Professor

Research Interests

Theoretical and algorithmic foundations of inverse problems, signal processing, and data analysis.

Teaching

• MATH2111  Matrix Algebra and Applications
• MATH4995  Capstone Project for Data Science

Selected Publications

  Article

1. 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


2. 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


3. A lightweight high-resolution algorithm based on deep learning for layer-wise defect detection in laser powder bed fusion
   • Author(s): Yan, Hualin; Cai, Jian-Feng; Zhao, Yingjian; Jiang, Zimeng; Zhang, Yingjie; Ren, Hang; Zhang, Yuhui; Li, Huaping; Long, Yu
   • Source: Measurement Science and Technology, v. 35, (2), February 2024, article number 025604
   • Year: 2024


4. 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


5. Solving Systems of Phaseless Equations via Riemannian Optimization With Optimal Sampling Complexity
   • Author(s): Cai, Jianfeng; Wei, Ke
   • Source: Journal of Computational Mathematics, May 2023, p. 1-30
   • Year: 2023


6. 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


7. 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


8. 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


9. 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


10. 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


11. Gradient Descent for Symmetric Tensor Decomposition
    • Author(s): Cai, Jianfeng; Liu, Haixia; Wang, Yang
    • Source: Annals of Applied Mathematics, v. 38, (4), November 2022, p. 385-413
    • Year: 2022


12. 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


13. Improved Harmonic Incompatibility Removal for Susceptibility Mapping via Reduction of Basis Mismatch
    • Author(s): Bao, Chenglong; Cai, Jianfeng; Choi, Jae Kyu; Dong, Bin; Wei, Ke
    • Source: Journal of Computational Mathematics, v. 40, (6), 2022, p. 914-937
    • Year: 2022


14. Enhanced Expressive Power and Fast Training of Neural Networks by Random Projections
    • Author(s): Cai, Jianfeng; Li, Dong; Sun, Jiaze; Wang, Ke
    • Source: CSIAM Transactions on Applied Mathematics, v. 2, (3), August 2021, p. 532-550
    • Year: 2021


15. 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


16. 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


17. 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


18. 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


19. 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


20. 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

  Conference paper

1. A Fast and Provable Algorithm for Sparse Phase Retrieval
   • Author(s): Cai, Jianfeng; Long, Yu; Wen, Ruixue; Ying, Jiaxi
   • Year: 2024


2. On the Convergence of Projected Bures-Wasserstein Gradient Descent under Euclidean Strong Convexity
   • Author(s): Fan, Junyi; Han, Yuxuan; Liu, Zijian; Cai, Jianfeng; Wang, Yang; Zhou, Zhengyuan
   • Year: 2024


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