FAN, Jun; HON, Yu Sing Sean; LAM, Kei Fong Andrew

Overview

The interdisciplinary field of imaging science is experiencing tremendous growth. New devices capable of imaging objects and structures from nanoscale to the astronomical scale are continuously being developed and improved, and as a result, the research of science and medicine has been extended in exciting and unexpected ways. The impact of this technology has been to generate new challenges associated with the problems of formation, acquisition, compression, transmission, and analysis of images. By their very nature, these challenges cut across the disciplines of physics, engineering, mathematics, biology, medicine, and statistics.

The Imaging Sciences Group works for fundamental results in imaging sciences, with a unique combination of mathematics and applications. The group is mathematically and computationally based, and members study methodology, models, and algorithms among diverse application areas of imaging sciences. The group members are a part of the Centre for Mathematical Imaging and Vision (CMIV) at Hong Kong Baptist University (http://www.math.hkbu.edu.hk/cmiv/). The objectives of the Centre is to promote basic and applied research in mathematical imaging and vision, computational imaging methods and image analysis and recognition, and to provide a research environment for faculty and graduate students with research interests in the aforementioned areas. Faculty members from various departments are involved in the CMIV and the CMIV facilitates their interaction with each other, as well as domestic and international visitors across universities and the industry. The CMIV is the site for several seminars and conferences for representatives from other universities, including the SIAM Conference on Imaging Sciences, which is the first SIAM Activity Group Meeting to be held in Asia and Hong Kong.

Research Interests

• Image Processing, including denoising, deblurring, decomposition, reconstruction and segmentation.
• Inverse Problems, including compressive sensing, inverse scattering and Super-resolution.
• Data Analysis, including social signal processing, visual surveillance, classification and learning, high-dimensional data mining, and network analysis.
• Applications, including computational photography, medical imaging and astronomical imaging.

 

FAN, Jun; LAM, Kei Fong Andrew; LIAO, Li Zhi

Overview

The optimization group in our department consists of three faculty members working on continuous optimization and one faculty member working on combinatorial optimization. The research of the continuous optimization team focuses on numerical optimization, neurodynamic optimization, nonconvex optimization and various applications, particularly data mining and networks. The research of combinatorial optimization works mainly on graph theory.

Research Interests

• Numerical Optimization, including nonlinear programming, variational inequalities, complementarity problems, and large-scale convex problems.
• Neurodynamic Optimization, including neural networks, neurodynamic models for interior point methods, and continuous models for optimization.
• Nonconvex Optimization, including sparse and low-rank optimization, matrix optimization, and network optimization.
• Graph Theory, including code and frequency assignment problems, graph coloring problems, spectral of graphs, and chemical indices of graph.

 

FAN, Jun; HON, Yu Sing Sean; LAM, Kei Fong Andrew; LING, Leevan

Overview

The Scientific Computing group focuses on development and analysis of algorithms and high-performance computing. Our group contains members with titles and achievements including SIAM Fellow, Fellow of the Fields Institute, First Prize winner in the natural science category of the 2007 Tertiary Institutions Science Technology Awards, David Borwein Distinguished Career Award winner of the Canadian Mathematical Society. Our members also serve the research community by providing editorial services in leading journals including the IMA Journal on Numerical Analysis, SIAM Journal on Numerical Analysis, Numerical Linear Algebra with Applications, Mathematics of Computation, Journal of Computational Physics, Journal of Scientific Computing, Engineering Analysis with Boundary Elements, and more.

To promote world-class research environments, we organize international conferences on various aspects of scientific computing. In particular, the International Conference on Scientific Computing and Partial Differential Equations is held regularly every 3 years. On average, our research group invites over 20 scholars every year to give colloquiums and seminars. New collaborations and innovative ideas are easily developed in this hospitable environment.

Research Interests

• Finite Element Methods, including conforming, nonconforming and hybrid-mixed finite element methods for solving second and fourth order, linear and nonlinear problems. Finite element methods for problems with singularities and problems on unbounded domains are also studied.
• Spectral Methods, which focuses mainly on its application to computational fluid dynamics, and its application for solving problems in unbounded domains.
• Meshless Methods, which focuses mainly on algorithm design, convergence analysis, and its application for solving PDEs.
• Domain Decomposition Methods, in which we consider preconditioners for various kinds of problems - selfadjoint or non-selfadjoint, linear or nonlinear, based on the finite element discretization and conjugate gradient iteration.
• Grid Generation, in which we develop automatic grid generation techniques for arbitrary domains using quadrilateral or triangle meshes. Applications include the tidal analysis of harbors and computer aided geometric design.
• Parallel Computing, which is concentrated on the development of parallel methodologies for large scale optimization, optimal control and numerical solutions for partial differential equations.
• Numerical PDEs, including efficient numerical schemes for solving acoustic, electromagnetic and elastic scattering problems as well as the corresponding inverse scattering problems.
• Matematerials, which focuses on the modeling, mathematical design and numerical simulations of various metamaterial devices.

 

CHENG, Ming-Yen; CHIU, Sung Nok; FAN, Jun; PENG, Heng; TONG, Tiejun; ZHU, Lixing

Overview

The statisticians in the Mathematics Department form a strong team, whose research is remarkably influential. Our people won the Humboldt research award, the State Natural Science award, IMS fellowship, ASA fellowship and ISI elected membership. Many of our publications have high citation numbers and most of us are serving as associate editors of leading journals. The HKBU statistics group has been recognized internationally.

Because of the wide applicability nature of statistical science and the diversified expertise among our team members, we have been very successful in various interdisciplinary researches. Our work is not only on cutting-edge methodology development but also on innovative applications, leading to publications in prestigious journals in statistics and in other disciplines.

As a platform, the University's Statistics Research and Consultancy Centre (SRCC) engages in both theoretical and applied statistics research and provides statistical consultancy and sponsors academic exchange and organizes international conferences. For example, International Conference on Statistics in Honour of Professor Kai-Tai Fang’s 65th Birthday in 2005 (157 participants) and The Ninth ICSA International Conference in 2013 (452 participants) were held at HKBU.

Research Interests

• Applied Probability, including stochastic geometry, random processes, and probabilistic modeling of molecular mechanisms in biology.
• Big Data, including big data in bio-medicine, big data analytics and applications in online education.
• Biostatistics and Bioinformatics, including clinical trial design, health informatics, meta-analysis, pattern recognition, and statistical genomics.
• Finance, including credit risk modeling, including financial econometrics, financial risk management, and industrial engineering.
• High-dimensional Data Analysis, including covariance matrix estimation, dimension reduction, machine learning, model-adaptive dimension reduction testing for regressions, pivotal variable detection in factor models, shrinkage estimation, variable selection, and their scientific applications.
• Regression, including econometrics related regression analysis, goodness-of-fit tests, model selection, nonparametric and semiparametric regression, shrinkage estimation, and variable selection.
• Spatial Statistics, including statistics for spatial point processes and random set models.
• Miscellanea, including data-analytic modeling, design of experiments, design methods for time-to-event data, efficient estimation and sampling, nonparametric and robust methods, resampling techniques, and survival analysis.