Selected Publications

Papers

• 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, https://doi.org/10.1007/s10851-024-01198-7, 2024.

• 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)

Patents

• 一种能谱CT图像重建方法、装置、设备及存储介质, 国家发明专利, 陈冲、高宇, 2024104403344.

Technical Reports

• 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)