Dr. Liu's Personal Website

Welcome

Xiaoxia Liu （刘晓霞）

Research Assistant Professor
Department of Applied Mathematics
The Hong Kong Polytechnic University
Hung Hom, Kowloon, Hong Kong

Tel: +852 2766 6348
Office: TU813, Yip Kit Chuen Bldg
Email: xiaoxia.liu at polyu.edu.hk

Interested research topics

Research Interests

Inverse Problems

Low-rank regularization, sparse representations, etc.

Image Processing

Image denoising, medical image reconstruction, data recovery, etc.

Optimization

Nonconvex nonsmooth optimization, proximal algorithms, etc.

Curriculum Vitae

Biography

Education

  • Ph.D. degree in Mathematics (Aug 2012 - Jun 2018)

    Syracuse University, United States
    Supervisors: Professor Yuesheng Xu and Professor Lixin Shen

  • B.Sc. degree in Information and Computational Science (Sep 2008 - Jun 2012)

    Sun Yat-Sen University, China

Work Experience

  • Research Assistant Professor (Jan 2022 - Present)

    Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong SAR

  • Associate Researcher (Apr 2021 - Jan 2022)

    College of Mathematics and Statistics, Shenzhen University, China

  • Postdoctoral Research Fellow (Oct 2018 - Dec 2020)

    College of Mathematics and Statistics, Shenzhen University, China
My Published Works

Research

  1. Hong Zhu#, Xiaoxia Liu#, Lin Huang, Zhaosong Lu, Jian Lu*, Michael K. Ng; Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery, Advances in Computational Mathematics, 50(75), 2024.
  2. Jian Lu#, Lin Huang#, Xiaoxia Liu*, Ning Xie*, Qingtang Jiang, Yuru Zou; 3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization, Inverse Problems, 40, 065010, 2024.
  3. Jian Lu, Huaxuan Hu, Yuru Zou, Zhaosong Lu, Xiaoxia Liu*, Keke Zu*, Lin Li; A nonlocal Kronecker-basis-representation method for low-dose CT sinogram recovery, Journal of Computational Mathematics, 42, 1080-1108, 2024.
  4. Jian Lu, Yuting Ye, Yiqiu Dong*, Xiaoxia Liu*, Yuru Zou; Impulse noise removal by L1 weighted nuclear norm minimization, Journal of Computational Mathematics, 41(6), 1171-1191, 2023.
  5. Jian Lu#, Chen Xu#, Zhenwei Hu, Xiaoxia Liu*, Qingtang Jiang, Deyu Meng and Zhouchen Lin; A new nonlocal low-rank regularization method with applications to magnetic resonance image denoising, Inverse Problems, 38(6), 065012, 2022.
  6. Chen Xu#, Xiaoxia Liu#, Jian Zheng, Lixin Shen, Qingtang Jiang, Jian Lu*; Nonlocal low-rank regularized two-phase approach for mixed noise removal, Inverse Problems, 37(8), 085001, 2021.
  7. Yuru Zou, Huaxuan Hu, Jian Lu, Qingtang Jiang, Guohui Song, Xiaoxia Liu*; A nonlocal low-rank regularization method for fractal image coding, Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 29(5): 0-2150125, 2021.
  8. Jian Lu, Jiapeng Tian, Qingtang Jiang, Xiaoxia Liu, Zhenwei Hu, Yuru Zou*; Rician noise removal via weighted nuclear norm penalization, Applied and Computational Harmonic Analysis, 53, 180-198, 2021.
  9. Xiaoxia Liu, Jian Lu*, Lixin Shen, Chen Xu, Yuesheng Xu; Multiplicative noise removal: Nonlocal low-rank model and its proximal alternating reweighted minimization algorithm, SIAM Journal on Imaging Sciences, 13(3): 1595-1629, 2020.  Codes
  10. Chen Xu, Yuting Ye, Zhenwei Hu, Yuru Zou, Lixin Shen, Xiaoxia Liu, Jian Lu*; A primal-dual algorithm for robust fractal image coding, Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 27(7):0-1950119, 2019.
# Co-first author(s)
* Corresponding author(s)
  1. 2D nonlocal low-rank model.  Download
  1. A projection algorithm for nonlocal low-rank tensor models with orthogonal constraints, The 25th International Symposium on Mathematical Programming (ISMP2024), Montreal, Canada (Jul 2024).
  2. Orthogonal constrained minimization with tensor l_{2,p} regularization for HSI denoising and destriping, ORSC Conference on Algorithms, Software and Applications (ASA2024), Xinxiang, China (Jun 2024).
  3. 3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization, SIAM Conference on Imaging Science (IS24), Atlanta, Georgia, U.S. (May 2024).
  4. Nonlocal low-rank regularization and its applications to medical image processing, SIAT-PolyU Joint Seminar, SIAT, Shenzhen, China (Aug 2023).
  5. Nonlocal low-rank models for image restoration, Annual Conference of Guangdong Computational Mathematics Society, virtual, (Dec 2021).
  6. Nonlocal low-rank model for multiplicative noise removal and its PARM algorithm, Seminar on Frontier Advances in Optimization Theory and Applications, SUSTech, Shenzhen, China (Nov 2020).
Taught Lectures at POLYU

Teaching

  • Semester 2 2023/2024:   AMA1120 Basic Mathematics II - Calculus and Linear Algebra.
  • Semester 2 2022/2023:   AMA3820 Operations Research Methods.
  • Semester 3 2021/2022:   AMA1120 Basic Mathematics II - Calculus and Linear Algebra.




Last updated: Jul 26, 2024.