Department of Mathematics, HKUST  

  CAI, Jian-Feng   蔡劍鋒

  PhD Chinese Univ of Hong Kong

Office: Room 3436  

Telephone: 3469 2248  

Email: jfcai@ust.hk  

URL:
https://www.math.hkust.edu.hk/~jfcai   
  Professor

Teaching

  • MATH3332  Data Analytic Tools

Research Interests

  • Design and analysis of efficient algorithms for problems in data science and imaging, using tools from computational harmonic analysis, approximation theory, numerical linear algebra, optimization, and probability.

       Selected Publications

Full Publication List [HKUST Scholarly Publications]  

Article   

  1. 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

  2. Scalable Incremental Nonconvex Optimization Approach for Phase Retrieval
    • Author(s): Li, Ji; Cai, Jianfeng; Zhao, Hongkai
    • Source: Journal of Scientific Computing, v. 87, (2), March 2021, article number 43
    • Year: 2021

  3. A stochastic alternating minimization method for sparse phase retrieval
    • Author(s): Cai, Jianfeng; Jiao, Yuling; Lu, Xiliang; You, Juntao
    • Source: 數學雜志=Journal of Mathematics, v. 40, (4), 2020, p. 379-388
    • Year: 2020

  4. 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

  5. Multi-Direction Dictionary Learning Based Depth Map Super-Resolution With Autoregressive Modeling
    • Author(s): Wang, Jin; Xu, Wei; Cai, Jianfeng; Zhu, Qing; Shi, Yunhui; Yin, Baocai
    • Source: IEEE Transactions on Multimedia, v. 22, (6), June 2020, article number 8861360, p. 1470-1484
    • Year: 2020

  6. 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

  7. Robust Inexact Alternating Optimization for Matrix Completion with Outliers
    • Author(s): Li, Ji; Cai, Jianfeng; Zhao, Hongkai
    • Source: Journal of Computational Mathematics, v. 38, (2), February 2020, p. 337-354
    • Year: 2020

  8. 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

  9. Fast Rank-One Alternating Minimization Algorithm for Phase Retrieval
    • Author(s): Cai, Jian-Feng ; Liu, Haixia; Wang, Yang
    • Source: Journal of Scientific Computing, v.79, (1), April 2019, p. 128-147
    • Year: 2019

  10. 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

  11. 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

  12. Vandermonde Factorization of Hankel Matrix for Complex Exponential Signal Recovery-Application in Fast NMR Spectroscopy
    • Author(s): Ying, Jiaxi; Cai, Jianfeng ; Guo, Di; Tang, Gongguo; Chen, Zhong; Qu, Xiaobo
    • Source: IEEE Transactions on Signal Processing, v. 66, (21), November 2018, article number 8457300, p. 5520-5533
    • Year: 2018

  13. 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

  14. Data recovery on a manifold from linear samples: theory and computation
    • Author(s): Rong, Yi ; Wang, Yang ; Cai, Jianfeng ; Xu, Zhiqiang
    • Source: Annals of Mathematical Sciences and Applications. , v. 3, (1), March 2018, p. 337-365
    • Year: 2018

  15. Image restoration: A wavelet frame based model for piecewise smooth functions and beyond
    • Author(s): Cai, Jianfeng; Dong, Bin; Shen, Zuowei
    • Source: Applied and Computational Harmonic Analysis. , v. 41, (1), July 2016, p. 94-138
    • Year: 2016

  16. 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, Gui-bo
    • Source: Applied and Computational Harmonic Analysis. , v. 41, (2), September 2016, p. 470-490
    • Year: 2016

  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. 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

  19. Correction: Low-rank regularization for learning gene expression programs
    • Author(s): Ye, Guibo; Tang, Mengfan; Cai, Jianfeng; Nie, Qing; Xie, Xiaohui
    • Source: PLoS ONE, v. 9, (1), 13 January 2014
    • Year: 2014

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. A framelet-based image inpainting algorithm
    • Author(s): Cai, Jian-Feng; Chan, Raymond H.; Shen, Zuowei
    • Source: Applied and Computational Harmonic Analysis. , v. 24, Issue 2, March 2008, p. 131-149
    • Year: 2008

Book chapter   

  1. Exploiting the Structure Effectively and Efficiently in Low-Rank Matrix Recovery
    • Author(s): Cai, Jianfeng ; Wei, Ke
    • Source: Handbook of Numerical Analysis, volume 19 / Series Editors: Professor Qiang Du. Elsevier, 2018, p. 21-51, Ch. 2
    • Year: 2018

Conference paper   

  1. Image Inpainting Based on Multi-frequency Probabilistic Inference Model
    • Author(s): Wang, Jin; Wang, Chen; Huang, Qingming; Shi, Yunhui; Cai, Jianfeng; Zhu, Qing; Yin, Baocai
    • Source: MM '20: Proceedings of the 28th ACM International Conference on Multimedia / Association for Computing Machinery. New York : Association for Computing Machinery, 2020, p. 1-9
    • Year: 2020

  2. 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

  3. Data-driven method for 3D axis-symmetric object reconstruction from single cone-beam projection data
    • Author(s): Luo, Shousheng; Meng, Ruyue; Wei, Suhua; Cai, Jianfeng; Tai, Xuecheng; Wang, Yang
    • Source: ACM International Conference Proceeding Series, August 2019, p. 288-292
    • Year: 2019

  4. Data-driven tight frame for Cryo-EM image denoising and conformational classification
    • Author(s): Xian, Yin ; Gu, Hanlin ; Wang, Wei CHEM; Huang, Xuhui CHEM; Yao, Yuan ; Wang, Yang ; Cai, Jianfeng
    • Source: 2018 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2018 - Proceedings, February 2019, article number 8646614, p. 544-548
    • Year: 2019

  5. Separation-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach
    • Author(s): Xu, Weiyu; Yi, Jirong; Dasgupta, Soura; Cai, Jianfeng ; Jacob, Mathews; Cho, Myong
    • Year: 2018

  6. 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

  7. 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

  8. 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

Preprint   

  1. Projected Wirtinger Gradient Descent for Low-Rank Hankel Matrix Completion in Spectral Compressed Sensing
    • Author(s): Cai, Jianfeng; Liu, Suhui; Xu, Weiyu
    • Source: arXiv, Jul 2015, Article number 1507.03707
    • Year: 2015

  2. Split Bregman method for sparse inverse covariance estimation with matrix iteration acceleration
    • Author(s): Ye, Guibo; Cai, Jianfeng; Xie, Xiaohui
    • Source: arXiv, Dec, 2010, Article noumber 1012.0975
    • Year: 2010