Space-time regularization for video decompression. (English) Zbl 1314.49021


49M29 Numerical methods involving duality
49M30 Other numerical methods in calculus of variations (MSC2010)
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
68U10 Computing methodologies for image processing
90C46 Optimality conditions and duality in mathematical programming


Full Text: DOI Link


[1] A. Agrawal and R. Raskar, Resolving objects at higher resolution from a single motion-blurred image, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), IEEE, Washington, DC, 2007, pp. 1–8.
[2] J. M. Bioucas-Dias and M. A. T. Figueiredo, A new twist: Two-step iterative shrinkage/thresholding algorithms for image restoration, Proc. IEEE Trans. Image Process., 16 (2007), pp. 2992–3004.
[3] K. Bredies, K. Kunisch, and T. Pock, Total generalized variation, SIAM J. Imaging Sci., 3 (2010), pp. 492–526. · Zbl 1195.49025
[4] A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, J. Math. Imaging Vision, 40 (2011), pp. 120–145. · Zbl 1255.68217
[5] W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, Terahertz imaging with compressed sensing and phase retrieval, Optics Lett., 33 (2008), pp. 974–976.
[6] M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F Kelly, and R. G. Baraniuk, Single-pixel imaging via compressive sampling, IEEE Signal Process. Mag., 25 (2008), pp. 83–91.
[7] E. Esser, X. Zhang, and T. F. Chan, A general framework for a class of first order primal-dual algorithms for convex optimization in imaging science, SIAM J. Imaging Sci., 3 (2010), pp. 1015–1046. · Zbl 1206.90117
[8] R. Fergus, A. Torralba, and W. T. Freeman, Random Lens Imaging, available online from http://hdl.handle.net/1721.1/33962, 2006.
[9] D. J. Le Gall, The MPEG video compression algorithm, Signal Process. Image Commun., 4 (1992), pp. 129–140.
[10] D. Le Gall, MPEG: A video compression standard for multimedia applications, Commun. ACM, 34 (1991), pp. 46–58.
[11] G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Model. Simul., 7 (2008), pp. 1005–1028. · Zbl 1181.35006
[12] J. Gilles and Y. Meyer, Properties of BV- G structures + textures decomposition models. Application to road detection in satellite images, IEEE Trans. Image Process., 19 (2010), pp. 2793–2800. · Zbl 1371.94141
[13] T. Goldstein and S. Osher, The split Bregman method for \(L1\)-regularized problems, SIAM J. Imaging Sci., 2 (2009), pp. 323–343. · Zbl 1177.65088
[14] T. Goldstein, L. Xu, K. F. Kelly, and R. Baraniuk, The STONE Transform: Multi-Resolution Image Enhancement and Real-Time Compressive Video, arXiv preprint arXiv:1311.3405, \burlhttp://arxiv.org/abs/1311.3405, 2013.
[15] T. Goldstein, E. Esser, and R. Baraniuk, Adaptive Primal-Dual Hybrid Gradient Methods for Saddle-Point Problems, arXiv preprint arXiv:1305.0546, http://arxiv.org/abs/1305.0546, 2013.
[16] J. Gu, S. Nayar, E. Grinspun, P. Belhumeur, and R. Ramamoorthi, Compressive structured light for recovering inhomogeneous participating media, in Proceedings of Computer Vision–ECCV 2008, Marseille, France, 2008, pp. 845–858.
[17] W. Guo and W. Yin, EdgeCS: Edge guided compressive sensing reconstruction, in Proceedings of Visual Communication and Image Processing, SPIE Proc. 7744, SPIE, Bellingham, WA, 2010, 77440L.
[18] W. Guo, J. Qin, and W. Yin, A New Detail-Preserving Regularity Scheme, UCLA CAM Technical report 13-04, University of California Los Angeles, Los Angeles, CA, 2013. · Zbl 1299.65130
[19] P. Hasler and D. V. Anderson, Cooperative analog-digital signal processing, in Proceedings of the 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Volume 4, IEEE, Washington, DC, 2002, pp. IV-3972–IV-3975.
[20] C. Li, W. Yin, and Y. Zhang, User’s Guide for TVAL3: TV Minimization by Augmented Lagrangian and Alternating Direction Algorithms, CAAM Report, Rice University, Houston, TX, 2009.
[21] C. Li, W. Yin, H. Jiang, and Y. Zhang, An efficient augmented Lagrangian method with applications to total variation minimization, Comput. Optim. Appl., 56 (2013), pp. 507–530. · Zbl 1287.90066
[22] P. Llull, X. Liao, X. Yuan, J. Yang, D. Kittle, L. Carin, G. Sapiro, and D. J. Brady, Coded Aperture Compressive Temporal Imaging, arXiv preprint arXiv:1302.2575, \burlhttp://arxiv.org/abs/1302.2575, 2013. · Zbl 1333.94011
[23] M. Lustig, D. Donoho, and J. M. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging, Magnetic Resonance in Medicine, 58 (2007), pp. 1182–1195.
[24] S. Marchesini, Ab Initio Compressive Phase Retrieval, arXiv preprint arXiv:0809.2006, http://arxiv.org/abs/0809.2006, 2008.
[25] Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures, Univ. Lecture Ser. 22, AMS, Providence, RI, 2001. · Zbl 0987.35003
[26] D. Needell and R. Ward, Stable image reconstruction using total variation minimization, SIAM J. Imaging Sci., 6 (2013), pp. 1035–1058. · Zbl 1370.94042
[27] S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, An iterative regularization method for total variation-based image restoration, Multiscale Model. Simul., 4 (2005), pp. 460–489. · Zbl 1090.94003
[28] A. Poglitsch, C. Waelkens, N. Geis, H. Feuchtgruber, B. Vandenbussche, L. Rodriguez, O. Krause, E. Renotte, C. Van Hoof, P. Saraceno, et al., The photodetector array camera and spectrometer (PACS) on the Herschel space observatory, Astronomy Astrophys., 518 (2010), L2.
[29] R. Raskar, A. Agrawal, and J. Tumblin, Coded exposure photography: Motion deblurring using fluttered shutter, ACM Trans. Graphics, 25 (2006), pp. 795–804.
[30] D. Reddy, A. Veeraraghavan, and R. Chellappa, P\(2\)C\(2\): Programmable pixel compressive camera for high speed imaging, in Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), IEEE, Washington, DC, 2011, pp. 329–336.
[31] L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259–268. · Zbl 0780.49028
[32] H. Schaeffer and S. Osher, A low patch-rank interpretation of texture, SIAM J. Imaging Sci., 6 (2013), pp. 226–262. · Zbl 1335.68287
[33] H. Schaeffer, Y. Yang, and S. Osher, Real-Time Adaptive Video Compressive Sensing, UCLA CAM Tech. Report, University of California Los Angeles, Los Angeles, CA, 2013.
[34] Y. Tendero, J.-M. Morel, and B. Rougé, The flutter shutter paradox, SIAM J. Imaging Sci., 6 (2013), pp. 813–847. · Zbl 1285.94013
[35] A. Wagadarikar, R. John, R. Willett, and D. Brady, Single disperser design for coded aperture snapshot spectral imaging, Appl. Optics, 47 (2008), pp. B44–B51.
[36] A. A. Wagadarikar, N. P. Pitsianis, X. Sun, and D. J. Brady, Video rate spectral imaging using a coded aperture snapshot spectral imager, Opt. Express, 17 (2009), pp. 6368–6388.
[37] M. Wakin, J. Laska, M. Duarte, D. Baron, S. Sarvotham, D. Takhar, K. F. Kelly, and R. G. Baraniuk, Compressive imaging for video representation and coding, in Picture Coding Symposium, Beijing, China, 2006.
[38] Y. Wang, J. Yang, W. Yin, and Y. Zhang, A new alternating minimization algorithm for total variation image reconstruction, SIAM J. Imaging Sci., 1 (2008), pp. 248–272. · Zbl 1187.68665
[39] J. Yang, X. Yuan, X. Liao, P. Llull, G. Sapiro, D. J. Brady, and L. Carin, Gaussian mixture model for video compressive sensing, in Proceedings of the IEEE International Conference on Image Processing, IEEE, Washington, DC, 2013, pp. 19–23. · Zbl 1374.94424
[40] J. Yang, X. Yuan, X. Liao, P. Llull, D. J. Brady, G. Sapiro, and L. Carin, Video compressive sensing using Gaussian mixture models , IEEE Trans. Image Process., 23 (2014), pp. 4863–4878. · Zbl 1374.94424
[41] Y. Yang, H. Schaeffer, W. Yin, and S. Osher, Mixing space-time derivatives for video compressive sensing, in Proceedings of the 2013 Asilomar Conference on Signals, Systems and Computers, IEEE, Washington, DC, 2013, pp. 158–162.
[42] X. Yuan, J. Yang, P. Llull, X. Liao, G. Sapiro, D. J. Brady, and L. Carin, Adaptive Temporal Compressive Sensing for Video, arXiv preprint arXiv:1302.3446, http://arxiv.org/abs/1302.3446, 2013.
[43] J. Zheng and E. L. Jacobs, Video compressive sensing using spatial domain sparsity, Optical Engrg., 48 (2009), 087006.
[44] M. Zhu and T. Chan, An Efficient Primal-Dual Hybrid Gradient Algorithm for Total Variation Image Restoration, UCLA CAM Tech. Report 08-34, University of California Los Angeles, Los Angeles, CA, 2008.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.