Professor

Research Interests

Theoretical and algorithmic foundations of problems related to information, data, and signals, with applications to inverse problems, signal processing, and machine learning.

Teaching

• MATH3322  Matrix Computation
• MATH5312  Advanced Numerical Methods II
• MATH6914W  Reading Course: Mathematical Foundations of Data Science III

Selected Publications

  Article

1. 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


2. 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


3. 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


4. 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


5. The Global Landscape of Phase Retrieval II: Quotient Intensity Models
   • Author(s): Cai, Jianfeng; Huang, Meng; Li, Dong; Wang, Yang
   • Source: Annals of Applied Mathematics, v. 38, (1), January 2022, p. 62-114
   • Year: 2022


6. 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, 2022, p. 1-77
   • Year: 2022


7. 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


8. 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


9. The Global Landscape of Phase Retrieval I: Perturbed Amplitude Models
   • Author(s): Cai, Jianfeng; Huang, Meng; Li, Dong; Wang, Yang
   • Source: Annals of Applied Mathematics, v. 37, (4), December 2021, p. 437-512
   • Year: 2021


10. Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery
    • Author(s): Cai, Hanqin; Cai, Jianfeng; Wang, Tianming; Yin, Guojian
    • Source: IEEE Transactions on Signal Processing, v. 69, 6 January 2021, article number 9316310, p. 809-821
    • Year: 2021


11. 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


12. Guarantees of riemannian optimization for low rank matrix completion
    • Author(s): Wei, Ke; Cai, Jianfeng; Chan, Tony Fan-cheong; Leung, Shing Yu
    • Source: Inverse Problems and Imaging, v. 14, (2), April 2020, p. 233-265
    • Year: 2020


13. 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, 2019
    • Year: 2019


14. 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


15. 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), 2014, p. 89-105
    • Year: 2014


16. 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


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


18. 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