马坚伟

Home Research People Publication Summer School Recent Work ... Recent Work 新建主栏目 Jianwei Ma 名称 Professor Cener of Geophysics School of Mathematics Institute of Artificial Intelligence Harbin Institute of Technology, Harbin 150001, China CONTACT 名称 Email: jma@hit.edu.cn EDUCATION 名称 1998.09 - 2002.08 Ph. D. Solid Mechanics, Tsinghua University 1994.09 - 1998.07 B. S. Engineering Mechanics, Dalian University of Technology WORK EXPERIENCE 名称 2011.07 - Harbin Institute of Technology, Professor 2010.06 - 2011.06 Florida State University, Scientist 2006.02 - 2010.06 Tsinghua University, Assistant/Associate Professor 2005.01 - 2006.02 University of Grenoble, Postdoc Visiting Position 2017.11 - 2018.01 University of California, Los Angeles 2015.12 - 2016.01 University of Gottingen 2014.03 - 2014.09 University of Texas at Austin 2009.03 - 2009.09 Ecole des Mines de Paris 2008.05 - 2008.06 University of Grenoble 2007.06 - 2007.09 Florida State University 2006.06 - 2006.08 Ecole Polytechnique Federale de Lausanne HONOR 名称 World's Top 2% Scientists (1960-2021), 2022 CGS Science and Technology Progress Award (secod prize), 2022 Natural Science of Heilongjiang Province (first prize), 2019 CGS Technology Innovation Awards (second prize), 2018 National High Level Talent Plan, 2017 NSFC Distinguished Young Scholar, 2016 National High Level Talent Plan (Youth), 2011 Longjiang Chair Professor, 2011 New Century Excellent Talents by Ministry of Education of China, 2011 Cheng-Yi Fu Awards by Chinese Geophysical Society (CGS), 2011 China Top 100 Most Impact Papers Published in International Journals, 2010 SELECTED RESEARCH GRANTS 名称 PI: National Key Research and Development program of China (Applied Mathematics) PI: National Key Research and Development Program of China (High performance computing on exploration) PI: NFSC (Geoscience Division) on deep learning 5D denoising (Key project) PI: NFSC (Geoscience Division) on exploration geophysics (Distinguished Young Scholars) PI: NSFC (Mathematical Division) on low-rank matrix completion and seismic applications PI: NSFC (Geoscience Division) on 3D data-driven tight frame for seismic data reconstruction PI: NSFC (Information Division) on dynamic configurable imaging system based on compressed sensing PI: NSFC (Geoscience Division) on curvelets for seismic wave equations PROFESSIONAL SOCIETIES 名称 Director, Professional Committee on AI Geophysics, Chinese geophysical Society, 2022 Vice Director, Professional Committee on Data Driven and Geoscience Development, Geological Society of China, 2022 Board of Directors, SEG Global Inc., 2020-2022 Member, SEG China Advisory Committee, 2021-2023 Guest Associate Editor: Geophysics, Special issue: advances in mathematical geophysics, 2022 Guest Associate Editor: The Leading Edge, Special issue: exploration geophysics in China, 2019 Associate Editor: IEEE Transactions on Geoscience and Remote Sensing (2022-2025), IEEE GRSL (2019-2022), Journal of Geophysics and Egnineering (2020-2023) Organizer for Workshop on AI Geophysics (2022) Technical Co-Chair for SEG 4th International Workshop on Mathematical Geophysics: Traditional & Learning (2021) Technical Co-Chair for SEG 3rd International Workshop on Mathematical Geophysics: Traditional vs Learning (2019) Organizer for HIT International Summer School on Mathematics and AI (2015, 2017, 2018, 2021) Technical Co-Chair for CPS/SEG International Geophysical Conference and Exposition (2018) Co-Chair for CPS/SEG Artificial Intelligence and Compressed Sensing Geophysical Workshop (2018) Co-Chair for International Workshop on Mathematical Geophysics (2015, 2017) Technical Co-Chair for SEG Workshop on Geophysical Compressed Sensing (2015) Co-Chair for International Workshop on Signal Processing, Optimization and Compressed Sensing (2013) Committee membe of CSIAM (2016-2021) IEEE Senior Member, SEGActive Member, EAGE member RESEARCH INTERESTS 名称 Seismic exploration: how to improve the resolution of oil/gas exploration by using mathematical methods? Compressed sensing: how to reconstruct unknown objects by using highly incomplete geophysical observation data? Sparse transforms: how to sparsely represent data by using less significant coefficients? Artificial intelligence: how to remove the seismic noise and improve imaging using deep learning? Data assimilation: how to optimize initial condition of equations for prediction by using real observation data? COLLABORATORS 名称 Prof. Anestis Antoniadis, University of Joseph Fourier, Grenoble, France Dr. Florian Bossmann, University of Goettingen, Germany Mr. Simons Bechouche, CEA, France Dr. Nathalie Brandenberg, Ecole Polytechnique Federale de Lausanne, Switzerland Prof. Herve Chauris, Ecole des Mines de Paris, France Prof. Francois Le Dimet, University of Joseph Fourier and INRIA, France Prof. Gorden Erlebacher, Florida State University, USA Prof. Sergey Fomel, University of Texas at Austin, USA Dr. Markus Fenn, University of Mannheim, Germany Prof. Felix Herrmann, University of British Columbia, Canada Prof. M Yousuff Hussaini, Florida State University, USA Prof. Jane Jiang, University of Huddersfield, UK Dr. Jens Krommweh, University of Duisburg-Essen, Germany Prof. Matthias Lutolf, Ecole Polytechnique Federate de Lausanne, Switzerland Prof. George McMechan, University of Texas at Dallas, USA Prof. Stanley Osher, University of California at Los Angeles, USA Prof. Gerlind Plonka, University of Goettingen, Germany Dr. Thanh-An Pham, Ecole Polytechnique Federate de Lausanne, Switzerland Prof. Mauricio Sacchi, University of Alberta, Canada Prof. Gabriele Steidl, University of Kaiserslautern, Germany Prof. Michael Unser, Ecole Polytechnique Federale de Lausanne, Switzerland Prof. Oleg Vasilyev, University of Colorado at Boulder, USA Prof. JohnVillasenor, University of California at Los Angeles, USA Prof. Bihan Wen, Nanyang Technological University, Singapore Prof. Jiangtao Wen, Tsinghua University (Computer Science), China Prof. Huizhu Yang, Tsinghua University (School of Aeropace), China Prof. Datian Ye, Tsinghua University (Biomedical Engineering), China Prof. Wotao Yin, University of California at Los Angeles, USA Prof. Xiaoqun Zhang, Shanghai Jiao Tong University, China Team Members 名称 Faculty: Siwei Yu Professor Wenlong Wang Associate Professor Florian Bossmann Associate Professor Pengliang Yang Associate Professor Rongzhi Lin Associate Professor Zhao Liu Lecturer Long Li Lecturer Yiran Jiang Lecturer Ph.D. Students: Hairong Wang, 2012-2017, Multi-component wave registration (Visit Prof. Mauricio Sacchi, 2014-2015); Lecturer at Harbin University of Science and Technology Siwei Yu, 2014-2017, Compressed sensing seismic interpolation (Visit Prof. Stanley Osher, 2014-2016), National Scholarship Award in 2016; Professor at Harbin Institute of Technology Yongna Jia, 2014-2017, Seismic interpolation by low-rank regularization and maching learning (Co-advisor); Associate Professor at Hebei University of Technology Lina Liu, 2014-2018, Structure dictionary learning for interpolation and denoising (Visit Prof. Gerlind Plonka, 2015-2017); Lecturer at Nanjing University of Information Science and Technology Zhao Liu, 2013-2019, Seismic denoising by advanced curvelet transforms and low-rank minimization; Lecturer at Harbin Institute of Technology Kuijie Cai, 2013-2019, Estimation and applications of local dips of seismic data; Lecturer at Harbin Engineering University Diriba Gemechu, 2015-2019, Seismic data processing by compound methods Tara Banjade, 2015-2020, Seismic data processing Yuhan Shui, 2015-2020, Time-variant wavelet and deconvolution (Visit Prof. Sergey Fomel, 2017-2018); Beijing Research Center, Aramco Xiaojing Wang, 2015-2020, Dictionary learning for adaptive seismic denoising （Visit Prof. Simon Foucart, 2018; Lecturer at Beijing Jiaotong University Long Li, 2016-2020, Variational data assimalition for oil spill dispersion (Visit Prof. Francois Le Dimet, 2017-2019); Lecturer at Harbin Institute of Technology Hao Zhang, 2016-2021, Seismic migration imaging and deep learning (Visit Prof. Stanley Osher, 2018-2020); Huawei at Hangzhou Fangshu Yang, 2016-2021, Deep learing for seismic inversion (Visit Prof. Michael Unser, 2018-2020); Lecturer at Harbin Institute of Technology (Weihai) Huimin Sun, 2017-now, Transfer learning for seismic signal processing Feiying Wang, 2017-now, Machine learning Yanqi Wu, 2018-now, Deep learning geophysics (Visit Prof. Stephane Operto, 2020-2022) Yin Li, 2018-now, Deep learning (Co-advisor) Xuemin Zhang, 2019-now, Deep learning applications for geophysics Chao Ding, 2019-now, AI migration Ruohan Zhang, 2019-now, AI deep geophysics (Visit Prof. Michel Campillo, 2020-2022) Qiao Meng, 2019-now, AI mathematics Bo Li, 2020-now, AI mathematics M.S. Students: Hairong Wang, 2010-2012 (Co-advisor) Yanfan Liu, 2011-2013 (Co-advisor), National Scholarship Award in 2012 Zhao Liu, 2011-2013 (Co-advisor) Lina Liu, 2012-2014 Yongna Jia, 2012-2014, National Scholarship Award in 2013 Shengnan Qi, 2012-2014 Qiangqiang Zhu, 2013-2015 Rui Shi, 2013-2015 Ling Liu, 2013-2015 (Co-advisor) Xiaojing Wang, 2014-2015 (Co-advisor) Yuhan Shui, 2014-2015 Long Li, 2014-2016 (Co-advisor), National Scholarship Award in 2015 Fangshu Yang, 2015-2016 Huimin Sun, 2015-2017 (Co-advisor) Feiying Wang, 2016-2017 Xiuyan Yang, 2017-2019，National Scholarship Award in 2018 Jing Wang, 2017-2019 Libin Zong, 2018-2020 (Co-advisor) Sitong Liu, 2018-2020 (Co-advisor) Binbin Ming, 2018-2020 (Co-advisor) Yuxin Wu, 2018-2020 Jiaying Su, 2018-2020 Yuxin Shan, 2019-2021, National Scholarship Award in 2020 Ran Li, 2019-2021 Ming Sun, 2019- 2021(Co-advisor) Mingming Huangfu,2019-2021 (Co-advisor) Shi Xie, 2019-2021 (Co-advisor) Yanmei Li, 2019-2021 (Co-advisor) Mengcao Zhao, 2020-2022 Mingming Liu, 2020-2021 Visitors 名称 2018: Michael I. Jordan, University of California, Berkeley, USA Stephane Mallat, Ecole Normale Superieure, France Yonnina Eldar, Israel Institue of Technology, Israel Stephen Wright, University of Wisconsin-Madison, USA Benjiamin Recht, University of California, Berkelery, USA Stefano Ermon, Stanford University, USA 2017: Christian Kümmerle, Technische University München, Germany Tony Cai, Wharton School, University of Pennsylvania, USA Francois X. Le Dimet, University of Grenoble, France Jurgen Schmidhuber, Swiss AI Lab IDSIA, Switzerland Michael I. Jordan, University of California, Berkeley, USA 2016: Alexey Matveev, Insitute of Petroleum Geology and Geophysics, Russia Philipp Petersen, TU Berlin, Germany Francois X. Le Dimet, University of Grenoble, France 2015: Georgy Loginov, Institute of Petroleum Geology and Geophysics, Nobosibirsk, Russia Jan H. Fitschen, Technische Universitat Kaiserslautern, Germany Johannes Persch, Technische Universitat Kaiserslautern, Germany Ming Jiang, CEA Saclay, France Sergey Fomel, University of Texas at Austin, USA Jeffrey Shragge, University of Western Australia, Australia Frederik Simons, Princeton University, USA Ru-shan Wu, University of California, Santa Cruz, USA Stanley Osher, UCLA, USA Michael Unser, EPFL, Switzerland Jianqing Fang, Princeton University, USA John Ball, University of Oxford 2014: Frorian Bossmann, University of Gottingen, Germany Francois Le Dimet, University of Grenoble, France 2013: Wotao Yin, University of Calfornia at Los Angeles, USA Xiaoming Yuan, HKBU, Hongkong Xinxin Li, HKBU, Hongkong Wenyi Tian, HKBU, Hongkong Chenglong Bao, National Univeristy of Singapore, Singapore 2012: Simon Beckouche, CEA Salcay, France Soren Hauser, TU Kaiserslautern, Germany 2011: Yi Yang, UCLA, USA 2010: Shaharyar Khwaja, Ryerson University, Canada 2009: Felix Herrmann, University of British Colombia, Canada Jens Krommweh, University Duisburg-Essen, Germany 2008: Wotao Yin, Rice University, USA Francois Le Dimet, University of Grenoble 1, France Publications 名称 MathGeo download MathGeo is an open-source software package from our group for sparse transform, artificial intelligence, seismic data processing and inversion to reproducible computational experiments. MathGeo2020 updated: https://gitee.com/sevenysw/MathGeo2020 JOURNAL PAPERS Q. Liu, J. Ma*, Generative interpolation via diffusion probabilistic model, Geophysics, 2023, accepted. Z. Yu, J. Ma*, First arrival enhancement and extrapolation via third-order cumulant interferometry method, IEEE TGRS, 2023, accepted. L. Li, J. Ma*, ISANet: Deep neural network approximating image sequence assimilation for tracking fluid flows, IEEE TGRS, 2023, revised. X. Wu, J. Ma*, S. Xu, Z. Bi, J. Yang, H. Gao, D. Xie, Z. Guo, J. Zhang*, Sensing prior constraints in deep neural networks for solving exploration geophysical problems, Proceedings of the National Academy of Sciences of the United States of America (PNAS), 2023, 120, e2219573120. F. Yang, J. Ma*, FWIGAN: Full waveform inversion via a physics-informed generative adversarial network, Journal of Geophysical Research: Solid Earth, 2023, 128, e2022JB025493. W. Wang, G. McMechan, J. Ma*, Re-weighted variational FWI, Geophysics, 2023, 88 (4), R499-R512. X. Zhang, J. Ma*, S. Yu, Non-convex tensor completion for five-dimensional seismic data reconstruction, IEEE Transactions on Geoscience and Remote Sensing, 2023, 61, 1-12. X. Wang, Y. Sui, W. Wang, J. Ma*, Random noise attenuation via an improved self-supervised deep learning method, Mathematical Geosciences, 2023, 55 (3), 401-422. Y. Wu, H. Aghamiry, S. Operto, J. Ma*, Helmholtz-equation solution in nonsmooth media by a physics-informed neural network incorporated quadratic terms and a perfectly matching layer condition, Geophysics, 2023, 88 (4), T185-T202. F. Yang, J. Ma*, Wasserstein distance-based full waveform inversion with a regularizer powered by learned gradient, IEEE Transactions on Geoscience and Remote Sensing, 2023, 61. S. Yu*, J. Ma, Simultaneous off-the-grid regularization and interpolation for 3D seismic data by a new combined sampling operator, Geophysics, 2023, 88 (4), V291-V302. R. Zhang, P. Boue, M. Campillo, J. Ma*, Quantifying P-wave secondary microseism events: a comparison of observed and modeled back projection, Geophysical Journal International, 2023, 234 (2), 933-947. H. Zhang, W. He, J. Ma*, The back-and-forth method for the quadratic Wasserstein distance-based full-waveform inversion, Geophysics, 2023, 88 (4), R469-R483. F. Bossmann*, J. Ma, ORKA: Object reconstruction using a K-approximation graph, Inverse Problems, 2022, 38 (12), 125009. L. Zhang, G. Zhang*, Z. Fan, J. Ma, A multi-task deep learning for simultaneous denoising and inversion of 3D gravity data, IEEE Transactions on Geoscience and Remote Sensing, 2022, 60, 1-17. Y. Chen, S. Yu*, J. Ma, A projection-onto-convex-sets network for 3D seismic data interpolation, Geophysics, 2023, 88 (3), V249-V265. Y. Sui, X. Wang, J. Ma*, Deep unfolding dictionary learning for seismic denoising, Geophysics, 2023, 88 (1), WA129-WA147. J. Ma, Q. Cheng, S. Fomel, M. Sacchi, R-S. Wu, Y. Liu, Y. Elita Li, Advances in mathematical geophysics--Introduction, Geophysics, 88 (1), WAI-WAII. X. Zhang, J. Ma*, H. Zhang, Curveture regularized manifold for seismic data interpolation, Geophysics, 2023, 88 (1), WA37-WA53. L. Liu, J. Ma*, DL2: Dictionary learning regularized with deep learning prior for simultaneous denoising and interpolation, Geophysics, 2023, 88 (1), WA13-WA25. H. Sun, F. Yang, J. Ma*, Seismic random noise attenuation via self-supervised transfer learning, IEEE Geoscience and Remote Sensing Letters, 2022, 19. C. Ding, J. Ma*, Automatic migration velocity analysis via deep learning, Geophysics, 2022, 87 (4), U135-U153. Y. Wu, J. Ma*, Rayleigh wave equations with couple stress: modeling and dispersion characteristic, Geophysics, 2022, 87 (1), T1-T13. L. Li, J. Ma*, F. Le Dimet, A. Vidard, Assimilation of images via dictiornary learning-based sparsity regularization strategy: an application for retrieving fluid flows, IEEE Transactions on Geoscience and Remote Sensing, 2022, 60, 5907120. S. Yu, J. Ma*, Deep learning for geophysics: current and future trends, Reviews of Geophysics, 2021, 59 (3), e2021RG000742. F. Yang, T. Pham, N. Brandenberg, M. Lutolf, J. Ma*, M. Unser, Robust phase unwrapping via deep image prior for quantitative phase imaging, IEEE Transactions on Image Processing, 2021, 30, 7025-7037. W. Wang*, G. McMechan, J. Ma, Elastic isotropic and anisotropic full wave-form inversions using automatic differentiation for gradient calculations in a framework of recurrent neural networks, Geophysics, 2021, 86 (6), R795-R810. S. Yu, W. Yang, H. Li, X. Wang, J. Ma*, Scattered ground roll intelligent attenuation based on deep learning, Chinese Science Bulletin, 2021, 66 (18), 2343-2354. W. Wang*, G. McMechan, J. Ma, F. Xie, Automatic velocity picking from semblances with a new deep learning regression strategy: comparison with a classification approach, Geophysics, 2021, 86 (2), U1-U13. J. Zhang, H. Zhu, S. Yu, J. Ma*, Constructing the seismograms of future earthquakes in Yunnan, China using compressed sensing, Seismological Research Letters, 2021, 92 (1), 261-274. H. Zhang, J. Ma*, Hartley spectral pooling for deep learning, CSIAM Transactions on Applied Mathematics, 2020,1 (3), 518-529. Y. Sui, J. Ma*, Blind sparse spike deconvolution with thin layers and structure, Geophysics, 2020, 85 (6), V481-V496. J. Ma*, Random low patch-rank method for interpolation of regularly missing traces, Journal of Harbin Institute of Technology (new series): special issue for the 100th anniversary, 2020, 27 (3), 205-216. F. Yang, T. Pham, H. Gupta, M. Unser, J. Ma*, Deep learning projector for optical diffraction tomography, Optics Express, 2020, 28 (3), 3905-3921. H. Zhang, X. Yang, J. Ma*, Can learning from natural image denoising be used for seismic data interpolation?, Geophysics, 2020, 85 (4), WA115-WA136. S. Yu, J. Ma*, B. Zhao, Off-the-grid VSP data regularization by a compressive sensing method, Geophysics, 2020, 85 (2), V157-V168. W. Wang*, J. Ma, Velocity model building in a cross-well acquisition geometry with image-trained artificial neural networks, Geophysics, 2020, 85 (2), U31-U46. X. Wang, J. Ma*, Adaptive dictionary learning for blind seismic data denoising, IEEE Geoscience and Remote Sensing Letters, 2020, 17 (7), 1273-1277. F. Bossmann, J. Ma*, Enhanced image approximation using shifted rank-1 reconstruction, Inverse Problems and Imaging, 2020, 14 (2), 267-290. X. Wang, B. Wen, J. Ma*, Denoising with weak feature preservation by group-sparsity transform learning, Geophysics, 2019, 84 (6), V351-368. S. Yu, J. Ma*, W. Wang, Deep learning for denoising, Geophysics, 2019, 84 (6), V333-V350. F. Yang, J. Ma*, Deep-learning inversion: a next generation seismic velocity model building method, Geophysics, 2019, 84 (4), R583-R599. Y. Sui, J. Ma*, A nonstationary sparse spike deconvolution with anelastic attenuation, Geophysics, 2019, 84 (2), R221-R234. L. Li, A. Vidard, F. Le Dimet, J. Ma*, Topological data assimilation using Wasserstein distance, Inverse Problems, 2019, 35, 015006. K. Cai, J. Ma*, Robust estimation of multiple local dips via multidirectional component analysis, IEEE Transactions on Geoscience and Remote Sensing, 2019, 57 (5), 2798-2810. Z. Liu J. Ma*, X. Yong, Line survey joint denoising via low rank minimization, Geophysics, 2019, 84 (1), V21-V32. L. Liu, J. Ma*, Structured graph dictionary learning and application on the seismic denoising, IEEE Transactions on Geoscience and Remote Sensing, 2019, 57 (4), 1883-1893. D. Gemechu, J. Ma*, X. Yong, A compound method for noise attenuation, Geophysical Prospecting, 2018, 66, 1548-1567. L. Liu, J. Ma*, G. Plonka, Sparse graph-regularized dictionary learning for random seismic noise, Geophysics, 2018, 83 (3), V213-V231. S. Yu, J. Ma*, S. Osher, Geometric mode decomposition, Inverse Problems and Imaging, 2018, 12 (4), 831-852. Y. Jia, S. Yu, J. Ma*, Intelligent interpolation by Monte Carlo machine learning, Geophysics, 2018, 83 (2), V83-V97. S. Yu, J. Ma*, Complex variational model decomposition for slop-preserving denoising, IEEE Transactions on Geoscience and Remote Sensing, 2018, 56 (1), 586 - 597. J. Ma*, S. Yu, Sparsity in compressive sensing, The Leading Edge, 2017, 36 (8), 308-314. (an invited short review). L. Li, F. Le Dimet, J. Ma*, A. Vidard, A level-set based image assimilation method: applications for predicting the movement of oil spills, IEEE Transactions on Geoscience and Remote Sensing, 2017, 55 (11), 6330-6343. L. Liu, G. Plonka, J. Ma*, Seismic data interpolation and denoising by learning a tensor tight frame, Inverse Problems, 2017, 33 (10), 105011. S. Yu, S. Osher, J. Ma*, Z. Shi, Noise attenuation in a low dimensional manifold, Geophysics, 2017, 82 (5), V321-V334. Y. Jia, J. Ma*, What can machine learning do for seismic data processing? an interpolation application, Geophysics, 2017, 82 (3), V163-V177. J. Fitschen*, J. Ma, S. Schuff, Removal of curtaining effects by a variational model with directional first and second order differences, Computer Vision and Image Understanding, 2017, 155, 24-32. H. Wang, M. Sacchi, J. Ma*, Linearized dynamic warping with L1-norm constraint for multi-component registration, Journal of Applied Geophysics, 2017, 139, 170-176. F. Bossmann, J. Ma*, Asymmetric chirplet transform--Part 2: phase, frequency, and chirp rate, Geophysics, 2016, 81 (6), V425-V439. C. Zhang, B. Sun*, J. Ma, H. Yang, Y. Hu, Splitting algorithm for high-order compact finite difference scheme in wave equation modeling, Geophysics, 2016, 81 (6), T295-T302. S. Yu, J. Ma*, S. Osher, Monte Carlo data-driven tight frame for seismic data recovery, Geophysics, 2016, 81 (4), V327-V340. Y. Chen, J. Ma*, S. Fomel, Double sparsity dictionary for seismic noise attenuation, Geophysics, 2016, 81 (2), V17-V30. F. Bossmann, J. Ma*, Asymmetric chirplet transform for sparse representation of seismic data, Geophysics, 2015, 80 (6), WD89-WD100. S. Yu, J. Ma*, X. Zhang, M. Sacchi, Interpolation and denoising of high-dimensional seismic data by learning a tight frame, Geophysics, 2015, 80 (5), V119-V132. S. Beckouche, J. Ma*, Simultaneously dictionary learning and denoising for seismic data, Geophysics, 2014, 79 (3), A27-A31. J. Liang, J. Ma*, X. Zhang, Seismic data restoration via data-driven tight frame, Geophysics, 2014, 79 (3), V65-V74. H. Wang, Y.-F. Chen, J. Ma*, Curvelet-based registration of multi-component seismic waves, Journal of Applied Geophysics, 2014, 104, 90-96. Y. Yang*, J. Ma, S. Osher, Seismic data reconstruction via matrix completion, Inverses Problem and Imaging, 2013, 7 (4), 1379-1392. J. Ma*, Three-dimensional irregular seismic data reconstruction via low-rank matrix completion, Geophysics, 2013, 78 (5), V181-V192. R. Shahidi*, G. Tang, J. Ma, F. Herrmann, Application of randomized sampling schemes to curvelet-based sparsity-promoting seismic data recovery, Geophysical Prospecting, 2013, 61 (5), 973-997. Q. Li, J. Ma*, G. Erlebacher, A new reweighted algorithm with support detection for compressed sensing, IEEE Signal Processing Letters, 2012, 19 (7), 419-422. Y. He, M. Y. Hussaini, J. Ma*, B. Shafei, G. Steidl, A new fuzzy c-means method with total variation regularization for segmentation of images with noisy and incomplete data, Pattern Recognition, 2012, 45, 3463-3471. J. Ma*, G. Plonka, M. Y. Hussaini, Compressive video sampling with approximate message passing decoding, IEEE Transactions on Circuits and Systems for Video Technology, 2012, 22 (9), 1354-1364. J. Wang, J. Ma*, B. Han, Qin Li, Split Bregman iterative algorithm for sparse reconstruction of electrical impedance tomography, Signal Processing, 2012, 92, 2952-2961. J. Xu, J. Ma*, D. Zhang, Y. Zhang, S. Lin, Improved total variation minimization method for compressive sensing by intra prediction, Signal Processing, 2012, 92, 2614-2623. S. Yu, A. S. Khwaja, J. Ma*, Compressed sensing of complex-value data, Signal Processing, 2012, 92, 357–362. K. Tsai, J. Ma*, D. Ye, J. Wu, Curvelet processing of MRI for local image enhancement, Int. J. Numerical Methods in Biomedical Engineering, 2012, 28 (6-7), 661-677. G. Tang*, J. Ma, H. Yang, Seismic denoising via learning sparse dictionary, Applied Geophysics, 2012, 9, 27-32. J. Ma*, M. Y. Hussaini, Extensions of compressed imaging: flying sensor, coded mask, and fast decoding, IEEE Transactions on Instrumentation and Measurement, 2011, 60 (9), 3128-3139. A. S. Khwaja, J. Ma*, Applications of compressed sensing for SAR moving target velocity estimation and image compression, IEEE Transactions on Instrumentation and Measurement, 2011, 60 (8), 2828-2860. B. Sun, H. Chauris*, J. Ma, 3D post-stack one-way migration using curvelets, Journal of Seismic Exploration, 2011, 20 (3), 257-271. G. Plonka*, J. Ma, Curvelet-wavelet regularized split Bregman iteration for compressed sensing, Int. J. Wavelet, Multiresolution Information Processing, 2011, 9 (1), 79-110. J. Ma*, Improved iterative curvelet thresholding for compressed sensing, IEEE Transactions on Instrumentation and Measurement, 2011, 60 (1), 126-136. J. Ma*, Compressed sensing by iterative thresholding of geometric wavelets: a comparing study, Int. J. Wavelet, Multiresolution Information Processing, 2011, 9, 63-77. G. Tang, J. Ma*, Applications of total variation based curvelet shrinkage for three-dimensional seismic denoising, IEEE Geoscience and Remote Sesing Letters, 2011, 8 (1), 103-107. J. Ma*, G. Plonka, The curvelet transform, IEEE Signal Processing Magazine, 2010, 27 (2), 118-133. J. Krommweh, J. Ma*, Tetrolet shrinkage with anisotropic TV minimization for image approximation, Signal Processing, 2010, 90, 2529-2539. J. Ma*, G. Plonka, H. Chauris, A new sparse representation of seismic data using adaptive easy-path wavelet transform, IEEE Geoscience and Remote Sensing Letters, 2010, 7 (3), 540-544. H. Shan, J. Ma*, Curvelet-based geodesic active contours for multiple objects image segmentation, Pattern Recognition Letters, 2010, 31 (5), 355-360. J. Liu*, J. Ba, J. Ma, H. Yang, An analysis of seismic attenuation in random porous media, Science in China, Series G, 2010, 53, 628-637. J. Ma*, Compressed sensing for surface characterization and metrology, IEEE Transactions on Instrumentation and Measurement, 2010, 59 (6), 1600-1615. T. Mi, J. Ma, H. Chauris*, H. Yang, Multilevel adaptive mesh modeling for wave propagation in layer media, Journal of Seismic Exploration, 2010, 19 (2), 121-139. J. Ma*, F.-X. Le Dimet, Deblurring from highly incomplete measurements for remote sensing, IEEE Transactions on Geoscience and Remote Sensing, 2009, 47 (3), 792-802. J. Ma*, A single-pixel imaging system for remote sensing using two-step iterative curvelet thresholding, IEEE Geoscience and Remote Sensing Letters, 2009, 6 (4), 676-680. J. Ma*, Single-pixel remote sensing, IEEE Geoscience and Remote Sensing Letters, 2009, 6 (2), 199-203. J. Ma*, M. Y. Hussaini, O. Vasilyev, F. Le Dimet, Multiscale Geometric analysis of turbulence by curvelets, Physics of Fluids, 2009, 21, 075104. H. Shan, J. Ma*, H. Yang, Comparisons of wavelets, contourlets and curvelets for seismic denoising, Journal of Applied Geophysics, 2009, 69, 103-115. B. Sun, J. Ma, H. Chauris*, H. Yang, Solving the wave equation in the curvelet domain: a multi-scale and multi-directional approach, Journal of Seismic Exploration, 2009, 18, 385-399. G. Plonka*, J. Ma, Nonlinear regularized reaction-diffusion filters for denoising of images with textures, IEEE Transactions on Image Processing, 2008, 17 (8), 1283-1294. X. Jiang*, W. Zeng, P. Scott, J. Ma, L. Blunt, Linear feature extraction based on complex ridgelet transform, Wear, 2008, 265, 428-433. J. Ma*, G. Plonka, Combined curvelet shrinkage and nonlinear anisotropic diffusion, IEEE Transactions on Image Processing, 2007, 16 (9), 2198-2206. J. Ma*, M. Y. Hussaini, There-dimensional curvelets for coherent vortex analysis of turbulence, Applied Physics Letters, 2007, 91, 184101. J. Ma*, Curvelets for surface characterization, Applied Physics Letters, 2007, 90, 054109. J. Ma*, Characterization of textual surfaces using wave atoms, Applied Physics Letters, 2007, 90, 264101. J. Ma*, Deblurring using singular integrals and curvelet shrinkage, Physics Letters A, 2007, 368, 245-250. G. Plonka*, J. Ma, Convergence of an iterative nonlinear scheme for denoising of piecewise constant images, Int. J. Wavelet, Multiresolution and Information Processing, 2007, 5, 975-995. J. Ma*, M. Fenn, Combined complex ridgelet shrinkage and total variation minimization, SIAM Journal on Scientific Computing, 2006, 28 (3), 984-1000. J. Ma*, A. Antoniadis, F.-X. Le Dimet, Curvelets-based snake for multiscale detection and tracking for geophysical fluids, IEEE Transactions on Geoscience and Remote Sensing, 2006, 44 (12), 3626-3638. J. Ma*, J. Xiang, P. Scott, Complex ridgelet for shift invariant characterization of surface topography with line singularities, Physics Letters A, 2005, 344, 423-431. J. Ma*, An exploration of multiresolution symplectic scheme for wave propagation using second generation wavelets, Physics Letters A, 2004, 328 (1), 36-46. SELECTED CONFERENCES H. Zhang, J. Ma, Optimal transport with a new preprocessing for deep-learning full waveform inversion, IEEE International Conference on Image Processing (ICIP), 2022, 1446-1450 W. Wang, G. McMechan, J. Ma, Elastic full wave-form inversion with recurrent neural networks, 90th SEG Annual Meeting, 2020. W. Wang, J. Ma, VMB-Net: A deep learning network for velocity model building in a cross-well acquisition geometry, 89th SEG Annual Meeting, 2019. X. Wang, J. Ma, Transform learning with group sparsity for random noise attenuation, 89th SEG Annual Meeting, 2019 Y. Sui, X. Wang, J. Ma, Seismic deconvolution with weak reflection using atomic norm optimization, 89th SEG Annual Meeting, 2019. W. Wang, J. Ma, PS wavefield decomposition with CNN-learned filters, 81th EAGE Annual Meeting, 2019. L. Long, A. Vidard, F. X. Le Dimet, J. Ma, Adaptive image assimilation for 2D velocity reconstruction, AOGS 16th Annual Meeting, 2019. W. Wang, F. Yang, J. Ma, Velocity model building with a modified fully convolutional network, 88th SEG Annual Meeting, 2018, pp. 2086-2090. W. Wang, F. Yang, J. Ma, Automatic salt detection with machine learning, 80th EAGE Annual Meeting, 2018. S. Yu, J. Ma, Deep learning for attenuating random and coherence noise simultaneously, 80th EAGE Annual Meeting, 2018. S. Yu, J. Ma, Deep learning for denoising, SEG International Geophysical Conference, 2018, pp. 461-464. J. Ma, Compressed sensing based high performance computing for seismic inversion, SEG Workshop on High Performance Computing, 2016, pp. 43. J. Ma, S. Yu, Seismic data interpolation with polar Fourier transform, SPG/SEG International Geophysical Conference, 2016, pp. 480-481. G. Tang, R. Shahidi, F. Herrmann, J. Ma, Higher dimensional blue-noise sampling schemes for curvelet-based seismic data recoery, 79th SEG Annual Meeting, 2009, pp. 191-195. X. Zhang, Z. Chen, J. Wen, J. Ma, Y. Han, J. Villasenor, A compressive sensing reconstruction algorithm for trinary and binary sparse signals using pre-mapping, Data Compression Conference (DCC), 2011, pp. 203-212. J. Xu, J. Ma, D. Zhang, Y. Zhang, S. Lin, Compressive video sensing based on user attention model, 28th Picture Coding Symposium (PCS), 2010, pp. 90-93. F. Le Dimet, A. Antoniadis, J. Ma, I. Herlin, E. Huot, J. Berroir, Assimilation of images in geophysical models, International Science and Technology for Space, 2006. INVITED BOOK CHAPTER J. Ma, A. S. Khwaja, M. Y. Hussaini, Compressed remote sensing, in Signal and Image Processing for Remote Sensing (Editor by Chi H. Chen), the second version, 2012, 73-90. G. Plonka, J. Ma, Curvelets, in Encyclopedia of Applied and Computational Mathematics (Editor by Bjorn Engquist), Springer Berlin, 2013. HIT International Summer School on Artificial Intelligence 名称 The HIT international summer school on artificial intelligence (i.e., the third international summer school on mathematics) will take place at the Harbin Institute of Technology, China, from July 20 to August 20, 2018. This summer school is to introduce the tutorial and some state-of-the-art methods of artificial intelligence to graduate students and researchers. There will be seven world@#%s leading scientists (including the father in statistical machine learning, the main founder of wavelet transform and wavelet scattering network, past chair of the mathematical optimization society, the member of the Israel academy of sciences and humanities, 2017 NIPS Test of Time Award winner, IJCAI 2018 Computers and Thought Award winner, SEG Clarence Karcher Award winner, etc.) to give a series of mini-courses. The courses include machine learning, deep learning, artificial intelligence, optimization algorithms, seismic data processing and imaging. More information can be found in the homepage: mss.hit.edu.cn HIT International Summer School on Pure and Applied Mathematics 名称 News: Homepage of the Summer School http://mss.hit.edu.cn is open now! mss2017.hit.edu.cn In 2015, the international summer school on pure and applied mathematics will take place at the Harbin Institute of Technology in Harbin, China, from July 6 to August 9. The purpose of this summer school is to introduce some of the basic ideas and state-of–the-art methods of pure and applied mathematics to graduate students and reseachers. In particular there will be ten world@#%s leading mathematicians (3 Fields Medal, Wolf Prize, Crafoord Prize, Gauss Prize, COPSS President@#%s Award, SIAM Kleinman Prize, SIAM Von Karman Prize, ICIAM Pioneer Prize, Former President of the International Mathematical Union, etc) to give a series of mini-courses. Open to international students from all countries. The school will be held in English. The program features plenary talks and mini-courses by the leading international mathematicians. Hosted by the Harbin Institute of Technology, Harbin. Students are housed on the campus. Limited travel grants can be applied. The online registration (no registration fee) will start from April 15, 2015 , http://mss2015.hit.edu.cn. Invited speakers: Sir John M. Ball Oxford University Ngo Bao Chau University of Chicago Bjorn Engquist University of Texas at Austin Jianqing Fan Princeton University Vladimir Manuilov Moscow State University Alexander Mishchenko Moscow State University Stanley Osher University of California, Los Angeles Stanislav Smirnov University of Geneva Michael Unser Swiss Federal Institute of Technology in Lausanne (EPFL) Shing-Tung Yau Harvard University Mini-courses and Time table (to to comfirmed): Pure Mathematics Mini-Courses Time Alexander Mishchenko Introduction to differential topology July 6- August Vladimir Manuilov Introcution to C*-algebras July 6- August Stanislav Smirnov Complex analysis July 13 - July 21 Shing-Tung Yau Differential geometry July 26 - July 30 Ngo Bao Chau Number theory and automorphic forms July 30 - August 6 Applied Mathematics Mini-courses Time Bjorn Engquist Mutiscale modeling and computation July 6 - July 12 Stanley Osher Sparse recovery, optimization and applications to image science, PDE, and numerical analysis July 12-July 19 Jianqing Fan High-dimensional statistical learning July 20-25 Michael Unser Sparse stochastic processes July 25-July30 John Ball Mathematics of solid and liquid crystals July 29-August 6 Abstract of mini-courses: Prof. John M. Ball Mathemetics of solid and liquid crystals Abstract: The course will discuss static models of solid and liquid crystals. As regards solid crystals the course will concentrate on materials that undergo solid phase transformations, how these can be modelled using nonlinear elasticity, the resulting microstructure morphology, and nucleation. Concerning liquid crystals the course will describe the Oseen-Frank and Landau – de Gennes theories, and the relation between them, together with new developments concerning the description of defects. While solid and liquid crystals represent very different kinds of material, the theories used to describe them have similar variational structures, and there are interesting common issues related to the choice of function spaces, the modelling of singularities, and topology. Prof. Ng？ B？o Chau Number theory and automorphic forms Abstract: Though number theory is probably as old as mathematics, it is still young for it still grows vigorously. I will lecture on problems in number theory which have motivated strong recent developments, in particular in interaction with automorphic forms and algebraic geometry. Prof. Jianqing Fan High-Dimensional Statistical Learning Abstract: High-dimensionality and Big Data characterize many contemporary statistical problems from genomics and genetics to finance and economics. We first outline a unified approach to ultrahigh dimensional variable selection problems and then focus on penalized likelihood methods which are fundamentally important building blocks to ultra-high dimensional variable selection. We will also introduce variable screening methods as well as various contemporary methods for covariance matrix estimation and graphical models. Algorithms for solving penalized likelihood methods as well as Big Data computing will also be introduced. Topics to be covered include (1) Impact of dimensionality(2) Penalized Least-Squares(3) Penalized Likelihood(4) Algorithms and Implementation(5) Big Data computing(g) Estimation of Large Covariance Matrices (6) Graphical models Prof. Bjorn Engquist Mustiscal Modelign and Computation Abstract: It is computationally very challenging to accurately represent the smallest scales over a domain that covers the largest scales in a multiscale problem. Classical practical cases are turbulence, high frequency wave propagation and the coupling of molecular and continuum formulations. As a background to the study of numerical multiscale methods we will consider a number of analytical techniques as, for example, homogenization theory for partial differential equations and averaging of dynamical systems. We will see how information theory can be a guide for discrete representation.We will introduce several numerical methods for numerical simulation of multiscale problems with a focus on the framework of the Heterogeneous Multiscale Method (HMM). This is a methodology for coupling numerical simulations of different scales. A macroscale model gets microscale data from detailed computations on smaller subsets of the full domain. We will study HMM both in the partial differential and dynamical systems settings. Various applications, for example, to epitaxial growth, crack propagation and flow in porous media will be presented. High frequency wave propagation will be approximated both by HMM and by more traditional fest methods. Prof. Vladimir Manuilov Introduction to C*-Algebras Abstract: C*-algebras were introduced by Gelfand and Naimark in 1943, and are now an important part of functional analysis with many applications in harmonic analysis and representation theory, non-commutative geometry and topology (it is often said that the C*-algebra theory is non-commutative topology), and mathematical physics (quantum mechanics and field theory, statistical physics). The aim of this course is to lay the foundations for further studies of the subject and its applications. The following subjects will be covered: (1) Spectral theory (2) Commutative C*-algebras (3) deals, quotients, homomorphisms (4) States, representations, Gelfand-Naimark-Segal Theorem (5) Some interesting classes and examples of C*-algebras (6) Constructions for C*-algebras (pull-backs, tensor and free products etc.) If time permits, an introduction to K-theory for C*-algebras will be given. Prerequisites: standard bachelor courses on analysis and topology, plus some knowledge in functional analysis (Hilbert space operators). Prof. Aleksander Mishchen Introduction of Differential topology Abstract: Differential topology may be defined as the study of those properties of differentiable manifolds which are invariant under diffeomorphism (differentiable homeomorphism). Typical problem falling under this heading are the following: (1) Given two differentiable manifolds, under what conditions are they diffeomorphic? (2) Given a differentiable manifold, is it the boundary of some differentiable manifold with boundary? (3) Given a differentiable manifold, is it parallelisable? All these problems concern more than the topology of the manifold, yet they do not belong to differential geometry, which usually assumes additional structure (e.g., a connection or a metric). The most powerful tools in this subject have been derived from the methods of algebraic topology. In particular, the theory of characteristic classes is crucial, where-by one passes from the manifold M to its tangent bundle, and thence to a cohomology class in M which depends on this bundle. Outline: 1. Smooth manifolds. 2. Tangent bundles. 3. Bundles. Vector bundles. 4. Calculus on smooth manifolds. Differential Foems. 5. Homology and Cohomology. De Rham Cohomology. 6. Connections and Curvatures. 5. Characteristic classes. Chern-Weil Theory. 6. Immersions and embeddings. Bordisms 7. Surgery. Smooth structures on homotopy type. Prerequisites: standard bachelor courses on analysis, algebra and topology. Prof. Stanley Osher Sparse Recovery, Optimization, and Applications to Image and Information Science, Applied Partial Differential Equationsand Numerical Analysis Abstract: Our modern world is dominated by visual communication via digital images and videos. This raises a variety of novel questions in mathematics. Tasks such as improving visual quality, detecting objects, or detecting motion become increasingly relevant and need to be automated due to the ongoing flood of data. Among the techniques used for these problems, variational methods play a prominent role. Simultaneously, exploiting sparsity has become a very important task in data science. A sparse signal is one which has very few nonzero elements or becomes so under a change of basis or through a transform. Compressed sensing and regularized inverse problems have made variational methods of the type used in imaging even more important. Moreover, continuous analogues of these discrete optimization problems are becoming more useful in applied partial differential equations and their numerical solution.We will review the basics and cover recent research in this area. Prof. Michael Unser Sparse stochastic processes Abstract: Sparse stochastic processes are continuous-domain processes that admit a parsimonious representation in some matched wavelet-like basis. Such models are relevant for image compression, compressed sensing, and, more generally, for the derivation of statistical algorithms for solving ill-posed inverse problems. This course is devoted to the study of the broad family of sparse processes that are specified by a generic (non-Gaussian) innovation model or, equivalently, as solutions of linear stochastic differential equations driven by white Lévy noise. It presents the mathematical tools for their characterization. The two leading threads that underly the exposition are - the statistical property of infinite divisibility, which induces two distinct types of behavior Gaussian vs. sparse at the exclusion of any other; - the structural link between linear stochastic processes and spline functions which is exploited to simplify the mathematics.The concepts are illustrated with the derivation of algorithms for the recovery of sparse signals, with applications to biomedical image reconstruction. In particular, this leads to a Bayesian reinterpretation of popular sparsity-promoting processing schemes such as total-variation denoising, LASSO, and wavelet shrinkage—as MAP estimators for specific types of sparse processes. The formulation also suggests alternative recovery procedures that minimize the estimation error. The course is targeted to an audience of graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistics.For more details, including table of content, see http://www.sparseprocesses.org. We look forward to welcoming you to Harbin this July! Contacting Organizers: Jianwei Ma (Department of Mathematics, jma@hit.edu.cn) 深度学习地震去噪 名称 地震数据的去噪可以看成是地球物理反问题，即从含噪数据中恢复原始数据。解决这个问题有两种思路，第一是从物理模型出发，建立和求解优化模型，获得原始数据。在去噪中通常需要设置一个与噪声相关的参数。对于含有随机噪声的实际数据，噪声方差未知，因此需要凭借人工经验不断尝试，会对结果带来不确定性影响。第二种思路不再假定具体的物理模型，而是从大数据出发，利用已有的数据样本和先验信息训练得到模型，并进行数据去噪。我们从数据出发，针对地震数据处理专门设计深度学习卷积神经网络以及训练样本库，用于无需调参的地震噪声压制（智能去噪），并通过迁移学习技术应用于实际数据。 图：卷积神经网络。Conv、ReLU、BN分布代表卷积层，非线性激活层和归一化层 图：曲波去噪和迁移学习去噪对比。迁移学习方法可以自动调整去噪程度，无需调整参数。 S. Yu, J. Ma*, W. Wang, Deep learning for denoising, Geophysics, 2017, revised. 深度学习反演-地下介质速度建模 名称 全波形反演是一种非线性优化问题，它的目标就是通过使地震勘测记录数据与模拟合成数据之间的残差最小化来估计地下介质模型。但是由于高昂的计算成本、反演中解的不唯一性以及对初始速度模型的依赖等不足，使得其尚未很好的应用到实际工业中。利用大数据的学习，而不是依赖于波动方程，可能为反演提供一条新途径。针对地震勘探中的速度建模问题，我们利用卷积神经网络，提出了一种直接从叠前地震数据反演速度模型的深度学习方法。从数据中自动挖掘有效特征信息，利用训练好的网络模型实现实时速度建模，且避免了传统全波形反演对于多个参数的依赖。 图： 基于深度学习速度建模示意图 图：全波形反演与基于深度学习速度建模对比。从上到下依次为：真实速度模型、全波形反演结果、深度学习反演结果 F. Yang, J. Ma*, Deep-learning inversion: a next generation seismic velocity model building method, Geophysics, 2019, 84 (4). 四维数据同化的地球物理流场预测 名称 地球物理流体的数值预报一般需要可信赖的初值、边值以及模型的物理参数。然而，这些数据通常具有不确定性，如观测数据含有噪声，观测存在位置偏差。数据驱动的同化方法可将模型变量、观测数据与背景场估计以优化的方式结合起来，间接反演不确定变量。传统的海洋污染预报只利用浓度观测信息，然而对于溢油污染以及观测缺失的情况，浓度观测难以获取。我们根据不同的初猜场信息，提出了两种基于水平集的图像数据同化方法，方法均通过同化观测数据中污染物的轮廓信息来识别模型参数与初始轮廓。其一，基于Euclidean度量的同化方法，该方法适用于初猜场的轮廓包含或含于真实初始轮廓；其二，在变分同化框架下结合水平集方法与基于优化输运理论的Wasserstein距离，该方法考虑初猜场与观测数据存在错位与形状误差的情况。 左图：同化前初猜场、真实状态。右图：融入轮廓观测同化后的分析场结果比较 左上、左下图：初猜场、观测和真实状态的预测结果。右上、右下图：基于L2范数、Wasserstein范数的同化结果预测比较。 1. L. Li, F.-X. Le Dimet, J. Ma*, and A. Vidard, A level-set-based image assimilation method: potential applications for predicting the movement of oil spills, IEEE Transactions on Geoscience and Remote Sensing, 2017, 55(11), 6330-6343. 2. L. Li, A. Vidard, F.-X. Le Dimet, J. Ma*, Topological data assimilation using Wasserstein distance, Inverse Problems, 2019, 35, 015006. 低维流形地震去噪 名称 如果平面中的点大致分布在一条直线上，我们可以通过线性拟合对点的分布规律进行逼近；如果点的分布较为复杂，则可通过样条函数进行拟合；如果样条函数也拟合不好，我们还可以通过一条光滑曲线进行拟合。这条光滑曲线可认为是二维欧氏空间中的一维流形空间。更一般的情况下，可以定义高维空间中的低维流形子空间。流形的维度即流形的自由度。一般来讲，如果将自然图像分块所形成的块集合看成高维空间中点的集合，那么这个集合位于一个低维流形上。比如分段光滑图像，其块尺度上的自由度为二，因此其分块集合位于一个二维流形上。地震数据也是如此，可以由地震数据块拟合成一个低维流形。假设数据中存在噪声，可以认为拟合出来的流形是不含噪声的，因此将数据块投影到拟合出来的流形上就实现了数据去噪。 左图：通过流形拟合平面上的点，通过投影实现去噪。 右图：地震数据经过分块形成流形。 左图：实际叠后数据去噪结果，右图：局部放大剖面 S. Yu, S. Osher, J. Ma*, Z. Shi, Noise attenuation in a low dimensional manifold, Geophysics, 2017, 82 (5), V321-V334 低维流形学习与机器学习也有密切关系！低维流形的定义中一个概念很重要，即“光滑”，如果利用不光滑的线段，我们可以拟合任意部分的点集，因此造成过拟合。“光滑”约束使得拟合出来的流形更符合实际情况，并且能够用于预测。机器学习中本质上也是对数据进行拟合，并且使用足够的参数可以拟合任意分布。过拟合对于预测不利，因此需要通过卷积网络、Dropout等方法来防止过拟合。低维流形学习与机器学习的关系更像是几何与代数的关系，从不同角度去解决拟合问题。 数据驱动紧框架 (Data-driven tight frame) 名称 Data-driven tight frame (DDTF)是一种新的自适应字典学习方法，它对字典元素给予了一个“紧框架”的约束（“紧框架”是一个比“正交”更松弛的约束条件，小波和曲波变换都属于“紧框架”字典），其学习过程的计算效率比传统的字典学习方法（如K-SVD）要快10-100倍。DDTF可作为地震数据稀疏表示的基本工具。目前我们已把其用在高维（3D和5D）地震勘探数据的去噪和插值。并相继提出了基于Monte Carlo (蒙特卡洛）DDTF、张量积DDTF、与Seislet结合的双稀疏学习字典，图基于的字典学习，来进一步提高计算效率和利用高维数据的几何结构性。 (a): 输入的地震数据; (b): 输入的初始滤波器; (c): DDTF学习得到的滤波器 四种不同方法进行同时插值和去噪的结果比较。 1. L. Liu, J. Ma*, Structured graph dictionary learning and application on the seismic denoising, IEEE Transactions on Geoscience and Remote Sensing, 2019, 57 (5), 2798-2810. 2. L. Liu, J. Ma*, G. Plonka, Sparse graph-regularized dictionary learning for random seismic noise, Geophysics, 2018, 83 (3), V213-V231. 3.. L. Liu, G. Plonka, J. Ma*, Seismic data interpolation and denoising by learning a tensor tight frame, Inverse Problems, 2017, 33 (10), 105011. 4. Y. Chen, J. Ma*, S. Fomel, Double sparsity dictionary for seismic noise attenuation, Geophysics, 2016, 81 (2), V17-V30. 5. S. Yu, J. Ma*, S. Osher, Monte Carlo data-driven tight frame for seismic data recovery, Geophysics, 2016, 81 (4), V327-V340. 6. S. Yu, J. Ma*, X. Zhang, M. Sacchi, Denoising and interpolation of high-dimensional seismic data by learning a tight frame, Geophysics, 2015, 80 (5), V119-V132. 7. J. Liang, J. Ma*, X. Zhang, Seismic data restoration via data-driven tight frame, Geophysics, 2014, 79 (3), V65-V74. 多方向成分分析（multidirectional component analysis) 名称 地震信号中的局部朝向信息对于地震资料解释和处理有重要作用。前者包括断层识别、不一致界面提取等；后者包括波场分离、速度估计、导向滤波等。我们提出了局部梯度向量矩阵的秩一约束方法来计算局部倾角，相较于传统的倾角估计方法（例如PWD: plan-wave destruction），新方法对随机噪声具有更好的鲁棒性，可同时实现随机噪声压制以及相关信号分离。其核心思想是，假设某块数据中只有一种主同相轴，那沿着该同相轴（或主特征）的局部梯队向量组成的矩阵，其秩应为一。以此为先验知识建立秩1约束优化模型（GVRO: gradient vector rank-one regularization），并扩展到可同时提取多个局部倾角的多方向成分分析（MDCA: multidirectional component analysis）。 图一：单方向同相轴的地震信号（左）及对应的梯队向量。其梯度向量矩阵秩数为一。 图二：模拟信号的成分分解。 （左） 含噪混合信号；（中） 分离的第一成分；（右）：分离的第二成分 图三： (a) 原始地震数据；(b) 分离的成分一；(c) 分离的成分二；(d) 分离的成分三。 1. K. Cai, J. Ma*, GVRO: gradient vector rank-one regularization with applications on seismic data processing, Geophysical Prospecting, 2018, revised. 2. K. Cai, J. Ma*, MDCA: multidirectional component analysis for robust estimation of multiple local dips, IEEE Transactions on Geoscience and Remote Sensing, 2019, 57 (5), 2798-2810. 时变子波及其地震反褶积 名称 由于散射、大地滤波等作用，地震子波在传播等过程中，其频率、相位等都时刻发生改变。因此利用传统稳态反褶积方法得到的反射系数其相对保幅性以及相位等都有一定的破坏。为解决此问题，我们引入Q值理论去模拟大地吸收衰减等过程并拓展了一种非稳态稀疏脉冲反褶积方法。 将非稳态地震子波看成稳定的震源子波与衰减函数的褶积，非稳态地震记录看成非稳态地震子波与反射系数的褶积。需先估计Q值，而后通过交替迭代优化震源子波与反射系数，可得到更加准确的反褶积结果。 上图: 模拟非稳态地震记录、传统反褶积方法、提出的方法。下图：实际测井数据、反褶积结果比较。 Y. Shui, J. Ma*, A nonstationary sparse spike deconvolution with anelastic attenuation, Geophysics, 2019, 84 (2), R221-R234. Asymmetric Chirplet Transform (不对称C-子波变换) 名称 由于地层的吸收，地震信号在时间序列上表现为不对称衰减。 为了能更好的稀疏表示地震信号，人们在构造稀疏变换的时候，一个基本的动机应该是去设计不对称衰减的基元。像傅里叶变换的周期基元（正玄函数）就不能很好表示这种衰减的非稳定态信号。我们提出了一种不对称C-子波变换，其基元具有自适应的非对称快速衰减的特性，可用于地震信号的分解和处理。变换的参数/系数如：包络线、旅行时、局部相位和频率均带有很强的物理意义。对地震解释、时变子波提取、波形反演均有可用武之地。 C-子波变换的部分基元展示 对1D信号（红色线）做C-子波变换得到的相位参数（蓝色线） 1. F. Bossmann, J. Ma*, Asymmetric chirplet transform II: phase, frequency, and chirp rate, Geophysics, 2016, 81 (6), V425-V439. 2. F. Bossmann, J. Ma*, Asymmetric chirplet transform for sparse representation of seismic data, Geophysics, 2015, 80 (6), WD89-WD100. Geometric Mode Decomposition （几何模态分解） 名称 针对著名的经验模态分解方法(EMD: Empirical Mode Decomposition）对含陡倾角等特征的地震数据处理的不足，提出了变分模态分解(VMD: Variational Mode Decomposition)，并在扩展到多维的过程中，进一步创新提出了几何模态分解（GMD: Geometrical Mode Decomposition）。此方法对波场特征分离、面波或多次波压制、插值等工作上都可能发挥作用。 基于新方法的地震数据分解示例 1. S. Yu, J. Ma*, Complex variational model decomposition for slop preserving denoising, IEEE Transactions on Geoscience and Remote Sensing, 2018, 56 (1), 586-597. 2. S. Yu, J. Ma*, S. Osher, Geometric mode decomposition, Inverse Problem and Imaging, 2018, 12 (4), 831-852. 基于低秩约束的多道集联合去噪 名称 地震数据处理的过程中经常需要处理一整条测线的多道集数据。如果我们将其看成视频，那其中的某一道集可当作视频中的一帧。借鉴视频去噪的思路，利用道集内部和之间的冗余性与相似性，提取相似的数据块重组成低秩矩阵，将去噪问题转化为求解秩最小化约束的优化问题。 图一：多道集联合低秩去噪示意图 图二：原始数据测线数据（上），单道集局部（中左）和去噪结果（中右），下图为红框的局部放大。 Z. Liu J. Ma*, X. Yong, Line survey joint denoising via low rank minimization, Geophysics, 2019, 84 (1), V21-V32. 基于分裂算法的快速高阶有限差分格式 名称 传统高阶紧支有限差分方法具有高精度的优点，但由于要求解多对角矩阵的逆，导致计算速度慢。我们采用了三种分裂算法，通过把多对角阵分解成多个三对角阵来提高波动方程模拟的计算速度，而且还保留了其计算精度高的优点；并与8、18、60阶的显式差分格式做了算例比较。 Sigsbee model (a) Eight-order optimal EFD, (b) the proposed CFD with M=3. (a) Eight-order optimal EFD, (b) the proposed CFD with M=3. (c) and (d) Closeup. 1. C. Zhang, B. Sun*, J. Ma, H. Yang, Splitting algorithm for high-order compact finite difference scheme in wave equation modeling, Geophysics, 2016, 81 (6), T295-T302. 压缩感知走进地球物理勘探（随笔） 名称 什么是压缩感知？ 压缩感知（CS：Compressed Sensing）描述的是：可从高度不完备的线性测量中高精度重构未知目标。创造性的把L1范数最小化和随机矩阵理论有机结合，可得到稀疏信号重建的最佳效果。它讲述了要重构一个连续信号，不再与香侬-奈奎斯特采样定理所说的“频带”有关，而是与未知信号的“稀疏度”有关。CS于2004年由E. Candes, D. Donoho, T. Tao 三位著名数学家提出，其中华裔天才数学家T.Tao (陶哲轩)的智商据说超过爱因斯坦，是人类史上智商最高的神人。CS技术入选了2007年美国十大科技进展。CS的主要几篇文献已被引用四万多次。 从数学上讲，CS本质是降维，从低维空间去研究高维空间。 从信号上讲，CS本质是采样，从频率相关到稀疏度相关。 从工程上讲，CS本质是成本，从物理测量成本转移到数学计算成本。 为什么CS这么火？ 从二十世纪四十年代开始，统治信号和信息领域的是香侬-奈奎斯特采样定理：要想从离散信号去恢复连续信号，离散信号的采样率至少应该是此连续信号最高频率的两倍。可以说大部分的信号采集相关的设备都是基于香侬定理设计的，如相机、雷达、核磁共振等等。CS理论出现后，其采样率将不在和信号的频带有关，而是和信号的稀疏度有关，打破了传统理论的束缚。所以很多基于传统理论设计的方法、软件和设备都可以得到升级换代。 单像素相机就是一个很好的例子，其反其道而行之，不再去追求千万像素的分辨率，而是用一个像素的时间序列成像就可用重构出高分辨率图像。 为什么CS能走进勘探？ 压缩感知是一个理论框架，不是单一的技术，其三要素是随机测量，目标的稀疏表示，稀疏促进的优化重构算法。地震勘探中，降低野外数据采集的成本而又能保证勘探精度，是一个很重要的问题。由于CS理论的出现，这个问题的考虑也由香侬采样的思路转变到稀疏重构的思路上来，会带来很多新的变革。CS所涉及的技术，在勘探的采集、处理、正演模拟、成像反演等方面都会带来改进或冲击。但其核心问题之一还是地震数据和地质目标的稀疏表示！ 淘宝的成功，在于改变了人们的交易方式。 腾讯的成功，在于改变了人们的沟通方式。 谷歌的成功，在于改变了人们的搜索方式。 C S 的成功，在于改变了信号的采集方式。 我所接触到的CS： 1998年在清华大学读博期间开始学习小波变换，从事波动方程多尺度模拟的研究。 2002年博士毕业后，在欧洲开始学做几何小波变换。从剑桥大学的Nick Kingbury那里学习了复数小波变换。而后转做脊波和曲波变换的信号处理应用，这两个几何小波变换正是压缩感知的创始人E. Candes的博士论文工作（导师是D. Donoho）。2006年在瑞士洛桑联邦理工访问小波专家Michael Unser和Martin Vetterli期间，参加了他们组织的一个小波会议上。会上首次接触到压缩感知的报告，并有幸与Candes教授当面交流了自己在曲波变换方面的工作，但此时自己并没有关注压缩感知。2007年到佛罗理达州立大学访问，开展曲波对流体湍流特征提取工作。有一次空闲，我问课题组的两位中国学生最近在干什么，回答说“在看压缩感知文献”，就是这句话让我重新关注并认真着手开始学习压缩感知。访问回国后，面向我国当时“嫦娥”探月卫星发射的大背景，成功将CS应用到了遥感成像。随即认识了Wotao Yin和Felix Herrmann 等较早从事CS的专家，并于2008年派出课题组学生唐刚前往加拿大UBC访问 Felix Herrmann教授一年，逐步开始CS在地震数据插值的应用。在2009年的地球物理年会上，做了题为“曲波变换和压缩感知在地震勘探中的成就和前景”的报告，2010年在著名期刊《IEEE Signal Processing Magazine》撰写了曲波变换的邀请综述， 在2011地球物理年会的“傅承义”获奖大会报告中做了“稀疏促进地震勘探”，并受《信号处理》期刊的邀请撰写了一篇中文的综述论文：压缩感知及其应用－从稀疏约束到低秩约束优化。 2011年到哈工大以后，课题组将工作重心放在CS在勘探中的创新应用。本着“不跟随”“自主创新“的理念，重点攻关CS的核心技术：地震数据的稀疏表示。课题组在该方向也相继取得了数据驱动紧框架、不对称C-子波变换、几何模式分解、双稀疏变换等技术，并在去噪、插值等方面得到较好应用。 目前正逐步开展地质目标导向的统计学习、基于CS的波动方程快速模拟和逆时偏移成像。 2013年在哈尔滨举办了优化和压缩感知的国际会议，2015年1月和S. Fomel, M. Sacchi, Ru-shan Wu共同在哈尔滨举办了以稀疏促进勘探为主题的第一届数学地球物理会议。2015年8月，与S. Fomel共同在每四年一届的ICIAM（国际工业与应用数学大会）上开设了压缩感知勘探为主题的专题讨论会。 2015年12月2-4号，在李幼铭研究员和张捷教授等前辈推动下，SEG（国际勘探地球物理学家协会）在北京成功举办了SEG压缩感知－地球物理应用新技术研讨会，注册参会人数达到180人。本人也有幸担任会议的两位主席之一，共同见证了近30位分别来自产、学、研的国内外专家的精彩报告。12月29号小范围CS研讨会在浙大继续召开，并在全国同时开设了18个视频分会场。目前CS已得到中石油和中石化等行业巨头的关注。 期待2016年，CS能真正走进我国油气勘探，去起到它应有的作用，也为当前油气行业寒冬带去一丝暖意。