IL, USA, 29 September–2 October 2015, pp. 1336–1343. IEEE (2015)
Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by error propagation, pp. 318–362. MIT Press, Cambridge (1986)
Sauer, T.: Numerical Analysis, 2nd edn. Addison-Wesley Publishing Company, USA (2011)
Shelhamer, E., Long, J., Darrell, T.: Fully convolutional networks for semantic segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 39(4), 640–651 (2017)
Shi, W., Jiang, F., Liu, S., Zhao, D.: Scalable convolutional neural network for image compressed sensing. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, 16–20 June 2019, pp. 12290–12299. Computer Vision Foundation/IEEE (2019)
Shi, W., Jiang, F., Liu, S., Zhao, D.: Image compressed sensing using convolutional neural network. IEEE Trans. Image Process. 29, 375–388 (2020)
Shi, W., Jiang, F., Zhang, S., Zhao, D.: Deep networks for compressed image sensing. In: 2017 IEEE International Conference on Multimedia and Expo, ICME 2017, Hong Kong, China, 10–14 July 2017, pp. 877–882. IEEE Computer Society (2017)
Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)
Xu, K., Zhang, Z., Ren, F.: LAPRAN: a scalable laplacian pyramid reconstructive adversarial network for flexible compressive sensing reconstruction. In: Ferrari, V., Hebert, M., Sminchisescu, C., Weiss, Y. (eds.) ECCV 2018. LNCS, vol. 11214, pp. 491–507. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01249-6_30
Yao, H., Dai, F., Zhang, D., Ma, Y., Zhang, S., Zhang, Y.: DR2-net: deep residual reconstruction network for image compressive sensing. Neurocomputing 359, 483–493 (2017)
Zhang, J., Zhao, D., Jiang, F., Gao, W.: Structural group sparse representation for image compressive sensing recovery. In: Bilgin, A., Marcellin, M.W., Serra-Sagristà, J., Storer, J.A. (eds.) 2013 Data Compression Conference, DCC 2013, Snowbird, UT, USA, 20–22 March 2013, pp. 331–340. IEEE (2013)
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Zheng, R., Zhang, Y., Huang, D., Chen, Q. (2020). Sequential Convolution and Runge-Kutta Residual Architecture for Image Compressed Sensing. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, JM. (eds) Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science(), vol 12354. Springer, Cham. https://doi.org/10.1007/978-3-030-58545-7_14
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