Jian-Feng Cai

Assistant Professor,
Department of Mathematics,
University of Iowa.

E-mail: jianfeng-cai@uiowa.edu        Phone: +1-319-335-0722        Office: MLH 325H

Education

Academic Experiences

  • Assistant Professor, Department of Mathematics, University of Iowa, 08/2011--
  • CAM Assistant Adjunct Professor, Department of Mathematics, University of California, Los Angeles, 07/2009--06/2011.
  • Research Scientist, Temasek Laboratories, National University of Singapore, 06/2007--06/2009.

Teaching in UIowa

Teaching in UCLA

  • Fall 2009: Math 151A Applied Numerical Methods A.
  • Winter 2010: Math 270C Mathematical Aspects of Scientific Computing: Computational Linear Algebra.
  • Fall 2010: Math 151A Applied Numerical Methods A.
  • Winter 2011: Math 151B Applied Numerical Methods B.

Research Areas

    Computational harmonic analysis, optimization, numerical linear algebra, and their applications to the imaging sciences and inverse problems.

Publications

Search for my publications and citations at Google Scholar
  1. J.-F. Cai, X. Jia, H. Gao, S.B. Jiang, Z. Shen, and H. Zhao, Cine cone beam CT reconstruction using low-rank matrix factorization: algorithm and a proof-of-princple study, preprint. pdf
  2. H. Zhang, J.-F. Cai, L. Cheng, and J. Zhu, Strongly Convex Programming for Exact Matrix Completion and Robust Principal Component Analysis, Inverse Problems and Imaging, accepted for publication. pdf
  3. J.-F. Cai, B. Dong, Z. Shen, and S. Osher, Image Restoration: Total Variation; Wavelet Frames; and Beyond, J. Amer. Math. Soc., accepted for publication. pdf
  4. J.-F. Cai, H. Ji, C. Liu, and Z. Shen, Framelet Based Blind Motion Deblurring from a Single Image, IEEE Transactions on Image Processing, 21(2):562--572, 2012. pdf
  5. 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
  6. H. Gao, J.-F. Cai, Z. Shen, and H. Zhao, Robust Principle Component Analysis Based Four-Dimensional Computed Tomography, Physics in Medicine and Biology, 56(11):3181--3198, 2011. (Featured Article) pdf
  7. 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.
  8. 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
  9. J.-F. Cai, and S. Osher, Fast Singular Value Thresholding without Singular Value Decomposition, UCLA CAM Report 10-24, 2010. pdf
  10. J.-F. Cai, R.H. Chan, and Z. Shen, Simultaneous Cartoon and Texture Inpainting, Inverse Probl. Imaging, 4(3):379--395, 2010. pdf
  11. J.-F. Cai, H. Ji, F. Shang and Z. Shen, Inpainting for Compressed Images, Appl. Comput. Harmon. Anal., 29(3): 368--381, 2010. pdf
  12. 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
  13. J.-F. Cai, and Z. Shen, Framelet based deconvolution, J. Comput. Math., 28(3): 289--308, 2010. pdf
  14. 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
  15. J.-F. Cai, S. Osher and Z. Shen, Split Bregman Methods and Frame Based Image Restoration, Multiscale Model. Simul., 8(2):337--369, 2009. pdf
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. J.-F. Cai, S. Osher and Z. Shen, Linearized Bregman Iterations for Compressed Sensing, Math. Comp., 78(267):1515--1536, 2009. pdf
  23. J.-F. Cai, S. Osher and Z. Shen, Linearized Bregman Iterations for Frame-Based Image Deblurring, SIAM J. Imaging Sciences, 2(1):226--252, 2009. pdf
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. X. Zhang, J. Cai, and Y. Wei, Interval Iterative Methods for Computing Moore-Penrose Inverse, Appl. Math. Comput., 183(1):522--532, 2006. pdf
  30. 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
  31. 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
  32. J. Cai, and Y. Wei, Displacement Structure of Weighted Pseudoinverses, Appl. Math. Comput., 153(2):317--335, 2004. pdf

Awards

Research Grants

Reviewer for Journals

  1. Advances in Computational Mathematics
  2. Annals of Statistics
  3. Applicable Analysis
  4. Applied and Computational Harmonic Analysis
  5. Communications in Computational Physics
  6. Computational Intelligence and Neuroscience
  7. Computational Statistics & Data Analysis
  8. East Asian Journal on Applied Mathematics
  9. EURASIP Journal on Advances in Signal Processing
  10. IEEE Singnal Processing Letters
  11. IEEE Transactions on Broadcasting
  12. IEEE Transactions on Circuits and Systems for Video Technology
  13. IEEE Transactions on Image Processing
  14. IEEE Transactions on Pattern Analysis and Machine Intelligence
  15. IEEE Transactions on Singnal Processing
  16. IET Image Processing
  17. Image and Vision Computing
  18. Inverse Problems
  19. Inverse Problems and Imaging
  20. Journal of Applied Mathematics and Computing
  21. Journal of Computational and Applied Mathematics
  22. Journal of Computational Physics
  23. Journal of Machine Learning Research
  24. Journal of Mathematical Imaging and Vision
  25. Journal of Scientific Computing
  26. Mathematical Reviews (MR)
  27. Mathematics of Computation
  28. Multiscale Modelling and Simulation
  29. Optics & Laser Technology
  30. Pacific Journal of Optimization
  31. Science China Mathematics
  32. SIAM Journal on Imaging Sciences
  33. SIAM Journal on Matrix Analysis and Applications
  34. SIAM Journal on Scientific Computing
  35. Signal Image and Video Processing
  36. Signal Processing

Talks and Activities

  1. 30-min talk, III Workshop on Medical Imaging, UC Irvine, April 7, 2012.
  2. Participant, Advances in Scientific Computing, Imaging Science and Optimization: Stan Osher's 70th Birthday Conference, UCLA, April 4--6, 2012.
  3. 40-min talk, International Conference on Mathematical Methods for Images, Sun Yat-Sen University, Guangzhou, August 4--6, 2010.
  4. Research Program in Image Processing, Park City Mathematics Institute ~ Institute for Advanced Study, Park City, Utah, June 27 -- July 17, 2010.
  5. Minisymposium talk, SIAM Conference on Imaging Science (IS10), Holiday Inn Chicago Mart Plaza, Chicago, April 12--14, 2010.
  6. 30-min talk, The 20th International Symposium of Mathematical Programming, Chicago, August 23--28, 2009.
  7. 50-min talk, International Workshop of Scientific Computing and its Applications, Fudan University, Shanghai, June 28--30, 2009.
  8. 40-min talk, Workshop on Numerical Linear Algebra and High Performance Computing, Fudan University, Shanghai, March 6--8, 2009.
  9. 30-min talk, Workshop on Mathematical Imaging and Digital Media, National University of Singapore, Singapore, June 16--20, 2008.
  10. 30-min talk, Chinese-French-Singaporean Joint Workshop on Wavelet Theory and Applications, National University of Singapore, Singapore, June 9--13, 2008.
  11. 20-min talk, Croucher Advanced Study Institute Mathematical & Algorithmic Challenges for Modeling & Analyzing Modern Data Sets, Hong Kong Baptist University, Hong Kong, Apr 21--25, 2008.
  12. 30-min talk, HKRGC Postgraduate Students Conference on Computer Imaging and Vision, Hong Kong Baptist University, Hong Kong, June 12--14, 2007.
  13. 30-min talk, Sino-France Summer School and Workshop on Mathematical Methods for Multi-Channel Image Processing, Institute of Automation, Chinese Academy of Science, Beijing, July 3--8,2006.
  14. Poster, Symposium on Scientific Computing, The University of Hong Kong, Hong Kong, Jan 12, 2004.
  15. 15-min talk, The 6th Conference of the Chinese Computational Mathematical Society, Nanjing Normal University, Nanjing, Oct 19--23, 2003.

Visiting/Seminar Speaker at

  1. Department of Mathematics, Iowa State University, Ames, IA, April 9, 2012.
  2. Department of Mathematics, University of California, Irvine, CA, July 27, 2011.
  3. Department of Mathematics, University of California, Riverside, CA, February 17, 2011.
  4. Department of Mathematics, University of Connecticut, Storrs, CT, February 10, 2011.
  5. Department of Mathematics, Michigan State University, East Lansing, MI, January 31 -- February 1, 2011.
  6. Department of Mathematics, Purdue University, West Lafayette, IN, January 28, 2011.
  7. Department of Mathematics, University of Iowa, Iowa City, IA, January 26, 2011.
  8. Department of Mathematics, University of Arizona, Tucson, AZ, January 18--19, 2011.
  9. Department of Mathematics, North Carolina State University, Raleigh, NC, January 12, 2011.
  10. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, September 1--10, 2010.
  11. Department of Computer Science, University of California, Irvine, August 25, 2010.
  12. Division of Mathematical Sciences, Nanyang Technological University, Singapore, August 19, 2010.
  13. Department of Electrical and Computer Engineering, National University of Singapore, July 29, 2010.
  14. Department of Mathematics, National University of Singapore, July 22--August 21, 2010.
  15. Department of Mathematics, University of California, Irvine, May 4, 2010.
  16. Department of Mathematics, Georgia Institute of Technology, Atlanta, April 4--11. 2010.
  17. Department of Mathematics, National University of Defense Technology, Changsha, January 15--19, 2009.
  18. Department of Mathematics, The Chinese University of Hong Kong, January 10--15, 2009.

Collaborators

  • Emmanuel Candès, Applied and Computational Mathematics, California Institute of Technology, USA.
  • Raymond Chan, Department of Mathematics, Chinese University of Hong Kong, China.
  • Carmine Di Fiore, Department of Mathematics, University of Roma "Tor Vergata", Italy.
  • Bin Dong, Department of Mathematics, University of California, San Diego, USA.
  • Hao Gao, Department of Mathematics, University of California, Los Angeles, USA.
  • Hui Ji, Department of Mathematics, National University of Singapore, Singapore.
  • Xun Jia, Department of Radiation Oncology, University of California, San Diego.
  • Steve B. Jiang, Department of Radiation Oncology, University of California, San Diego.
  • Chaoqiang Liu, Temasek Laboratories, National University of Singapore, Singapore.
  • Benedetta Morini, Department of Energy Engineering "Sergio Stecco", University of Florence, Italy.
  • Michael Ng, Department of Mathematics, Hong Kong Baptist University, China.
  • Mila Nikolova, CMLA, ENS de Cachan, France.
  • Stanley Osher, Department of Mathematics, University of California, Los Angeles, USA.
  • Fuchun Shang, Temasek Laboratories, National University of Singapore, Singapore.
  • Lixin Shen, Department of Mathematics, Syracuse University, USA.
  • Zuowei Shen, Department of Mathematics, National University of Singapore, Singapore.
  • Hai-Wei Sun, Department of Mathematics, University of Macau, Macao, China.
  • Yimin Wei, School of Mathematical Sciences, Fudan University, China.
  • Xiaohui Xie, Department of Computer Science, University of California, Irvine, USA.
  • Shu-Ling Yang, School of Applied Mathematics, Guangdong University of Technology, Guangzhou, China.
  • Gui-Bo Ye, Department of Computer Science, University of California, Irvine, USA.
  • Xian Zhang, Institute of Mathematics, Fudan University, China.
  • Hongkai Zhao, Department of Mathematics, University of California, Irvine, USA.