Jian-Feng Cai

Professor,
Department of Mathematics,
Hong Kong University of Science and Technology.

E-mail: jfcai@ust.hk        Phone: +852 3469 2248        Office: 3459

Short Vita

  • Department of Mathematics, Hong Kong University of Science and Technology.
    • Professor, 2019--
    • Associate Professor, 2015--2019.
  • Department of Mathematics, University of Iowa.
    • Assistant Professor, 2011--2015.
  • Department of Mathematics, University of California, Los Angeles.
    • CAM Assistant Adjunct Professor, 2009--2011.
  • Temasek Laboratories, National University of Singapore.
    • Research Scientist, 2007--2009.
  • Department of Mathematics, Chinese University of Hong Kong.
    • Ph.D. in Mathematics, 2004--2007.
  • Department of Mathematics, Fudan University.
    • M.Sc. in Computational Mathematics, 2001--2004.
    • B.Sc. in Computational Mathematics, 1996--2000.

Research Interests

My research interests are on the theoretical and algorithmic foundations of problems related to information, data, and signals. My previous research focuses mainly on the efficient representation, sensing, and analysis of high-dimensional data, with applications to medical imaging, compressed sensing, signal processing, and machine learning.

Publications (Search for my publications and citations at Google Scholar)

Preprints

  • J.-F. Cai, J. Chen, A. Ma, and T. Wu, On Subsample Size of Quantile-Based Randomized Kaczmarz, preprint. pdf
  • J.-F. Cai, Y. Jiao, Y. Li, X. Lu, J.Z. Yang, and J. You, Online Quantum State Tomography via Stochastic Gradient Descent, preprint. pdf
  • J.-F. Cai, W. Huang, H. Wang, and K. Wei, Tensor Completion via Tensor Train Based Low-Rank Quotient Geometry under a Preconditioned Metric, preprint. pdf
  • J.-F. Cai, J.K. Choi, and K. Wei, Approximation Theory of Total Variation Minimization for Data Completion, preprint. pdf

Published Papers

  1. F. Bian, J. Zheng, Z. Liu, J. Luo, and J.-F. Cai, Finding Low-Rank Matrix Weights in DNNs via Riemannian Optimization: RAdaGrad and RAadmW, The Thirty-ninth Annual Conference on Neural Information Processing Systems (NeurIPS 2025), to appear. pdf
  2. J. Li, J.-F. Cai, Y. Chen, and D. Xia, Online Tensor Learning: Computational and Statistical Trade-offs, Adaptivity and Optimal Regret, Annals of Statistics, to appear. pdf
  3. J.-F. Cai, Z. Xu, and Z. Xu, Interlacing Polynomial Method for Matrix Approximation via Generalized Column and Row Selection, Foundations of Computational Mathematics, to appear. pdf
  4. J.-F. Cai, T. Wu, and R. Xia, Fast Non-convex Matrix Sensing with Optimal Sample Complexity, Proceedings of the 41st Conference on Uncertainty in Artificial Intelligence (UAI 2025), PMLR 244:497--520, 2025.
  5. Y. Zhang, F. Bian, X. Zhang, and J.-F. Cai, Preconditioned Riemannian Gradient Descent Algorithm for Low-Multilinear-Rank Tensor Completion, Proceedings of the 42nd International Conference on Machine Learning (ICML 2025), PMLR 267:74490--74514, 2025.
  6. J.-F. Cai, Z. Xian, and J. Ying, Fast and Provable Algorithms for Sparse PCA with Improved Sample Complexity, Proceedings of the 42nd International Conference on Machine Learning (ICML 2025), PMLR 267:6319--6340, 2025.
  7. Y. Shen, J. Li, J.-F. Cai, and D. Xia, Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regression, Annals of Statistics, 53(1):374--399, 2025. pdf
  8. F. Bian, J. Liu, X. Zhang, H. Gao, and J.-F. Cai, Flash Proton Radiation Therapy via a Stochastic Three-Operator Splitting Method, Inverse Problems, 41:025007, 2025. pdf
  9. J.-F. Cai, J.K. Choi, and J. Yang, Approximation Theory of Wavelet Frame Based Image Restoration, Applied and Computational Harmonic Analysis, 74:101712, 2025. pdf
  10. F. Bian, J.-F. Cai, X. Quan, and Y. Wang, A Preconditioned Fast Iterative Hard Thresholding Algorithm for Spectrally Sparse Signal Reconstruction, 2024 IEEE 13rd Sensor Array and Multichannel Signal Processing Workshop (SAM), 2024
  11. J. Fan, Y. Han, Z. Liu, J.-F. Cai, Y. Wang, and Z. Zhou, On the Convergence of Projected Bures-Wasserstein Gradient Descent under Euclidean Strong Convexity, Proceedings of the 41st International Conference on Machine Learning (ICML), PMLR 235:12832-12857, 2024.
  12. J. Fan, Y. Han, J. Zeng, J.-F. Cai, Y. Wang, Y. Xiang, and J. Zhang, RL in Markov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model, Proceedings of The 27th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 238:2035-2043, 2024. pdf
  13. J.-F. Cai, Y. Long, R. Wen, and J. Ying, A Fast and Provable Algorithm for Sparse Phase Retrieval, International Conference on Learning Representations (ICLR), 2024. pdf
  14. F. Bian, J.-F. Cai, and R. Zhang, A Preconditioned Riemannian Gradient Descent Algorithm for Low-Rank Matrix Recovery, SIAM Journal on Matrix Analysis and Applications, 45(4):2075--2103, 2024. pdf
  15. J.-F. Cai, J.K. Choi, J. Li, and G. Yin, Restoration Guarantee of Image Inpainting via Low Rank Patch Matrix Completion, SIAM Journal on Imaging Sciences, 17(3):1879--1908, 2024. pdf
  16. M.-C. Hsu, E.-J. Kuo, W.-H. Yu, J.-F. Cai, and M.-H. Hsieh, Quantum state tomography via nonconvex Riemannian gradient descent, Physical Review Letters, 132(24):240804, 2024. pdf
  17. J.-F. Cai, Z. Xu, and Z. Xu, Interlacing Polynomial Method for the Column Subset Selection Problem, International Mathematics Research Notices, 2024(9): 7798--7819, 2024. pdf
  18. J.-F. Cai and K. Wei, Solving Systems of Phaseless Equations via Riemannian Optimization with Optimal Sampling Complexity, Journal of Computational Mathematics, 42(3):755--783, 2024. pdf
  19. J.-F. Cai, J.V.M. Cardoso, D.P. Palomar, and J. Ying, Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity, Advances in Neural Information Processing Systems 36 (NeurIPS 2023), 2023. (23 pages) pdf
  20. X. Wu, Z. Yang, J.-F. Cai, and Z. Xu, Spectral Super-Resolution on the Unit Circle Via Gradient Descent, 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2023. (5 pages)
  21. J.-F. Cai, J. Li, and D. Xia, Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization, Journal of the American Statistical Association, 118(544):2588--2604, 2023. pdf
  22. H Yan, J.-F. Cai, Y Zhao, Z Jiang, Y Zhang, H Ren, Y Zhang, H Li, and Y Long, A lightweight high-resolution algorithm based on deep learning for layer-wise defect detection in laser powder bed fusion, Measurement Science and Technology, 35(2):025604, 2023.
  23. J. Yi, S. Dasgupta, J.-F. Cai, M. Jacob, J. Gao, M. Cho, and W. Xu, Separation-free super-resolution from compressed measurements is possible: an orthonormal atomic norm minimization approach, Information and Inference: A Journal of the IMA, 12(3):2351--2405, 2023.
  24. H.Q.Cai, J.-F. Cai, and J. You, Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion, SIAM Journal on Scientific Computing, 45(3):A1172--A1198, 2023. pdf
  25. J.-F. Cai, M. Huang, D. Li, and Y. Wang, Nearly Optimal Bounds for the Global Geometric Landscape of Phase Retrieval, Inverse Problems, 39(7):075011, 2023. pdf
  26. J.-F. Cai, J. Li, and J. You, Provable Sample-Efficient Sparse Phase Retrieval Initialized by Truncated Power Method, Inverse Problems, 39(7):075008, 2023. pdf
  27. J.-F. Cai, H. Liu, and Y. Wang, Gradient Descent for Symmetric Tensor Decomposition, Annals of Applied Mathematics, 38(4):385--413, 2022. pdf
  28. J.-F. Cai, Y. Jiao, X. Lu, and J. You, Sample-Efficient Sparse Phase Retrieval via Stochastic Alternating Minimization, IEEE Transactions on Signal Processing, 70:4951--4966, 2022. pdf
  29. C. Bao, J.-F. Cai, J.K. Choi, B. Dong, and K. Wei, Improved Harmonic Incompatibility Removal for Susceptibility Mapping via Reduction of Basis Mismatch, Journal of Computational Mathematics, 40(6):914--937, 2022. pdf
  30. J.-F. Cai, J. Li, and D. Xia, Provable Tensor-Train Format Tensor Completion by Riemannian Optimization, Journal of Machine Learning Research, 23(123):1--77, 2022. pdf
  31. J.-F. Cai, R. Chen, J. Fan, and H. Gao, Minimum-Monitor-Unit Optimization via a Stochastic Coordinate Descent Method, Physics in Medicine and Biology, 67(1):015009, 2022.
  32. J.-F. Cai, M. Huang, D. Li, and Y. Wang, Solving Phase Retrieval with Random Initial Guess Is Nearly as Good as by Spectral Initialization, Applied and Computational Harmonic Analysis, 58:60--84, 2022. pdf
  33. J.-F. Cai, J. Li, X. Lu, and J. You, Sparse Signal Recovery From Phaseless Measurements via Hard Thresholding Pursuit, Applied and Computational Harmonic Analysis, 56:367--390, 2022. pdf
  34. J.-F. Cai, J.K. Choi, J. Li, and K. Wei, Image Restoration: Structured Low Rank Matrix Framework for Piecewise Smooth Functions and Beyond, Applied and Computational Harmonic Analysis, 56:26--60, 2022. pdf
  35. J.-F. Cai, M. Huang, D. Li, and Y. Wang, The Global Landscape of Phase Retrieval II: Quotient Intensity Models, Annals of Applied Mathematics, 38(1):62--114, 2022. pdf
  36. J.-F. Cai, M. Huang, D. Li, and Y. Wang, The Global Landscape of Phase Retrieval I: Perturbed Amplitude Models, Annals of Applied Mathematics, 37(4):437--512, 2021. pdf
  37. J.-F. Cai, D. Li, J. Sun, and K. Wang, Enhanced Expressive Power and Fast Training of Neural Networks by Random Projections, CSIAM Transactions on Applied Mathematics, 2(3):532--550, 2021. pdf
  38. H. Wang, J.-F. Cai, T. Wang, and K. Wei, Fast Cadzow's Algorithm and a Gradient Variant, Journal of Scientific Computing, 88:41, 2021. pdf
  39. J. Li, J.-F. Cai, and H. Zhao, Scalable Incremental Nonconvex Optimization Approach for Phase Retrieval from Minimal Measurements, Journal of Scientific Computing, 87:43, 2021. pdf
  40. H.Q. Cai, J.-F. Cai, T. Wang, and G. Yin, Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery, IEEE Transactions on Signal Processing, 69:809--821, 2021. pdf
  41. J.-F. Cai, J.K. Choi, and K. Wei, Data Driven Tight Frame for Compressed Sensing MRI Reconstruction via Off-the-Grid Regularization, SIAM Journal on Imaging Sciences, 13(3):1272--1301, 2020. pdf
  42. J. Wang, W. Xu, J.-F. Cai, Q. Zhu, Y. Shi, and B. Yin, Multi-Direction Dictionary Learning Based Depth Map Super-Resolution with Autoregressive Modeling, IEEE Transactions on Multimedia, 22(6):1470--1484, 2020.
  43. Z. Li, J.-F. Cai, and K. Wei, Towards the Optimal Construction of a Loss Function without Spurious Local Minima for Solving Quadratic Equations, IEEE Transactions on Information Theory, 66(5): 3242--3260, 2020. pdf
  44. K. Wei, J.-F. Cai, T.F. Chan and S. Leung, Guarantees of Riemannian Optimization for Low Rank Matrix Completion, Inverse Problems and Imaging, 14(2):233--265, 2020. pdf
  45. J. Li, J.-F. Cai, and H. Zhao, Robust Inexact Alternating Optimization for Matrix Completion with Outliers, Journal of Computational Mathematics, 38(2):337--354, 2020.
  46. Y. Yang, W. Ma, Y. Zheng, J.-F. Cai, and W. Xu, Fast Single Image Reflection Suppression via Convex Optimization, 2019 IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 8141--8149, Long Beach, 2019. pdf
  47. J.-F. Cai, H. Liu, and Y. Wang, Fast Rank One Alternating Minimization Algorithm for Phase Retrieval, Journal of Scientific Computing, 79(1):128--147, 2019. pdf
  48. H.Q. Cai, J.-F. Cai, and K. Wei, Accelerated Alternating Projections for Robust Principal Component Analysis, Journal of Machine Learning Research, 20(20):1--33, 2019. pdf Code
  49. J.-F. Cai, T. Wang, and K. Wei, Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion, Appl. Comput. Harmon. Anal., 46(1):94--121, 2019. pdf Supplementary Material
  50. J.-F. Cai and K. Wei, Exploiting the Structure Effectively and Efficiently in Low Rank Matrix Recovery, Handbook of Numerical Analysis, Volume 19, pp. 21--51, 2018. pdf
  51. W. Xu, J. Yi, S. Dasgupta, J.-F. Cai, M. Jacob, and M. Cho, Separation-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach, 2018 IEEE International Symposium on Information Theory (ISIT), 2018. pdf
  52. J. Ying, J.-F. Cai, D. Guo, G. Tang, Z. Chen, X. Qu, Vandermonde Factorization of Hankel Matrix for Complex Exponential Signal Recovery -- Application in Fast NMR Spectroscopy, IEEE Trans. Signal Process., 66(21), 5520--5533, 2018. pdf
  53. J.-F. Cai, T. Wang, and K. Wei, Spectral Compressed Sensing via Projected Gradient Descent, SIAM J. Optim., 28(3):2625--2653, 2018. pdf
  54. J.-F. Cai, Y. Rong, Y. Wang, and Z. Xu, Data Recovery on a Manifold from Linear Samples: Theory and Computation, Annals of Mathematical Sciences and Applications, 3(1):337--365, 2018. pdf
  55. J.-F. Cai, W. Xu, and Y. Yang, Large Scale 2D Spectral Compressed Sensing in Continuous Domain, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 5905--5909, 2017. pdf
  56. J. Ying, H. Lu, Q. Wei, J.-F. Cai, D. Guo, J. Wu, Z. Chen, X. Qu, Hankel matrix nuclear norm regularized tensor completion for N-dimensional exponential signals, IEEE Trans. Signal Process., 65(14):3702--3717, 2017. pdf
  57. H. Liu, J.-F. Cai, and Y. Wang, Subspace Clustering by (k, k)-sparse Matrix Factorization, Inverse Probl. Imaging, 11(3):539--551, 2017. pdf
  58. M. Cho, J.-F. Cai, S. Liu, Y.C. Eldar, and W. Xu, Fast Alternating Projected Gradient Descent Algorithms for Recovering Spectrally Sparse Signals, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4638--4642, 2016.
  59. B. Zhang, W. Xu, J.-F. Cai, and L. Lai, Precise Phase Transition of Total Variation Minimization, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4518--4522, 2016. pdf
  60. Y. Wang, G. Wang, S. Mao, W. Cong, Z. Ji, J.-F. Cai, and Y. Ye, A Spectral Interior CT by a Framelet-Based Reconstruction Algorithm, Journal of X-Ray Science and Technology, 24(6): 771--785, 2016.
  61. Y. Wang, G. Wang, S. Mao, W. Cong, Z. Ji, J.-F. Cai, and Y. Ye, A framelet-based iterative maximum-likelihood reconstruction algorithm for spectral CT, Inverse Problems, 32(11):115021(16pp), 2016.
  62. K. Wei, J.-F. Cai, T.F. Chan and S. Leung, Guarantees of Riemannian Optimization for Low Rank Matrix Recovery, SIAM J. Matrix Anal. & Appl., 37(3):1198--1222, 2016. pdf
  63. Y. Liu, Z. Zhan, J.-F. Cai, D. Guo, Z. Chen, and X. Qu, Projected Iterative Soft-thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging, IEEE Trans. Med. Imag., 35(9): 2130--2140, 2016. pdf
  64. J.-F. Cai, X. Qu, W. Xu, and G.-B. Ye, Robust Recovery of Complex Exponential Signals from Random Gaussian Projections via Low Rank Hankel Matrix Reconstruction, Appl. Comput. Harmon. Anal., 41(2):470--490, 2016. pdf
  65. Z. Zhan, J.-F. Cai, D. Guo, Y. Liu, Z. Chen, and X. Qu, Fast Multi-class Dictionaries Learning with Geometrical Directions in MRI Reconstruction, IEEE Trans. Biomed. Eng., 63(9):1850--1861, 2016. Code
  66. J.-F. Cai, B. Dong, and Z. Shen, Image Restorations: A Wavelet Frame Based Model for Piecewise Smooth Functions and Beyond, Appl. Comput. Harmon. Anal., 41(1):94--138, 2016. pdf
  67. J.-F. Cai, S. Liu, and W. Xu, A fast algorithm for reconstruction of spectrally sparse signals in super-resolution, Proc. SPIE 9597, Wavelets and Sparsity XVI, 95970A, 2015. pdf
  68. J.-F. Cai and W. Xu, Guarantees of Total Variation Minimization for Signal Recovery, Inf. Inference, 4(4):328--353, 2015. pdf (A preliminary short version is published in Allerton 2013)
  69. M. Cho, K.V. Mishra, J.-F. Cai, and W. Xu, Block Iterative Reweighted Algorithms for Super-Resolution of Spectrally Sparse Signals, IEEE Signal Process. Lett., 22(12): 2319--2323, 2015. pdf
  70. Y. Liu, J.-F. Cai, Z. Zhan, D. Guo, J. Ye, Z. Chen, X. Qu, Balanced sparse model for tight frames in compressed sensing magnetic resonance imaging, PLoS One, Vol. 10, e0119584, 2015. Code
  71. J. Wang, and J.-F. Cai, Data-Driven Tight Frame for Multi-Channel Images and Its Application to Joint Color-Depth Image Reconstruction, J. Oper. Res. Soc. China, 3(2):99--115, 2015. pdf
  72. X. Qu, M. Mayzel, J.-F. Cai, Z. Chen, and V. Orekhov, Accelerated NMR Spectroscopy with Low-Rank Reconstruction, Angew. Chem. Int. Ed., 54(3):852--854, 2015.
  73. J. Wang, J.-F. Cai, Y. Shi, and B. Yin, Incoherent Dictionary Learning for Sparse Representation Based Image Denoising, IEEE International Conference on Image Processing (ICIP), Paris, 2014. pdf
  74. W. Xu, J.-F. Cai, K.V. Mishra, M. Cho, and A. Kruger, Precise semidefinite programming formulation of atomic norm minimization for recovering d-dimensional (D>=2) off-the-grid frequencies, Information Theory and Applications Workshop (ITA), San Diego, 2014. pdf
  75. J.-F. Cai, X. Jia, H. Gao, S. Jiang, Z. Shen, and H. Zhao, Cine cone beam CT reconstruction using low-rank matrix factorization: algorithm and a proof-of-princple study, IEEE Trans. Med. Imag., 33(8):1581--1591, 2014. pdf
  76. J.-F. Cai, H. Ji, Z. Shen, and G.-B. Ye, Data-driven tight frame construction and image denoising, Appl. Comput. Harmon. Anal., 37(1):89--105, 2014. pdf Code
  77. C. Bao, J.-F. Cai, and H. Ji, Fast sparsity-based orthogonal dictionary learning and image restoration, 2013 International Conference on Computer Vision (ICCV), pp. 3384--3391, 2013. pdf
  78. J.-F. Cai and W. Xu, Guarantees of Total Variation Minimization for Signal Recovery, Proceedings of 51st Annual Allerton Conference on Communication, Control, and Computing, pp. 1266--1271, 2013.
  79. J.-F. Cai, and S. Osher, Fast Singular Value Thresholding without Singular Value Decomposition, Methods Appl. Anal., 20(4):335--352, 2013. pdf
  80. W. Zhou, J.-F. Cai, and H. Gao, Adaptive tight frame based medical image reconstruction: proof-of-concept study in computed tomography, Inverse Probl., 29(12):125006(pp. 1--18), 2013. pdf
  81. G. Ye, M. Tang, J.-F. Cai, Q. Nie, and X. Xie, Low-Rank Regularization for Learning Gene Expression Programs, PLoS One, 8(12):e82146(pp. 1--9), 2013.
  82. W. Xu, M. Wang, J.-F. Cai, and K. Tang, Sparse Error Correction from Nonlinear Measurements with Applications in Bad Data Detection for Power Networks, IEEE Trans. Signal Processing, 61(24):6175--6187, 2013. pdf
  83. H. Zhang, J.-F. Cai, L. Cheng, and J. Zhu, Strongly Convex Programming for Exact Matrix Completion and Robust Principal Component Analysis, Inverse Probl. Imaging, 6(2):357--372, 2012. pdf
  84. J.-F. Cai, B. Dong, S. Osher, and Z. Shen, Image Restoration: Total Variation; Wavelet Frames; and Beyond, J. Amer. Math. Soc., 25(4):1033-1089, 2012. pdf
  85. J.-F. Cai, H. Ji, C. Liu, and Z. Shen, Framelet Based Blind Motion Deblurring from a Single Image, IEEE Trans. Image Process., 21(2):562--572, 2012. pdf Code
  86. J.-F. Cai, Z. Shen, and G.-B. Ye, Approximation of Frame Based Missing Data Recovery, Appl. Comput. Harmon. Anal., 31(2):185--204, 2011. pdf
  87. H. Gao, J.-F. Cai, Z. Shen, and H. Zhao, Robust Principle Component Analysis Based Four-Dimensional Computed Tomography, Phys. Med. Biol., 56(11):3181--3198, 2011. pdf
  88. S.-L. Yang, J.-F. Cai, and H.-W. Sun, Multigrid algorithm from cyclic reduction for Markovian queueing networks, Appl. Math. Comput., 217(16): 6990--7000, 2011.
  89. J.-F. Cai, R. Chan, L.X. Shen, and Z.W. Shen, Tight Frame Based Method for High-Resolution Image Reconstruction, Proceedings to the Conference on Wavelet Analysis and its Application, Zhuhai, China, August, 2007, Contemporary Applied Mathematics, Vol 14, pp. 1--36, 2010. pdf
  90. J.-F. Cai, R.H. Chan, and Z. Shen, Simultaneous Cartoon and Texture Inpainting, Inverse Probl. Imaging, 4(3):379--395, 2010. pdf
  91. J.-F. Cai, H. Ji, F. Shang and Z. Shen, Inpainting for Compressed Images, Appl. Comput. Harmon. Anal., 29(3): 368--381, 2010. pdf
  92. J.-F. Cai, E.J. Candès and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM J. Optim., 20(4): 1956--1982, 2010. pdf Code
  93. J.-F. Cai, and Z. Shen, Framelet based deconvolution, J. Comput. Math., 28(3): 289--308, 2010. pdf
  94. J.-F. Cai, R.H. Chan, and M. Nikolova, Fast Two-Phase Image Deblurring under Impulse Noise, J. Math. Imaging Vis., 36(1): 46--53, 2010. pdf Code
  95. J.-F. Cai, S. Osher and Z. Shen, Split Bregman Methods and Frame Based Image Restoration, Multiscale Model. Simul., 8(2):337--369, 2010. pdf Code Code
  96. J.-F. Cai, H. Ji, C. Liu and Z. Shen, High-quality curvelet-based motion deblurring using an image pair, 2009 IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 1566--1573, Miami, 2009. pdf
  97. J.-F. Cai, H. Ji, C. Liu and Z. Shen, Blind motion deblurring from a single image using sparse approximation, 2009 IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 104--111, Miami, 2009. pdf
  98. J.-F. Cai, S. Osher and Z. Shen, Convergence of the Linearized Bregman Iteration for $\ell_1$-Norm Minimization, Math. Comp., 78(268):2127--2136, 2009. pdf
  99. J.-F. Cai, H. Ji, C. Liu and Z. Shen, Blind motion deblurring using multiple images, J. Comput. Physics, 228(14):5057--5071, 2009. pdf
  100. J.-F. Cai, R.H. Chan, L. Shen, and Z. Shen, Simultaneously Inpainting in Image and Transformed Domains, Numer. Math., 112(4):509--533, 2009. pdf
  101. J.-F. Cai, R.H. Chan, L. Shen, and Z. Shen, Convergence Analysis of Tight Framelet Approach for Missing Data Recovery, Adv. Comput. Math., 31(1--3):87--113, 2009. pdf
  102. J.-F. Cai, S. Osher and Z. Shen, Linearized Bregman Iterations for Compressed Sensing, Math. Comp., 78(267):1515--1536, 2009. pdf
  103. J.-F. Cai, S. Osher and Z. Shen, Linearized Bregman Iterations for Frame-Based Image Deblurring, SIAM J. Imaging Sci., 2(1):226--252, 2009. pdf Code
  104. J.-F. Cai, R.H. Chan, and M. Nikolova, Two-phase Approach for Deblurring Images Corrupted by Impulse Plus Gaussian Noise, Inverse Probl. Imaging, 2(2):187--204, 2008. pdf Code
  105. J.-F. Cai, R.H. Chan, L. Shen, and Z. Shen, Restoration of Chopped and Nodded Images by Framelets, SIAM J. Sci. Comput., 30(3):1205--1227, 2008. pdf
  106. J.-F. Cai, R.H. Chan, and Z. Shen, A Framelet-Based Image Inpaiting Algorithm, Appl. Comput. Harmon. Anal., 24(2):131--149, 2008. pdf
  107. J.-F. Cai, R.H. Chan, and B. Morini, Minimization of an Edge-Preserving Regularization Functional by Conjugate Gradient Type Methods, Image Processing Based on Partial Differential Equations, in Series: Mathematics and Visualization, Springer Berlin Heidelberg, pp. 107--120, 2007. pdf
  108. J.-F. Cai, R.H. Chan, and C. Di Fiore, Minimization of a Detail-preserving Regularization Functional for Impulse Noise Removal, J. Math. Imaging Vis., 29(1):79--91, 2007. pdf Code
  109. X. Zhang, J. Cai, and Y. Wei, Interval Iterative Methods for Computing Moore-Penrose Inverse, Appl. Math. Comput., 183(1):522--532, 2006. pdf
  110. J.-F. Cai, M.K. Ng, and Y.-M. Wei, Modified Newton's Algorithm for Computing the Group Inverses of Singular Toeplitz Matrices, J. Comput. Math., 24(5):647--656, 2006. pdf
  111. Y. Wei, J. Cai, and M.K. Ng, Computing Moore-Penrose Inverses of Toeplitz Matrices by Newton's Iteration, Math. Comput. Modelling, 40(1--2):181--191, 2004. pdf
  112. J. Cai, and Y. Wei, Displacement Structure of Weighted Pseudoinverses, Appl. Math. Comput., 153(2):317--335, 2004. pdf

Awards

  • Best Teaching Award, MSc in Big Data Technology, HKUST, 2024.
  • Highly Cited Researchers, Clarivate Analytics, 2017, 2018.
  • School Research Award, School of Science, HKUST, 2017.

Research Grants

Graduate Students

  • Zhuozhi Xian, PhD in Mathematics, HKUST, 08/2025. First job: Postdoc, Department of ECE, HKUST.
  • Xueyang Quan, PhD in Mathematics, HKUST, 08/2025. First job: Teaching Associate, Department of Mathematics, HKUST.
  • Jiayi Li, PhD in Mathematics, HKUST, 01/2025. First job: Postdoc, Department of Mathematics, HKUST.
  • Junyi Fan, PhD in Mathematics, HKUST, 08/2024. First job: Researcher, Huawei Theory Lab.
  • Jingyang Li, PhD in Mathematics, HKUST, 06/2023. First job: Postdoctoral Assistant Professor, Department of Mathematics/Department of Statistics, University of Michigan.
  • Ruixue Wen, PhD in Mathematics, HKUST, 08/2022. First job: High school teacher.
  • Juntao You, PhD in Mathematics, HKUST, 06/2021. First job: Huawei Technologies Co. Ltd.
  • Zhenzhen Li, PhD in Mathematics, HKUST, 06/2020. First job: Postdoc, Department of Computing and Mathematical Sciences, California Institute of Technology.
  • Jiaze Sun, MPhil in Mathematics, HKUST, 06/2019. First job: PhD Student, Electrical and Electronic Engineering, Imperial College London.
  • Yang Yang, PhD in AMCS, U Iowa, 12/2018. First job: Senior Software Engineer, ASML Hermes Microvision Inc., San Jose.
  • HanQin Cai, PhD in AMCS, U Iowa, 05/2018. First job: PIC Assistant Adjunct Professor, Department of Mathematics, University of California, Los Angeles.
  • Tianming Wang, PhD in AMCS, U Iowa, 05/2018. First job: Postdoctoral Fellow, Institute for Computational Engineering & Sciences, University of Texas at Austin.
  • Suhui Liu, PhD in Mathematics, U Iowa, 05/2017. First job: Lecturer, Wuhan Institute of Technology.
  • Tianyi Zhang, PhD in AMCS, U Iowa, 08/2015. First job: Algorithmic Trader, Shanghai Cyndi Investment Co. Ltd.