Selected Publications

Papers

• Convergence Analysis of the Nonlinear Kaczmarz Method for Systems of Nonlinear Equations with Componentwise Convex Mappings and Applications to Image Reconstruction in Multispectral CT (with Y. Gao), SIAM Journal on Imaging Sciences, 18(1):120-151, 2025. (DOI)

• Analysis of Solution Existence, Uniqueness, and Stability of Discrete Basis Sinograms in Multispectral CT (with Y. Gao and X. Pan), Journal of Mathematical Imaging and Vision, 66(4):741-757, 2024. (DOI)

• The subdivision-based IGA-EIEQ numerical scheme for the Cahn−Hilliard−Darcy system of two-phase Hele-Shaw flow on complex curved surfaces (with Q. Pan, Y. Huang, X. Yang and J. Zhang), Computer Methods in Applied Mechanics and Engineering, 420:116709 (19pp), 2024. (DOI)

• Subdivision-based IGA coupled EIEQ method for the Cahn−Hilliard phase-field model of homopolymer blends on complex surfaces (with Q. Pan, T. Rabczuk, J. Zhang and X. Yang), Computer-Aided Design, 164:103589 (14pp), 2023. (DOI)

• The subdivision-based IGA-EIEQ numerical scheme for the binary surfactant Cahn−Hilliard phase-field model on complex curved surfaces (with Q. Pan, T. Rabczuk, J. Zhang and X. Yang), Computer Methods in Applied Mechanics and Engineering, 406:115905 (21pp), 2023. (DOI)

• A novel hybrid IGA-EIEQ numerical method for the Allen−Cahn/Cahn−Hilliard equations on complex curved surfaces (with Q. Pan, Y. J. Zhang and X. Yang), Computer Methods in Applied Mechanics and Engineering, 404:115767 (21pp), 2023. (DOI)

• An Extended Primal-Dual Algorithm Framework for Nonconvex Problems: Application to Image Reconstruction in Spectral CT (with Y. Gao and X. Pan), Inverse Problems, 38(8):085011 (44pp), 2022. (DOI)

• An Efficient Algorithm to Compute the X-ray Transform (with R. Wang, C. Bajaj and O. Öktem), International Journal of Computer Mathematics, 99(7):1325-1343, 2022. (The code is available upon request. DOI)

• Subdivision Based Isogeometric Analysis for Geometric Flows (with Q. Pan and T. Rabczuk), International Journal for Numerical Methods in Engineering, 123(2):610-633, 2022. (DOI)

• Spatiotemporal Imaging with Diffeomorphic Optimal Transportation, Inverse Problems, 37(11):115004 (30pp), 2021. (DOI)

• Image reconstruction through metamorphosis (with B. Gris and O. Öktem), Inverse Problems, 36(2):025001 (27pp), 2020. (DOI)

• A New Variational Model for Joint Image Reconstruction and Motion Estimation in Spatiotemporal Imaging (with B. Gris and O. Öktem), SIAM Journal on Imaging Sciences, 12(4):1686-1719, 2019. (DOI)

• Isogeometric Analysis for Surface PDEs with Extended Loop Subdivision (with Q. Pan, T. Rabczuk and Gang Xu), Journal of Computational Physics, 398:108892 (22pp), 2019. (DOI)

• Indirect Image Registration with Large Diffeomorphic Deformations (with O. Öktem), SIAM Journal on Imaging Sciences, 11(1):575-617, 2018. (DOI)

• Isogeometric Analysis of Minimal Surfaces on the Basis of Extended Catmull−Clark Subdivision (with Q. Pan, T. Rabczuk, G. Xu and K. Pan), Computer Methods in Applied Mechanics and Engineering, 337:128-149, 2018. (DOI)

• Isogeometric Finite Element Approximation of Minimal Surfaces Based on Extended Loop Subdivision (with Q. Pan and G. Xu), Journal of Computational Physics, 343:324-339, 2017. (DOI)

• Shape-Based Image Reconstruction Using Linearized Deformations (with O. Öktem, N. Domanic, P. Ravikumar and C. Bajaj), Inverse Problems, 33(3):035004 (33pp), 2017. (DOI)

• A General Framework of Piecewise-Polynomial Mumford−Shah Model for Image Segmentation (with J. Leng and G. Xu), International Journal of Computer Mathematics, 94(10):1981-1997, 2017. (DOI, Published with bad picture showing, Original version in UCLA CAM Reports 13-50, 2013)

• A New Linearized Split Bregman Iterative Algorithm for Image Reconstruction in Sparse-View X-Ray Computed Tomography (with G. Xu), Computers and Mathematics with Applications, 71(8):1537-1559, 2016. (DOI, Original version in UCLA CAM Reports 13-66, 2013)

• Blended Finite Element Method and Its Convergence for Three-dimensional Image Reconstruction Using L²-Gradient Flow (with G. Xu), Communications in Mathematical Sciences, 12(6):989-1015, 2014. (DOI)

• Gradient-Flow-Based Semi-Implicit Finite-Element Method and Its Convergence Analysis for Image Reconstruction (with G. Xu), Inverse Problems, 28(3):035006 (24pp), 2012. (DOI)

• Construction of Geometric Partial Differential Equations for Level Sets (with G. Xu), Journal of Computational Mathematics, 28(1):105-121, 2010. (DOI)

Monographs

• Numerical Methods for Image Reconstruction (in Chinese, 图像重构的数值方法) (with G. Xu and M. Li), Science Press, Beijing, China, 2015. (PDF for Cover and Table of Contents)

Technical Reports

• AFIRE: Accurate and Fast Image Reconstruction Algorithm for Geometric-inconsistency Multispectral CT (with Y. Gao), arXiv:2505.24793.

• A Mathematical Study of Joint Image Reconstruction and Motion Estimation Using Optimal Control (with Z. Wei), arXiv:2310.13635.

• Convergence Analysis of Nonlinear Kaczmarz Method for Systems of Nonlinear Equations with Component-wise Convex Mapping (with Y. Gao), arXiv:2309.15003.

• Solution Existence, Uniqueness, and Stability of Discrete Basis Sinograms in Multispectral CT (with Y. Gao and X. Pan), arXiv:2305.03330.

• An Extended Primal-Dual Algorithm Framework for Nonconvex Problems with Application to Nonlinear Imaging (with Y. Gao and X. Pan), arXiv:2109.07174.

• A General Framework of Piecewise-Polynomial Mumford-Shah Model for Image Segmentation (with J. Leng and G. Xu), UCLA CAM Reports 13-50, 2013. (PDF)

• The Linearized Split Bregman Iterative Algorithm and Its Convergence Analysis for Robust Tomographic Image Reconstruction (with G. Xu), UCLA CAM Reports 13-66, 2013. (PDF)