Research Interest

In the past decade, my research interests mainly focused on the development of variational models and fast algorithms to accomplish advanced imaging goals in image denosing and segmentation. To this end, with my collaborators, I introduced a few curvature-based variational models and also designed efficient numerical methods to minimize these models using augmented Lagrangian methods (ALMs). Recently, I am working on data sciences by using differential geometry, PDEs, and numerical methods. Specifically, I am studying the geometric features of data in high-dimensional Euclidean spaces in order to understand data.

Publication

  1. Wei Zhu, Finding Cheeger cuts via 1-Laplacian of graphs, ​Accepted by Numerical Mathematics: Theory , Methods and Applications, Nov. 2024.
  2. Wenli Yang, Zhongyi Huang, and Wei Zhu, Fusing infrared and visible images via a first-order model. Accepted by Numerical Mathematics: Theory, Methods and Applications, Nov., 2023.
  3. Wei Zhu, A second-order image denoising model for contrast preservation, Accepted by Communications on Applied Mathematics and Computation, Oct., 2023.
  4. Wenli Yang, Zhongyi Huang, and Wei Zhu, A first-order Rician denoising and deblurring model. Inverse Problems and Imaging, 2023, 17(6): 1139-1164. doi: 10.3934/ipi.2023011.
  5. Miaoyu Dai, Zhongyi Huang, and Wei Zhu, Convex Splitting Method for Strongly Anisotropic Solid-State Dewetting Problems in Two Dimensions. East Asian J. Appl. Math., 12 (2022), pp. 791-820.
  6. Wenli Yang, Zhongyi Huang, and Wei Zhu, Image super-resolution reconstruction by Huber regularization and tailored finite point method. Accepted by Journal of Computational Mathematics, 2022.
  7. Xiakai Wang, Zhongyi Huang, and Wei Zhu, Multi-phase segmentation using modified complex Cahn-Hilliard equations, 
    Numer. Math. Theor. Meth. Appl., 15 (2022), pp. 442-463.
  8. Wei Zhu, A first-order image restoration model that promotes image contrast preservation. J Sci Comput 88, 46 (2021). https://doi.org/10.1007/s10915-021-01557-1.
  9. Wei Zhu, Image denoising using L^{p}-norm of mean curvature of image surface. J Sci Comput 83, 32 (2020). https://doi.org/10.1007/s10915-020-01216-x
  10. Sung Ha Kang, Xuecheng Tai, and Wei Zhu, Survey of geometry inspired variational segmentation: interface model, curvature terms and fast computation. HNA - 19 & 20 Processing, Analyzing and Learning of Images, Shapes, and Forms Part 1 and 2.
  11. Wei Zhu, A first-order image denoising model for staircase reduction. Adv. Comput. Math, 45, 3217-3239, 2019.
  12. Wenli Yang, Zhongyi Huang, and Wei Zhu, Image segmentation using the Cahn-Hilliard equation. J Sci Comput 79, 1057–1077 (2019). https://doi.org/10.1007/s10915-018-00899-7.
  13. ​Wenli Yang, Zhongyi Huang, and Wei Zhu, An efficient tailored finite point method for Rician denoising and deblurring. Communications in Computational Physics, 24 (2018), pp. 1169-1195.
  14. Xuan He, Wei Zhu, and Xue-Cheng Tai, Segmentation by elastica energy with L^1 and L^2 curvature: a performance comparison. Numerical Mathematics: Theory, Methods and Applications, 12 (2019), pp. 285-311.
  15. Wei Zhu, A numerical study of a mean curvature denoising model using a novel augmented Lagrangian method. Inverse Problems and Imaging, 11(6), pp. 975-996, 2017.
  16. Maryam Yashtini, Sung Ha Kang, and Wei Zhu, Efficient Alternating Minimization Methods For Variational Edge-weighted Colorization Models. Advances in Computational Mathematics, 45 (2019), no. 3, 1735-1767.
  17. Egil Bae, Xue-Cheng Tai, and Wei Zhu, Augmented Lagrangian method for an Euler’s elastica based segmentation model that promotes convex contours. Inverse Problems and Imaging, 11(1), pp. 1-23, 2017.
  18. Wei Zhu, Simulation on Liquid crystal elastomers using spectral method with a new preconditioner. Adv. Comput. Math., 41(4) pp. 853-879, 2015.
  19. Sung Ha Kang, Wei Zhu, and Jackie Shen, Illusory Shapes via Corner Fusion. SIAM J. Imaging Sci., 7, pp. 1907-1936, 2014.
  20. Wei Zhu, Xue-Cheng Tai, and Tony F. Chan, A fast algorithm for a mean curvature based image denoising using augmented Lagrangian method.  A. Bruhn et al. (Eds.): Global Optimization Methods, LNCS 8293, pp. 104-118, 2014.
  21. Andy M. Yip and Wei Zhu, Shape from shading using mean curvature. In preparation.
  22. Wei Zhu, Xue-Cheng Tai, and Tony F. Chan, Image segmentation using Euler’s elastica as the regularization. Journal of Scientific Computing, 57, pp. 414-438, 2013.
  23. Andy M. Yip and Wei Zhu, A fast modified Newton method for curvature based denoising of 1D signals. Inverse Problems and Imaging, 7(3), pp. 1075-1097, 2013.
  24. Wei Zhu, Xue-Cheng Tai, and Tony F. Chan, Augmented Lagrangian method for a mean curvature based image denoising model. Inverse Problems and Imaging, 7(4), pp. 1409-1432, 2013.
  25. Wei Zhu, Sung Ha Kang, and George Biros, A geodesic-active-contour-based variational model for short axis cardiac-MR image segmentation.  International Journal of Computer Mathematics, 90(1), pp. 124-139, 2013.
  26. Wei Zhu and Tony F. Chan, Image denoising using mean curvature of image surface. SIAM J. Imaging Sci., 5, pp. 1-32, 2012.
  27. Wei Zhu, Michael Shelley, and Peter Palffy-Muhoray, Modeling and simulation of liquid crystal elastomers. Physical Review E 83, 051703 (2011).
  28. Wei Zhu, Dajun Xing, Michael Shelley, and Robert Shapley, Correlation between spatial-frequency and orientation-selectivity in V1 cortex: implications of a large-scale network model. Vision Research, (2010) 50(22):2261-73.
  29. Wei Zhu, Michael Shelley, and Robert Shapley, A neuronal network model of primary visual cortex explains spatial frequency selectivity.  Journal of Computational Neuroscience. 26:2 (2009), pp. 271-287.
  30. Wei Zhu and Tony F. Chan, A variational model for capturing illusory contours using curvature. Journal of Mathematical Imaging and Vision, 27(2007), pp. 29-40.
  31. Wei Zhu, Tony F. Chan, and Selim Esedoglu, Segmentation with depth: A level set approach. SIAM Journal on Scientific Computing, 28 (2006), pp. 1957-1973.
  32. Tony F. Chan and Wei Zhu, Level set based shape prior segmentation. Proc. IEEE Conf. on Computer Vision and Pattern Recognition, CVPR (2) pp. 1164-1170, San Diego, June 2005.