Global Minimization of the Active Contour Model with TV-Inpainting and Two-Phase Denoising. - Shingyu Leung; Stanley J. Osher (VLSM, 2005)

A Local Level Set Method for Paraxial Geometrical Optics. - Jianliang Qian; Shingyu Leung (SIAM J. Sci. Comput., 2006)

Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime. - Shingyu Leung; Jianliang Qian (J. Comput. Phys., 2009)

A grid based particle method for moving interface problems. - Shingyu Leung; Hongkai Zhao (J. Comput. Phys., 2009)

A grid based particle method for evolution of open curves and surfaces. - Shingyu Leung; Hongkai Zhao (J. Comput. Phys., 2009)

Expectation-Maximization Algorithm with Local Adaptivity. - Shingyu Leung; Gang Liang; Knut Solna; Hongkai Zhao (SIAM J. Imaging Sci., 2009)

The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation. - Shingyu Leung; Jianliang Qian (J. Comput. Phys., 2010)

An Eulerian approach for computing the finite time Lyapunov exponent. - Shingyu Leung (J. Comput. Phys., 2011)

A grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion. - Shingyu Leung; John S. Lowengrub; Hongkai Zhao (J. Comput. Phys., 2011)

Expectation-maximization algorithm with total variation regularization for vector-valued image segmentation. - Jun Liu 029; Yin-Bon Ku; Shingyu Leung (J. Vis. Commun. Image Represent., 2012)

A Generic Convexification and Graph Cut Method for Multiphase Image Segmentation. - Jun Liu 029; Xue-Cheng Tai; Shingyu Leung (EMMCVPR, 2013)

A Splitting Algorithm for Image Segmentation on Manifolds Represented by the Grid Based Particle Method. - Jun Liu 029; Shingyu Leung (J. Sci. Comput., 2013)

A cell based particle method for modeling dynamic interfaces. - Sean Y. Hon; Shingyu Leung; Hongkai Zhao (J. Comput. Phys., 2014)

VIALS: An Eulerian tool based on total variation and the level set method for studying dynamical systems. - Guoqiao You; Shingyu Leung (J. Comput. Phys., 2014)

An Eulerian method for computing the coherent ergodic partition of continuous dynamical systems. - Guoqiao You; Shingyu Leung (J. Comput. Phys., 2014)

A new continuous max-flow algorithm for multiphase image segmentation using super-level set functions. - Jun Liu 029; Xue-Cheng Tai; Shingyu Leung; Haiyang Huang 001 (J. Vis. Commun. Image Represent., 2014)

A Penalization-Regularization-Operator Splitting Method for Eikonal Based Traveltime Tomography. - Roland Glowinski; Shingyu Leung; Jianliang Qian (SIAM J. Imaging Sci., 2015)

A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces. - Tony Wong; Shingyu Leung (J. Sci. Comput., 2016)

Guarantees of Riemannian Optimization for Low Rank Matrix Recovery. - Ke Wei 001; Jian-Feng Cai 001; Tony F. Chan; Shingyu Leung (SIAM J. Matrix Anal. Appl., 2016)

Operator-Splitting Based Fast Sweeping Methods for Isotropic Wave Propagation in a Moving Fluid. - Roland Glowinski; Shingyu Leung; Jianliang Qian (SIAM J. Sci. Comput., 2016)

A fast Huygens sweeping method for capturing paraxial multi-color optical self-focusing in nematic liquid crystals. - Wingfai Kwan; Shingyu Leung; Xiao-Ping Wang 002; Jianliang Qian (J. Comput. Phys., 2017)

A Level Set Based Variational Principal Flow Method for Nonparametric Dimension Reduction on Riemannian Manifolds. - Hao Liu 028; Zhigang Yao; Shingyu Leung; Tony F. Chan (SIAM J. Sci. Comput., 2017)

Eulerian Methods for Visualizing Continuous Dynamical Systems using Lyapunov Exponents. - Guoqiao You; Tony Wong; Shingyu Leung (SIAM J. Sci. Comput., 2017)

Eulerian Based Interpolation Schemes for Flow Map Construction and Line Integral Computation with Applications to Lagrangian Coherent Structures Extraction. - Guoqiao You; Shingyu Leung (J. Sci. Comput., 2018)

An Improved Eulerian Approach for the Finite Time Lyapunov Exponent. - Guoqiao You; Shingyu Leung (J. Sci. Comput., 2018)

A Simple Explicit Operator-Splitting Method for Effective Hamiltonians. - Roland Glowinski; Shingyu Leung; Jianliang Qian (SIAM J. Sci. Comput., 2018)

Modified Virtual Grid Difference for Discretizing the Laplace-Beltrami Operator on Point Clouds. - Meng Wang; Shingyu Leung; Hongkai Zhao (SIAM J. Sci. Comput., 2018)

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation. - Roland Glowinski; Hao Liu 028; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2019)

Correction to: A Finite Element/Operator-Splitting Method for the Numerical Solution of the Two Dimensional Elliptic Monge-Ampère Equation. - Roland Glowinski; Hao Liu 028; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2019)

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge-Ampère Equation. - Hao Liu 028; Roland Glowinski; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2019)

An Alternating Direction Explicit Method for Time Evolution Equations with Applications to Fractional Differential Equations. - Hao Liu 028; Shingyu Leung (CoRR, 2020)

On the Numerical Solution of Nonlinear Eigenvalue Problems for the Monge-Ampère Operator. - Roland Glowinski; Shingyu Leung; Hao Liu 028; Jianliang Qian (CoRR, 2020)

Fast Construction of Forward Flow Maps using Eulerian Based Interpolation Schemes. - Guoqiao You; Shingyu Leung (J. Sci. Comput., 2020)

Efficient Algorithms for Computing Multidimensional Integral Fractional Laplacians via Spherical Means. - Boxi Xu; Jin Cheng; Shingyu Leung; Jianliang Qian (SIAM J. Sci. Comput., 2020)

Computing the finite time Lyapunov exponent for flows with uncertainties. - Guoqiao You; Shingyu Leung (J. Comput. Phys., 2021)

Eulerian algorithms for computing some Lagrangian flow network quantities. - Guoqiao You; Shingyu Leung (J. Comput. Phys., 2021)

A Level Set Method for the Dirichlet k-Partition Problem. - Kwunlun Chu; Shingyu Leung (J. Sci. Comput., 2021)

Fast Huygens Sweeping Methods for a Class of Nonlocal Schrödinger Equations. - Kaho Ho; Shingyu Leung; Jianliang Qian (J. Sci. Comput., 2021)

A Level-Set Adjoint-State Method for Transmission Traveltime Tomography in Irregular Domains. - Shingyu Leung; Jianliang Qian; Jiangtao Hu (SIAM J. Sci. Comput., 2021)

An Efficient Operator-Splitting Method for the Eigenvalue Problem of the Monge-Ampère Equation. - Hao Liu 028; Shingyu Leung; Jianliang Qian (CoRR, 2022)

Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems. - Wai Ming Chau; Shingyu Leung (CoRR, 2022)

Sparse subsampling of flow measurements for finite-time Lyapunov exponent in domains with obstacles. - Yu-Keung Ng; Guoqiao You; Shingyu Leung (J. Comput. Appl. Math., 2023)

Spherical Essentially Non-oscillatory (SENO) Interpolation. - Ki Wai Fong; Shingyu Leung (J. Sci. Comput., 2023)

A Simple Embedding Method for Scalar Hyperbolic Conservation Laws on Implicit Surfaces. - Chun Kit Hung; Shingyu Leung (SIAM J. Sci. Comput., 2023)

Hadamard integrators for wave equations in time and frequency domain: Eulerian formulations via butterfly algorithms. - Yuxiao Wei; Jin Cheng; Shingyu Leung; Robert Burridge; Jianliang Qian (CoRR, 2024)

A Constrained Least-Squares Ghost Sample Points (CLS-GSP) Method for Differential Operators on Point Clouds. - Ningchen Ying; Kwunlun Chu; Shingyu Leung (CoRR, 2024)

Solving Partial Differential Equations on Evolving Surfaces via the Constrained Least-Squares and Grid-Based Particle Method. - Ningchen Ying; Shingyu Leung (CoRR, 2024)

Operator-Splitting/Finite Element Methods for the Minkowski Problem. - Hao Liu 028; Shingyu Leung; Jianliang Qian (SIAM J. Sci. Comput., 2024)

SLERP-TVDRK (STVDRK) Methods for Ordinary Differential Equations on Spheres. - Shingyu Leung; Wai Ming Chau; Young Kyu Lee (J. Sci. Comput., 2024)

An adaptive ray-tracing method for eikonal equations on spheres using STVDRK integrators and SENO interpolations. - Wai Ming Chau; Shingyu Leung (J. Comput. Phys., 2025)

A Spherical Crank-Nicolson Integrator Based on the Exponential Map and the Spherical Linear Interpolation. - Shingyu Leung (CoRR, 2025)