jfcai

CAI, Jian-Feng
蔡劍鋒

(PhD Chinese Univ of Hong Kong)

Phone: (852) 3469 2248
Email: jfcai@ust.hk
Office: Room 3459
Home Page

Professor



Research Interests

Algorithmic and mathematical foundation of information and data, with applications in signal processing, inverse problems, and machine learning.

Teaching

  • MATH5312  Advanced Numerical Methods II

Selected Publications

  Article

  1. Tensor completion via tensor train based low-rank quotient geometry under a preconditioned metric
    • Author(s): Cai, Jian Feng; Huang, Wen; Wang, Haifeng; Wei, Ke
    • Source: Numerical linear algebra with applications, v. 33, (1), article number e70056
    • Year: 2026

  2. Fast Non-convex Matrix Sensing with Optimal Sample Complexity
    • Author(s): Cai, Jian Feng; Wu, Tong; Xia, Ruizhe
    • Source: Proceedings of Machine Learning Research, v. 286, p. 497-507
    • Year: 2025

  3. Interlacing Polynomial Method for Matrix Approximation via Generalized Column and Row Selection
    • Author(s): Cai, Jian Feng; Xu, Zhiqiang; Xu, Zili
    • Source: Foundations of Computational Mathematics
    • Year: 2025

  4. Flash proton radiation therapy via a stochastic three-operator splitting method
    • Author(s): Bian, Fengmiao; Liu, Jiulong; Zhang, Xiaoqun; Gao, Hao; Cai, Jianfeng
    • Source: Inverse Problems, v. 41, (2), 28 February 2025 , article number 025007
    • Year: 2025

  5. Computationally efficient and statistically optimal robust high-dimensional linear regression
    • Author(s): Shen, Yinan; Li, Jingyang; Cai, Jianfeng; Xia, Dong
    • Source: Annals of Statistics, v. 53, (1), February 2025, p. 374-399
    • Year: 2025

  6. Approximation theory of wavelet frame based image restoration
    • Author(s): Cai, Jian-Feng; Choi, Jae Kyu; Yang, Jianbin
    • Source: Applied and Computational Harmonic Analysis, v. 74, January 2025, article number 101712
    • Year: 2025

  7. A PRECONDITIONED RIEMANNIAN GRADIENT DESCENT ALGORITHM FOR LOW-RANK MATRIX RECOVERY
    • Author(s): Bian, Fengmiao; Cai, Jianfeng; Zhang, Rui
    • Source: SIAM Journal of Matrix Analysis and Applications, v. 45, (4), December 2024, p. 2075-2103
    • Year: 2024

  8. Restoration Guarantee of Image Inpainting via Low Rank Patch Matrix Completion
    • Author(s): Cai, Jianfeng; Choi, Jae Kyu; Li, Jingyang; Yin, Guojian
    • Source: SIAM Journal on Imaging Sciences, v. 17, (3), September 2024, p. 1879-1908
    • Year: 2024

  9. Quantum State Tomography via Nonconvex Riemannian Gradient Descent
    • Author(s): Hsu, Ming-Chien; Kuo, En-Jui; Yu, Wei-Hsuan; Cai, Jianfeng; Hsieh, Min-Hsiu
    • Source: Physical Review Letters, v. 132, (24), June 2024, article number 240804, p. 1-7
    • Year: 2024

  10. Interlacing Polynomial Method for the Column Subset Selection Problem
    • Author(s): Cai, Jian-Feng; Xu, Zhiqiang; Xu, Zili
    • Source: International Mathematics Research notices, January 2024
    • Year: 2024

  11. Separation-free super-resolution from compressed measurements is possible: an orthonormal atomic norm minimization approach
    • Author(s): Yi, Jirong; Dasgupta, Soura; Cai, Jian-Feng; Jacob, Mathews; Gao, Jingchao; Cho, Myung; Xu, Weiyu
    • Source: Information and Inference: A Journal of the IMA, v. 12, (3), August 2023, article number iaad033
    • Year: 2023

  12. Structured Gradient Descent for Fast Robust Low-rank Hankel Matrix Completion
    • Author(s): Cai, Hanqin; Cai, Jianfeng; You, Juntao
    • Source: SIAM Journal on Scientific Computing, v. 45, (3), June 2023, p. A1172-A1198
    • Year: 2023

  13. Nearly optimal bounds for the global geometric landscape of phase retrieval
    • Author(s): Cai, Jianfeng; Huang, Meng; Li, Dong; Wang, Yang
    • Source: Inverse Problems, v. 39, (7), July 2023, article number 075011
    • Year: 2023

  14. Provable sample-efficient sparse phase retrieval initialized by truncated power method
    • Author(s): Cai, Jianfeng; Li, Jingyang; You, Juntao
    • Source: Inverse Problems, v. 39, (7), June 2023, article number 075008
    • Year: 2023

  15. Sparse Signal Recovery From Phaseless Measurements Via Hard Thresholding Pursuit
    • Author(s): Cai, Jianfeng; Li, Jingzhi; Lu, Xiliang; You, Juntao
    • Source: Applied and Computational Harmonic Analysis, v. 56, January 2022, p. 367-390
    • Year: 2022

  16. Solving phase retrieval with random initial guess is nearly as good as by spectral initialization
    • Author(s): Cai, Jianfeng; Huang, Meng; Li, Dong; Wang, Yang
    • Source: Applied and Computational Harmonic Analysis, v. 58, May 2022, p. 60-84
    • Year: 2022

  17. Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization
    • Author(s): Cai, Jian-Feng; Li, Jingyang; Xia, Dong
    • Source: Journal of the American Statistical Association, April 2022
    • Year: 2022

  18. Image Restoration: Structured Low Rank Matrix Framework for Piecewise Smooth Functions and Beyond
    • Author(s): Cai, Jianfeng; Choi, Jae Kyu; Li, Jingyang; Wei, ke
    • Source: Applied and Computational Harmonic Analysis, v. 56, January 2022, p. 26-60
    • Year: 2022

  19. Provable Tensor-Train Format Tensor Completion by Riemannian Optimization
    • Author(s): Cai, Jianfeng; Li, Jingyang; Xia, Dong
    • Source: Journal of Machine Learning Research, v. 23, April 2022, article number 123, p. 1-77
    • Year: 2022

  20. Sample-Efficient Sparse Phase Retrieval via Stochastic Alternating Minimization
    • Author(s): Cai, Jianfeng; Jiao, Yuling; Lu, Xiliang; You, Juntao
    • Source: IEEE Transactions on Signal Processing, v. 70, 12 October 2022, article number 9917336, p. 4951-4966
    • Year: 2022

  21. Data Driven Tight Frame for Compressed Sensing MRI Reconstruction via Off-the-Grid Regularization
    • Author(s): Cai, Jianfeng; Choi, Jae Kyu; Wei, Ke
    • Source: SIAM Journal on Imaging Sciences, v. 13, (3), 2020, p. 1272-1301
    • Year: 2020

  22. Towards the optimal construction of a loss function without spurious local minima for solving quadratic equations
    • Author(s): Li, Zhenzhen; Cai, Jianfeng; Wei, Ke
    • Source: IEEE Transactions on Information Theory, v. 66, (5), May 2020, article number 8918236, p. 3242-3260
    • Year: 2020

  23. Fast and provable algorithms for spectrally sparse signal reconstruction via low-rank Hankel matrix completion
    • Author(s): Cai, Jianfeng; Wang, Tianming; Wei, Ke
    • Source: Applied and Computational Harmonic Analysis, v. 46, (1), January 2019, p. 94-121
    • Year: 2019

  24. Accelerated Alternating Projections for Robust Principal Component Analysis
    • Author(s): Cai, HanQin; Cai, Jian-Feng; Wei, Ke
    • Source: Journal of Machine Learning Research, v. 20, February 2019, article number 20
    • Year: 2019

  25. Spectral Compressed Sensing via Projected Gradient Descent
    • Author(s): Cai, Jianfeng; Wang, Tianming; Wei, Ke
    • Source: SIAM Journal on Optimization, v. 28, (3), September 2018, p. 2625-2653
    • Year: 2018

  26. Guarantees of Riemannian Optimization for Low Rank Matrix Recovery
    • Author(s): Wei, Ke; Cai, Jianfeng; Chan, Tony F.; Leung, Shing Yu
    • Source: SIAM Journal on Matrix Analysis and Applications, v. 37, (3), 2016, p. 1198-1222
    • Year: 2016

  27. Projected Iterative Soft-thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging
    • Author(s): Liu, Yunsong; Zhan, Zhiang; Cai, Jianfeng; Guo, Di; Chen, Zhong; Qu, Xiaobu
    • Source: IEEE Transactions on Medical Imaging, v. 35, (9), September 2016, article number 7448403, p. 2130-2140
    • Year: 2016

  28. Accelerated NMR Spectroscopy with Low-Rank Reconstruction
    • Author(s): Qu, Xiaobo; Mayzel, Maxim; Cai, Jian Feng; Chen, Zhong; Orekhov, Vladislav
    • Source: Angewandte Chemie - International Edition, v. 54, (3), January 2015, p. 852-854
    • Year: 2015

  29. Cine cone beam CT reconstruction using low-rank matrix factorization: algorithm and a proof-of-princple study
    • Author(s): Cai, Jian Feng; JIa, Xun; Gao, Hao; Jiang, Steve; Shen, Zuowei; Zhao, Hongkai
    • Source: IEEE Transactions on Medical Imaging, v. 33, (8), 2014, article number 6803058, p. 1581-1591
    • Year: 2014

  30. Data-driven tight frame construction and image denoising
    • Author(s): Cai, Jianfeng; Ji, Hui; Shen, Zuowei; Ye, Guibo
    • Source: Applied and Computational Harmonic Analysis, v. 37, (1), July 2014, p. 89-105
    • Year: 2014

  31. Framelet Based Blind Motion Deblurring from a Single Image
    • Author(s): Cai, Jian-Feng; Ji, Hui; Liu, Chaoqiang; Shen, Zuowei
    • Source: IEEE Transactions on Image Processing, v.21, (2), February 2012, Article number 5981391, p. 562-572
    • Year: 2012

  32. Image Restoration: Total Variation; Wavelet Frames; and Beyond
    • Author(s): Cai, Jianfeng; Dong, Bin; Osher, Stanley; Shen, Zuowei
    • Source: Journal of the American Mathematical Society, v. 25, (4), 2012, p. 1033-1089
    • Year: 2012

  33. Approximation of frame based missing data recovery
    • Author(s): Cai, Jian-Feng; Shen, Zuowei; Ye, Guibo
    • Source: Applied and Computational Harmonic Analysis, v. 31, (2), September 2011, p. 185-204
    • Year: 2011

  34. Robust Principle Component Analysis Based Four-Dimensional Computed Tomography
    • Author(s): Gao, Hao; Cai, Jianfeng; Shen, Zuowei; Zhao, Hongkai
    • Source: Physics in Medicine and Biology, v.56, (11), 2011, p. 3181-3198
    • Year: 2011

  35. A singular value thresholding algorithm for matrix completion
    • Author(s): Cai, Jian Feng; Candès, Emmanuel J.; Shen, Zuowei
    • Source: SIAM Journal on Optimization, v. 20, (4), p. 1956-1982
    • Year: 2010

  36. Linearized Bregman Iterations for Compressed Sensing
    • Author(s): Cai, Jian-Feng; Osher, Stanley J.; Shen, Zuowei
    • Source: Mathematics of Computation, v. 78, Issue 267, July 2009, p. 1515-1536
    • Year: 2009

  37. Simultaneously Inpainting in Image and Transformed Domains
    • Author(s): Cai, Jian-Feng; Chan, Raymond H.; Shen, Lixin; Shen, Zuowei
    • Source: Numerische Mathematik, v. 112, Issue 4, June 2009, p. 509-533
    • Year: 2009

  38. Split Bregman Methods and Frame Based Image Restoration
    • Author(s): Cai, Jian-Feng; Osher, Stanley; Shen, Zuowei
    • Source: Multiscale Modeling and Simulation, v. 8, Issue 2, 2009, p. 337-369
    • Year: 2009

  39. Blind motion deblurring using multiple images
    • Author(s): Cai, Jian-Feng; Ji, Hui; Liu, Chaoqiang; Shen, Zuowei
    • Source: Journal of Computational Physics, v. 228, Issue 14, 1 August 2009, p. 5057-5071
    • Year: 2009

  40. Linearized Bregman Iterations for Frame-Based Image Deblurring
    • Author(s): Cai, Jian-Feng; Osher, Stanley; Shen, Zuowei
    • Source: Siam Journal On Imaging Sciences, v. 2, Issue 1, 2009, p. 226-252
    • Year: 2009

  Conference paper

  1. Preconditioned Riemannian gradient descent algorithm for low-multilinear-rank tensor completion
    • Author(s): Zhang, Yuanwei; BIAN, Fengmiao; Zhang, Xiaoqun; CAI, Jianfeng
    • Source: Paper presented at International Conference on Machine Learning (ICML 2025), Vancouver, Canada
    • Year: 2025

  2. RL in Markov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model
    • Author(s): Fan, Junyi; Han, Yuxuan; Zeng, Jialin; Cai, Jianfeng; Wang, Yang; Xiang, Yang; Zhang, Jiheng
    • Source: Proceedings of Machine Learning Research, v. 238, May 2024, p. 2035-2043
    • Year: 2024

  3. Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity
    • Author(s): Cai, Jianfeng; De Miranda Cardoso, Jose Vinicius; P. Palomar, Daniel; Ying, Jiaxi
    • Source: Advances in Neural Information Processing Systems, v. 36, December 2023
    • Year: 2023

  4. Spectral Super-Resolution on the Unit Circle Via Gradient Descent
    • Author(s): Wu, Xunmeng; Yang, Zai; Cai, Jianfeng; Xu, Zongben
    • Source: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, May 2023, article number 10096359
    • Year: 2023

  5. Fast Single Image Reflection Suppression via Convex Optimization
    • Author(s): Yang, Yang; Ma, Wenye; Zheng, Yin; Cai, Jianfeng; Xu, Weiyu
    • Source: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, v. 2019, June 2019, p. 8133-8141
    • Year: 2019

  6. Robust Recovery of Complex Exponential Signals from Random Gaussian Projections via Low Rank Hankel Matrix Reconstruction
    • Author(s): Cai, Jianfeng; Qu, Xiaobo; Xu, Weiyu; Ye, Guibo
    • Source: Applied and Computational Harmonic Analysis, v. 41, (2), September 2016, p. 470-490
    • Year: 2016

  7. Precise semidefinite programming formulation of atomic norm minimization for recovering d-dimensional (D ≥ 2) off-the-grid frequencies
    • Author(s): Xu, Weiyu; Cai, Jianfeng; Mishra, Kumar Vijay; Cho, Myung; Kruger, Anton
    • Source: 2014 Information Theory and Applications Workshop, ITA 2014 - Conference Proceedings, 2014, article number 6804267
    • Year: 2014

  8. Fast Sparsity-based Orthogonal Dictionary Learning and Image Restoration
    • Author(s): Bao, Chenglong; Cai, Jianfeng; Ji, Hui
    • Source: Proceedings of the IEEE International Conference on Computer Vision, 2013, article number 6751532, p. 3384-3391
    • Year: 2013

  9. Blind motion deblurring from a single image using sparse approximation
    • Author(s): Cai, Jian-Feng; Ji, Hui; Liu, Chaoqiang
    • Source: 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009; Miami, United States, 20 June 2009, Article number 5206743, p. 104-111
    • Year: 2009

  10. High-quality curvelet-based motion deblurring from an image pair
    • Author(s): Cai, Jian-Feng; Ji, Hui; Liu, Chaoqiang
    • Source: 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, Miami, FL; United States, 20 June 2009, p. 1566-1573
    • Year: 2009