Professor

Research Interests

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

Selected Publications

  Article

1. On the Subsample Size of Quantile-Based Randomized Kaczmarz
   • Author(s): CAI, Jianfeng; Chen, Junren; Ma, Anna; WU, Tong
   • Source: SIAM Journal on Matrix Analysis and Applications, v. 47, (2), p. 802-823
   • Year: 2026


2. Spectral compressed sensing via structured matrix optimization
   • Author(s): Cai, Jian Feng; Wu, Xunmeng; Yang, Zai; You, Juntao
   • Source: Handbook of Statistics, v. 54, p. 91-118
   • Year: 2026


3. 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


4. 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


5. 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


6. 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


7. 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


8. 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


9. 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


10. 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


11. 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


12. 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


13. 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


14. 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


15. 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


16. 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


17. 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


18. 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


19. 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


20. 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


21. 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


22. 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


23. 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


24. 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


25. 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


26. 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


27. 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


28. 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


29. 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


30. 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


31. 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


32. 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


33. 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


34. 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


35. 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


36. 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


37. 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


38. 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


39. 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


40. 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


41. 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


42. 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. Finding Low-Rank Matrix Weights in DNNs via Riemannian Optimization: RAdaGrad and RAdamW
   • Author(s): BIAN, Fengmiao; ZHENG, Jinyang; LIU, Ziyun; LUO, Jianzhou; CAI, Jianfeng
   • Source: Paper presented at 39th Annual Conference on Neural Information Processing Systems, NeurIPS 2025, San Diego, United States
   • Year: 2025


2. 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


3. 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


4. 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


5. 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


6. 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


7. 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


8. 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


9. 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


10. 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


11. 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