Publications
(Search for my publications and citations at Google Scholar)
Preprints
- J.-F. Cai, Z. Xu, and Z. Xu,
Interlacing Polynomial Method for Matrix Approximation via Generalized Column and Row Selection,
preprint.
- J.-F. Cai, J. Li, and D. Xia,
Online Tensor Learning: Computational and Statistical Trade-offs, Adaptivity and Optimal Regret,
preprint.
- J.-F. Cai, W. Huang, H. Wang, and K. Wei,
Tensor Completion via Tensor Train Based Low-Rank Quotient Geometry under a Preconditioned Metric,
preprint.
- J.-F. Cai, J.K. Choi, and K. Wei,
Approximation Theory of Total Variation Minimization for Data Completion,
preprint.
- Y. Shen, J. Li, J.-F. Cai, and D. Xia,
Computationally Efficient and Statistically Optimal Robust Low-rank Matrix Estimation,
preprint.
Journal Papers
- J.-F. Cai, J.K. Choi, and J. Yang,
Approximation Theory of Wavelet Frame Based Image Restoration,
Applied and Computational Harmonic Analysis, to appear.
- F. Bian, J.-F. Cai, and R. Zhang,
A Preconditioned Riemannian Gradient Descent Algorithm for Low-Rank Matrix Recovery,
SIAM Journal on Matrix Analysis and Applications, to appear.
- J.-F. Cai, J.K. Choi, J. Li, and G. Yin,
Restoration Guarantee of Image Inpainting via Low Rank Patch Matrix Completion,
SIAM Journal on Imaging Sciences, 17(3):1879--1908, 2024.
- M.-C. Hsu, E.-J. Kuo, W.-H. Yu, J.-F. Cai, and M.-H. Hsieh,
Quantum state tomography via nonconvex Riemannian gradient descent,
Physical Review Letters, 132(24):240804, 2024.
- J.-F. Cai, Z. Xu, and Z. Xu,
Interlacing Polynomial Method for the Column Subset Selection Problem,
International Mathematics Research Notices, 2024(9): 7798--7819, 2024.
- J.-F. Cai and K. Wei,
Solving Systems of Phaseless Equations via Riemannian Optimization with Optimal Sampling Complexity,
Journal of Computational Mathematics, 42(3):755--783, 2024.
- J.-F. Cai, J. Li, and D. Xia,
Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization,
Journal of the American Statistical Association, 118(544):2588--2604, 2023.
- J. Yi, S. Dasgupta, J.-F. Cai, M. Jacob, J. Gao, M. Cho, and W. Xu,
Separation-free super-resolution from compressed measurements is possible: an orthonormal atomic norm minimization approach,
Information and Inference: A Journal of the IMA, 12(3):2351--2405, 2023.
- H.Q.Cai, J.-F. Cai, and J. You,
Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion,
SIAM Journal on Scientific Computing, 45(3):A1172--A1198, 2023.
- J.-F. Cai, M. Huang, D. Li, and Y. Wang,
Nearly Optimal Bounds for the Global Geometric Landscape of Phase Retrieval,
Inverse Problems, 39(7):075011, 2023.
- J.-F. Cai, J. Li, and J. You,
Provable Sample-Efficient Sparse Phase Retrieval Initialized by Truncated Power Method,
Inverse Problems, 39(7):075008, 2023.
- J.-F. Cai, H. Liu, and Y. Wang,
Gradient Descent for Symmetric Tensor Decomposition,
Annals of Applied Mathematics, 38(4):385--413, 2022.
- J.-F. Cai, Y. Jiao, X. Lu, and J. You,
Sample-Efficient Sparse Phase Retrieval via Stochastic Alternating Minimization,
IEEE Transactions on Signal Processing, 70:4951--4966, 2022.
- C. Bao, J.-F. Cai, J.K. Choi, B. Dong, and K. Wei,
Improved Harmonic Incompatibility Removal for Susceptibility Mapping via Reduction of Basis Mismatch,
Journal of Computational Mathematics, 40(6):914--937, 2022.
- J.-F. Cai, J. Li, and D. Xia,
Provable Tensor-Train Format Tensor Completion by Riemannian Optimization,
Journal of Machine Learning Research, 23(123):1--77, 2022.
- J.-F. Cai, R. Chen, J. Fan, and H. Gao,
Minimum-Monitor-Unit Optimization via a Stochastic Coordinate Descent Method,
Physics in Medicine and Biology, 67(1):015009, 2022.
- J.-F. Cai, M. Huang, D. Li, and Y. Wang,
Solving Phase Retrieval with Random Initial Guess Is Nearly as Good as by Spectral Initialization,
Applied and Computational Harmonic Analysis, 58:60--84, 2022.
- J.-F. Cai, J. Li, X. Lu, and J. You,
Sparse Signal Recovery From Phaseless Measurements via Hard Thresholding Pursuit,
Applied and Computational Harmonic Analysis, 56:367--390, 2022.
- J.-F. Cai, J.K. Choi, J. Li, and K. Wei,
Image Restoration: Structured Low Rank Matrix Framework for Piecewise Smooth Functions and Beyond,
Applied and Computational Harmonic Analysis, 56:26--60, 2022.
- J.-F. Cai, M. Huang, D. Li, and Y. Wang,
The Global Landscape of Phase Retrieval II: Quotient Intensity Models,
Annals of Applied Mathematics, 38(1):62--114, 2022.
- J.-F. Cai, M. Huang, D. Li, and Y. Wang,
The Global Landscape of Phase Retrieval I: Perturbed Amplitude Models,
Annals of Applied Mathematics, 37(4):437--512, 2021.
- J.-F. Cai, D. Li, J. Sun, and K. Wang,
Enhanced Expressive Power and Fast Training of Neural Networks by Random Projections,
CSIAM Transactions on Applied Mathematics, 2(3):532--550, 2021.
- H. Wang, J.-F. Cai, T. Wang, and K. Wei,
Fast Cadzow's Algorithm and a Gradient Variant,
Journal of Scientific Computing, 88:41, 2021.
- J. Li, J.-F. Cai, and H. Zhao,
Scalable Incremental Nonconvex Optimization Approach for Phase Retrieval from Minimal Measurements,
Journal of Scientific Computing, 87:43, 2021.
- H.Q. Cai, J.-F. Cai, T. Wang, and G. Yin,
Accelerated Structured Alternating Projections for Robust Spectrally Sparse Signal Recovery,
IEEE Transactions on Signal Processing, 69:809--821, 2021.
- J.-F. Cai, J.K. Choi, and K. Wei,
Data Driven Tight Frame for Compressed Sensing MRI Reconstruction via Off-the-Grid Regularization,
SIAM Journal on Imaging Sciences, 13(3):1272--1301, 2020.
- J. Wang, W. Xu, J.-F. Cai, Q. Zhu, Y. Shi, and B. Yin,
Multi-Direction Dictionary Learning Based Depth Map Super-Resolution with Autoregressive Modeling,
IEEE Transactions on Multimedia, 22(6):1470--1484, 2020.
- Z. Li, J.-F. Cai, and K. Wei,
Towards the Optimal Construction of a Loss Function without Spurious Local Minima for Solving Quadratic Equations,
IEEE Transactions on Information Theory, 66(5): 3242--3260, 2020.
- K. Wei, J.-F. Cai, T.F. Chan and S. Leung,
Guarantees of Riemannian Optimization for Low Rank Matrix Completion,
Inverse Problems and Imaging, 14(2):233--265, 2020.
- J. Li, J.-F. Cai, and H. Zhao,
Robust Inexact Alternating Optimization for Matrix Completion with Outliers,
Journal of Computational Mathematics, 38(2):337--354, 2020.
- J.-F. Cai, H. Liu, and Y. Wang,
Fast Rank One Alternating Minimization Algorithm for Phase Retrieval,
Journal of Scientific Computing, 79(1):128--147, 2019.
- H.Q. Cai, J.-F. Cai, and K. Wei,
Accelerated Alternating Projections for Robust Principal Component Analysis,
Journal of Machine Learning Research, 20(20):1--33, 2019.
Code
- 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., 46(1):94--121, 2019.
Supplementary Material
- J. Ying, J.-F. Cai, D. Guo, G. Tang, Z. Chen, X. Qu,
Vandermonde Factorization of Hankel Matrix for Complex Exponential Signal Recovery -- Application in Fast NMR Spectroscopy,
IEEE Trans. Signal Process., 66(21), 5520--5533, 2018.
- J.-F. Cai, T. Wang, and K. Wei,
Spectral Compressed Sensing via Projected Gradient Descent,
SIAM J. Optim., 28(3):2625--2653, 2018.
- 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, 3(1):337--365, 2018.
- 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.
- H. Liu, J.-F. Cai, and Y. Wang,
Subspace Clustering by (k, k)-sparse Matrix Factorization,
Inverse Probl. Imaging, 11(3):539--551, 2017.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- 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.
- J.-F. Cai and W. Xu,
Guarantees of Total Variation Minimization for Signal Recovery,
Inf. Inference, 4(4):328--353, 2015.
(A preliminary short version is published in Allerton 2013)
- 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.
- 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
- 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.
- 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.
- 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.
- 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.
Code
- J.-F. Cai, and S. Osher,
Fast Singular Value Thresholding without Singular Value Decomposition,
Methods Appl. Anal., 20(4):335--352, 2013.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
Code
- 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.
- 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.
- 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.
- J.-F. Cai, R.H. Chan, and Z. Shen,
Simultaneous Cartoon and Texture Inpainting,
Inverse Probl. Imaging, 4(3):379--395, 2010.
- J.-F. Cai, H. Ji, F. Shang and Z. Shen,
Inpainting for Compressed Images,
Appl. Comput. Harmon. Anal., 29(3): 368--381, 2010.
- J.-F. Cai, E.J. Candès and Z. Shen,
A singular value thresholding algorithm for matrix completion,
SIAM J. Optim., 20(4): 1956--1982, 2010.
Code
- J.-F. Cai, and Z. Shen,
Framelet based deconvolution,
J. Comput. Math., 28(3): 289--308, 2010.
- 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.
Code
- J.-F. Cai, S. Osher and Z. Shen,
Split Bregman Methods and Frame Based Image Restoration,
Multiscale Model. Simul., 8(2):337--369, 2010.
Code
Code
- 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.
- J.-F. Cai, H. Ji, C. Liu and Z. Shen,
Blind motion deblurring using multiple images,
J. Comput. Physics, 228(14):5057--5071, 2009.
- 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.
- 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.
- J.-F. Cai, S. Osher and Z. Shen,
Linearized Bregman Iterations for Compressed Sensing,
Math. Comp., 78(267):1515--1536, 2009.
- 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.
Code
- 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.
Code
- 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.
- J.-F. Cai, R.H. Chan, and Z. Shen,
A Framelet-Based Image Inpaiting Algorithm,
Appl. Comput. Harmon. Anal., 24(2):131--149, 2008.
- 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.
Code
- X. Zhang, J. Cai, and Y. Wei,
Interval Iterative Methods for Computing Moore-Penrose Inverse,
Appl. Math. Comput., 183(1):522--532, 2006.
- 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.
- 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.
- J. Cai, and Y. Wei,
Displacement Structure of Weighted Pseudoinverses,
Appl. Math. Comput., 153(2):317--335, 2004.
Proceeding Papers and Book Chapters
- J. Fan, Y. Han, Z. Liu, J.-F. Cai, Y. Wang, and Z. Zhou,
On the Convergence of Projected Bures-Wasserstein Gradient Descent under Euclidean Strong Convexity,
The 41st International Conference on Machine Learning (ICML), 2024.
- J. Fan, Y. Han, J. Zeng, J.-F. Cai, Y. Wang, Y. Xiang, and J. Zhang,
RL in Markov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model,
The 27th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 238:2035-2043, 2024.
- J.-F. Cai, Y. Long, R. Wen, and J. Ying,
A Fast and Provable Algorithm for Sparse Phase Retrieval,
International Conference on Learning Representations (ICLR), 2024.
- J.-F. Cai, J.V.M. Cardoso, D.P. Palomar, and J. Ying,
Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity,
Thirty-seventh Conference on Neural Information Processing Systems (NeurIPS), 2023. (23 pages)
- X. Wu, Z. Yang, J.-F. Cai, and Z. Xu,
Spectral Super-Resolution on the Unit Circle Via Gradient Descent,
2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2023. (5 pages)
- Y. Yang, W. Ma, Y. Zheng, J.-F. Cai, and W. Xu,
Fast Single Image Reflection Suppression via Convex Optimization,
2019 IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 8141--8149, Long Beach, 2019.
- J.-F. Cai and K. Wei,
Exploiting the Structure Effectively and Efficiently in Low Rank Matrix Recovery,
Handbook of Numerical Analysis, Volume 19, pp. 21--51.
- 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,
2018 IEEE International Symposium on Information Theory (ISIT), 2018.
- 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), pp. 5905--5909, 2017.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
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