Jian-Feng Cai

Associate Professor,
Department of Mathematics,
Hong Kong University of Science and Technology.

E-mail: jfcai@ust.hk        Phone: +852 3469 2248        Office: 3443

Short Vita


  • Spring 2018: MATH 3322 Matrix Computation
  • Spring 2018: MATH 6380M Mathematical Foundations of Imaging II
  • Spring 2018: MSBD 5004 Mathematical Methods for Data Analysis

Research Interests

My research mainly focuses on the design and analysis of efficient algorithms for real-world problems (e.g., data analysis, signal/image processing, machine learning), using tools from computational harmonic analysis, approximation theory, numerical linear algebra, optimization, and probability.

Publications (Search for my publications and citations at Google Scholar)


  • H.Q. Cai, J.-F. Cai, and K. Wei, Accelerated Alternating Projections for Robust Principal Component Analysis, preprint. pdf
  • W. Xu, J. Yi, S. Dasgupta, J.-F. Cai, M. Jacob, and M. Cho, Separation-Free Super-Resolution from Compressed Measurements is Possible: an Orthonormal Atomic Norm Minimization Approach, preprint. pdf
  • J.-F. Cai, H. Liu, and Y. Wang, Fast Rank One Alternating Minimization Algorithm for Phase Retrieval, preprint. pdf
  • J.-F. Cai, T. Wang, and K. Wei, Spectral Compressed Sensing via Projected Gradient Descent, preprint. pdf
  • K. Wei, J.-F. Cai, T.F. Chan and S. Leung, Guarantees of Riemannian Optimization for Low Rank Matrix Completion, preprint. pdf

Journal Papers

  1. J.-F. Cai, Y. Rong, Y. Wang, and Z. Xu, Data Recovery on a Manifold from Linear Samples: Theory and Computation, Annals of Mathematical Sciences and Applications, to appear. pdf
  2. J.-F. Cai, T. Wang, and K. Wei, Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion, Appl. Comput. Harmon. Anal., to appear. pdf Supplementary Material
  3. J. Ying, H. Lu, Q. Wei, J.-F. Cai, D. Guo, J. Wu, Z. Chen, X. Qu, Hankel matrix nuclear norm regularized tensor completion for N-dimensional exponential signals, IEEE Trans. Signal Process., 65(14):3702--3717, 2017. pdf
  4. H. Liu, J.-F. Cai, and Y. Wang, Subspace Clustering by (k, k)-sparse Matrix Factorization, Inverse Probl. Imaging, 11(3):539--551, 2017.
  5. Y. Wang, G. Wang, S. Mao, W. Cong, Z. Ji, J.-F. Cai, and Y. Ye, A Spectral Interior CT by a Framelet-Based Reconstruction Algorithm, Journal of X-Ray Science and Technology, 24(6): 771--785, 2016.
  6. Y. Wang, G. Wang, S. Mao, W. Cong, Z. Ji, J.-F. Cai, and Y. Ye, A framelet-based iterative maximum-likelihood reconstruction algorithm for spectral CT, Inverse Problems, 32(11):115021(16pp), 2016.
  7. K. Wei, J.-F. Cai, T.F. Chan and S. Leung, Guarantees of Riemannian Optimization for Low Rank Matrix Recovery, SIAM J. Matrix Anal. & Appl., 37(3):1198--1222, 2016. pdf
  8. Y. Liu, Z. Zhan, J.-F. Cai, D. Guo, Z. Chen, and X. Qu, Projected Iterative Soft-thresholding Algorithm for Tight Frames in Compressed Sensing Magnetic Resonance Imaging, IEEE Trans. Med. Imag., 35(9): 2130--2140, 2016. pdf
  9. J.-F. Cai, X. Qu, W. Xu, and G.-B. Ye, Robust Recovery of Complex Exponential Signals from Random Gaussian Projections via Low Rank Hankel Matrix Reconstruction, Appl. Comput. Harmon. Anal., 41(2):470--490, 2016. pdf
  10. Z. Zhan, J.-F. Cai, D. Guo, Y. Liu, Z. Chen, and X. Qu, Fast Multi-class Dictionaries Learning with Geometrical Directions in MRI Reconstruction, IEEE Trans. Biomed. Eng., 63(9):1850--1861, 2016. Code
  11. J.-F. Cai, B. Dong, and Z. Shen, Image Restorations: A Wavelet Frame Based Model for Piecewise Smooth Functions and Beyond, Appl. Comput. Harmon. Anal., 41(1):94--138, 2016. pdf
  12. J.-F. Cai and W. Xu, Guarantees of Total Variation Minimization for Signal Recovery, Inf. Inference, 4(4):328--353, 2015. pdf (A preliminary short version is published in Allerton 2013)
  13. M. Cho, K.V. Mishra, J.-F. Cai, and W. Xu, Block Iterative Reweighted Algorithms for Super-Resolution of Spectrally Sparse Signals, IEEE Signal Process. Lett., 22(12): 2319--2323, 2015. pdf
  14. Y. Liu, J.-F. Cai, Z. Zhan, D. Guo, J. Ye, Z. Chen, X. Qu, Balanced sparse model for tight frames in compressed sensing magnetic resonance imaging, PLoS One, Vol. 10, e0119584, 2015. Code
  15. J. Wang, and J.-F. Cai, Data-Driven Tight Frame for Multi-Channel Images and Its Application to Joint Color-Depth Image Reconstruction, J. Oper. Res. Soc. China, 3(2):99--115, 2015. pdf
  16. X. Qu, M. Mayzel, J.-F. Cai, Z. Chen, and V. Orekhov, Accelerated NMR Spectroscopy with Low-Rank Reconstruction, Angew. Chem. Int. Ed., 54(3):852--854, 2015.
  17. J.-F. Cai, X. Jia, H. Gao, S. Jiang, Z. Shen, and H. Zhao, Cine cone beam CT reconstruction using low-rank matrix factorization: algorithm and a proof-of-princple study, IEEE Trans. Med. Imag., 33(8):1581--1591, 2014. pdf
  18. J.-F. Cai, H. Ji, Z. Shen, and G.-B. Ye, Data-driven tight frame construction and image denoising, Appl. Comput. Harmon. Anal., 37(1):89--105, 2014. pdf Code
  19. J.-F. Cai, and S. Osher, Fast Singular Value Thresholding without Singular Value Decomposition, Methods Appl. Anal., 20(4):335--352, 2013. pdf
  20. W. Zhou, J.-F. Cai, and H. Gao, Adaptive tight frame based medical image reconstruction: proof-of-concept study in computed tomography, Inverse Probl., 29(12):125006(pp. 1--18), 2013. pdf
  21. G. Ye, M. Tang, J.-F. Cai, Q. Nie, and X. Xie, Low-Rank Regularization for Learning Gene Expression Programs, PLoS One, 8(12):e82146(pp. 1--9), 2013.
  22. W. Xu, M. Wang, J.-F. Cai, and K. Tang, Sparse Error Correction from Nonlinear Measurements with Applications in Bad Data Detection for Power Networks, IEEE Trans. Signal Processing, 61(24):6175--6187, 2013. pdf
  23. H. Zhang, J.-F. Cai, L. Cheng, and J. Zhu, Strongly Convex Programming for Exact Matrix Completion and Robust Principal Component Analysis, Inverse Probl. Imaging, 6(2):357--372, 2012. pdf
  24. J.-F. Cai, B. Dong, S. Osher, and Z. Shen, Image Restoration: Total Variation; Wavelet Frames; and Beyond, J. Amer. Math. Soc., 25(4):1033-1089, 2012. pdf
  25. J.-F. Cai, H. Ji, C. Liu, and Z. Shen, Framelet Based Blind Motion Deblurring from a Single Image, IEEE Trans. Image Process., 21(2):562--572, 2012. pdf Code
  26. J.-F. Cai, Z. Shen, and G.-B. Ye, Approximation of Frame Based Missing Data Recovery, Appl. Comput. Harmon. Anal., 31(2):185--204, 2011. pdf
  27. H. Gao, J.-F. Cai, Z. Shen, and H. Zhao, Robust Principle Component Analysis Based Four-Dimensional Computed Tomography, Phys. Med. Biol., 56(11):3181--3198, 2011. pdf
  28. S.-L. Yang, J.-F. Cai, and H.-W. Sun, Multigrid algorithm from cyclic reduction for Markovian queueing networks, Appl. Math. Comput., 217(16): 6990--7000, 2011.
  29. J.-F. Cai, R.H. Chan, and Z. Shen, Simultaneous Cartoon and Texture Inpainting, Inverse Probl. Imaging, 4(3):379--395, 2010. pdf
  30. J.-F. Cai, H. Ji, F. Shang and Z. Shen, Inpainting for Compressed Images, Appl. Comput. Harmon. Anal., 29(3): 368--381, 2010. pdf
  31. J.-F. Cai, E.J. Candès and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM J. Optimiz., 20(4): 1956--1982, 2010. pdf Code
  32. J.-F. Cai, and Z. Shen, Framelet based deconvolution, J. Comput. Math., 28(3): 289--308, 2010. pdf
  33. J.-F. Cai, R.H. Chan, and M. Nikolova, Fast Two-Phase Image Deblurring under Impulse Noise, J. Math. Imaging Vis., 36(1): 46--53, 2010. pdf Code
  34. J.-F. Cai, S. Osher and Z. Shen, Split Bregman Methods and Frame Based Image Restoration, Multiscale Model. Simul., 8(2):337--369, 2010. pdf Code Code
  35. J.-F. Cai, S. Osher and Z. Shen, Convergence of the Linearized Bregman Iteration for $\ell_1$-Norm Minimization, Math. Comp., 78(268):2127--2136, 2009. pdf
  36. J.-F. Cai, H. Ji, C. Liu and Z. Shen, Blind motion deblurring using multiple images, J. Comput. Physics, 228(14):5057--5071, 2009. pdf
  37. J.-F. Cai, R.H. Chan, L. Shen, and Z. Shen, Simultaneously Inpainting in Image and Transformed Domains, Numer. Math., 112(4):509--533, 2009. pdf
  38. J.-F. Cai, R.H. Chan, L. Shen, and Z. Shen, Convergence Analysis of Tight Framelet Approach for Missing Data Recovery, Adv. Comput. Math., 31(1--3):87--113, 2009. pdf
  39. J.-F. Cai, S. Osher and Z. Shen, Linearized Bregman Iterations for Compressed Sensing, Math. Comp., 78(267):1515--1536, 2009. pdf
  40. J.-F. Cai, S. Osher and Z. Shen, Linearized Bregman Iterations for Frame-Based Image Deblurring, SIAM J. Imaging Sci., 2(1):226--252, 2009. pdf Code
  41. J.-F. Cai, R.H. Chan, and M. Nikolova, Two-phase Approach for Deblurring Images Corrupted by Impulse Plus Gaussian Noise, Inverse Probl. Imaging, 2(2):187--204, 2008. pdf Code
  42. J.-F. Cai, R.H. Chan, L. Shen, and Z. Shen, Restoration of Chopped and Nodded Images by Framelets, SIAM J. Sci. Comput., 30(3):1205--1227, 2008. pdf
  43. J.-F. Cai, R.H. Chan, and Z. Shen, A Framelet-Based Image Inpaiting Algorithm, Appl. Comput. Harmon. Anal., 24(2):131--149, 2008. pdf
  44. J.-F. Cai, R.H. Chan, and C. Di Fiore, Minimization of a Detail-preserving Regularization Functional for Impulse Noise Removal, J. Math. Imaging Vis., 29(1):79--91, 2007. pdf Code
  45. X. Zhang, J. Cai, and Y. Wei, Interval Iterative Methods for Computing Moore-Penrose Inverse, Appl. Math. Comput., 183(1):522--532, 2006. pdf
  46. J.-F. Cai, M.K. Ng, and Y.-M. Wei, Modified Newton's Algorithm for Computing the Group Inverses of Singular Toeplitz Matrices, J. Comput. Math., 24(5):647--656, 2006. pdf
  47. Y. Wei, J. Cai, and M.K. Ng, Computing Moore-Penrose Inverses of Toeplitz Matrices by Newton's Iteration, Math. Comput. Modelling, 40(1--2):181--191, 2004. pdf
  48. J. Cai, and Y. Wei, Displacement Structure of Weighted Pseudoinverses, Appl. Math. Comput., 153(2):317--335, 2004. pdf

Proceeding Papers

  1. J.-F. Cai, W. Xu, and Y. Yang, Large Scale 2D Spectral Compressed Sensing in Continuous Domain, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2017.
  2. M. Cho, J.-F. Cai, S. Liu, Y.C. Eldar, and W. Xu, Fast Alternating Projected Gradient Descent Algorithms for Recovering Spectrally Sparse Signals, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4638--4642, 2016.
  3. B. Zhang, W. Xu, J.-F. Cai, and L. Lai, Precise Phase Transition of Total Variation Minimization, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4518--4522, 2016. pdf
  4. J.-F. Cai, S. Liu, and W. Xu, A fast algorithm for reconstruction of spectrally sparse signals in super-resolution, Proc. SPIE 9597, Wavelets and Sparsity XVI, 95970A, 2015. pdf
  5. J. Wang, J.-F. Cai, Y. Shi, and B. Yin, Incoherent Dictionary Learning for Sparse Representation Based Image Denoising, IEEE International Conference on Image Processing (ICIP), Paris, 2014. pdf
  6. W. Xu, J.-F. Cai, K.V. Mishra, M. Cho, and A. Kruger, Precise semidefinite programming formulation of atomic norm minimization for recovering d-dimensional (D>=2) off-the-grid frequencies, Information Theory and Applications Workshop (ITA), San Diego, 2014. pdf
  7. C. Bao, J.-F. Cai, and H. Ji, Fast sparsity-based orthogonal dictionary learning and image restoration, 2013 International Conference on Computer Vision (ICCV), pp. 3384--3391, 2013. pdf
  8. J.-F. Cai and W. Xu, Guarantees of Total Variation Minimization for Signal Recovery, Proceedings of 51st Annual Allerton Conference on Communication, Control, and Computing, pp. 1266--1271, 2013.
  9. J.-F. Cai, R. Chan, L.X. Shen, and Z.W. Shen, Tight Frame Based Method for High-Resolution Image Reconstruction, Proceedings to the Conference on Wavelet Analysis and its Application, Zhuhai, China, August, 2007, Contemporary Applied Mathematics, Vol 14, pp. 1--36, 2010. pdf
  10. J.-F. Cai, H. Ji, C. Liu and Z. Shen, High-quality curvelet-based motion deblurring using an image pair, 2009 IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 1566--1573, Miami, 2009. pdf
  11. J.-F. Cai, H. Ji, C. Liu and Z. Shen, Blind motion deblurring from a single image using sparse approximation, 2009 IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 104--111, Miami, 2009. pdf
  12. J.-F. Cai, R.H. Chan, and B. Morini, Minimization of an Edge-Preserving Regularization Functional by Conjugate Gradient Type Methods, Image Processing Based on Partial Differential Equations, in Series: Mathematics and Visualization, Springer Berlin Heidelberg, pp. 107--120, 2007. pdf


Research Grants


  • Suhui Liu, PhD in Mathematics, University of Iowa, 2017. First job: Lecturer, Wuhan Institute of Technology.
  • Tianyi Zhang, PhD in Applied Mathematics and Computational Sciences, University of Iowa, 2015. First job: Algorithmic Trader, Shanghai Cyndi Investment Co. Ltd.