Research Activities - K Chen, Liverpool Comput Maths

Research

Activities

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Variational Image Processing Research Results Demo:
                (1) Salt-Pepper [Impulse noise]     (2) Denoising [Gaussian noise]

                (3) Denoising video MG solution (4) Segmentation video
                (5) Image segmentation by multigrids     (6) Image inpainting by MG
                (7) Image registration by optimisation a)                                 b)

                (8) Image selective segmentation and reconstruction and (Note: the dots are the given geometric constraints and the precise selection is by a variational PDE model. For 3D case, the dots are only needed on 3 slices -- see the plot demo software: online here -- try it.)

General Interests: Having authored more than 100 publications, I have wide general research interests in applied mathematics (as reflected in the range of selected papers you have seen): Partial differential equations (FEM, FDM, FVM), Boundary integral equations (BEM's), Numerical linear algebra (LA). Mathematical modelling (MM): waves, acoustics, imaging science, semi-conductors, power systems, fluids mechanics. Current projects and activities include (click subjects for a tutorial):

Inverse Problems and Applications: Variational Image Processing including Image Reconstruction
Iterative methods: Preconditioning techniques. Parallel Computing.
Wavelets: Fast Wavelet Transforms.
Boundary integral equation methods for general PDE's. Domain Decomposition.
Voltage stability and bifurcation of electrical power systems.
Grid generation: Adaptive Methods for PDE's, Computational fluid dynamics
Mesoscale Particle Modelling Methods: Dissipative Particle Dynamics.

The Researchers at the Liverpool Research Team:

Current Projects @ (CMIT and LCMH) :

2019--: Mr Sukhdeep Singh Bal (Joint PhD - Year 1), NTHU-UoL project.
2019--: Ms H Jones (Joint PhD - Year 1), Oncology Image Analysis, UoL Risk CDT (EPSRC)
2018--: Ms A Erhle (Joint PhD - Year 2), "Modeling of tenden images", UoL GTA / Vet Sci
2017--: Mr L Burrows (PhD - Year 3), "Efficient algorithms for image segmentation and artefacts removal", (UK EPSRC iCASE) CMIt
2017--: Mr S Hawre (Joint PhD - Year 3), "Efficient models for registration of surfaces", UoL GTA
2017--: Dr A Theljani (PDRA), "Effective models for coregistration of modality images", EPSRC LCMH funding

Recent successfully completed Ph.D / M.Phil projects:

2019--: Dr D P Zhang, "Diffeomorphic registration models" CSC/UoL funding, CMIT
currently a PDRA at CUHK
2019--: Dr A Thompson, "Image motion correction" (UK EPSRC iCase) CMIT
currently a PDRA at SZ University
2019--: Dr M Roberts, "Image segmentation modeling" (UK EPSRC iCase) CMIT -- PhD thesis`
currently a research scientist at Astra-Zeneca (Cambridige)
2019--: Dr A Jumaat "Efficient algorithms for image segmentation" , Malaysian government scholarship
currently an assistant professor at Mara University of Technology
2017: Dr J Zhang, "Effective Imagistration Methods", DLUT funded. Main publications: EAJAM 2017, CMA 2016 and AMM 2016
currently an assistant professor at Liao-cheng University
2016: Dr J Spencer, "Variational Methods for Image Segmentation", (UoL GTA funding) -- Thesis
currently PDRA at University of Exeter
2015: Dr M Abrahim, "Variational Models and Numerical Algorithms for Effective Image Registration", National Defense University of Malaysia scholarship funded: Thesis
currently an assistant professor at National Defense University of Malaysia
2015: Dr B Williams, "Variational models and algorithms for blind image deconvolution with applications" (UK EPSRC Case funded). Thesis
currently a lecturer at Lancaster University
2012-2013: Mr M Ali (Visiting PhD - Year 3), "Imaging and Graph-cuts" (Pakistan) CMIT
2013 : Dr Lavdi Rada (now postdoc in Turkey), "Variational Models and Numerical Algorithms for Selective Image Segmentation", (UoL) GTA funded
, PhD Thesis, Main publications: (see publications) Commun. Comput. Phys. 2012, plus 5 submitted journal papers.
currently an assistant professor at Bahcesehir University
2012 : Dr Jianping Zhang (collaborating PhD, now postdoc in Hong Kong), "Image segmentation". Completed in March 2012. Main publications: (see publications) Int J. Comp. Math, SIAM J. Numer Anal.
currently an associate professor at the School of Mathematics, Xiang-tan University
2012 : Dr Fenlin Yang (collaborating PhD, now lecturer in Jishou University), "Nonlinear homotopy algorithms for imaging". Completed in Jan 2012. Main publications: (see publications) Appl. Numer Math, Int. J. Numer Anal. Model., J Comput. Math.
currently an assistant professor at Jishou University
2010 : Dr Noppadol Chumchob, (PhD, now an assistant professor in Silpakorn University), "Variational Image registration modeling and fast algorithms", completed in 2010. Main publications: (see publications)
International Journal of Numerical Analysis and Modeling, SIAM J. Multiscale Modelling and Simulation

currently an assistant professor at the Department of Mathematics, Faculty of Science, Silpakorn University
2009 : Dr Carlos Brito, (PhD, now an assistant professor in Universidad Autonoma de Yucatan), "Variational Image impainting modeling and fast algorithms", completed in 2009. Main publications: (see publications)
Journal of Computational Mathematics, IEEE Transactions on Image Processing, Int Journal of Modern Matheamtics,
SIAM J. Imaging Sciences, SIAM J. Multiscale Modelling and Simulation

2008: Dr Noor Badshah (PhD, now an assitant professor in Peshawar University), "Fast Iterative Methods for Variational Image Segmentation Models", completed in Dec 2008
Main publications: (see publications)
Communications in Computational Physics, IEEE Transactions on Image Processing.

2006: Dr Joe Savage (PhD, now a researcher in a London company) "Fast iterative solution of inverse problems with application to image processing", UK EPSRC GTA funded, completed in May 2006. (See papers: 1, 2, 3)
2004: Dr Martyn Hughes , UK EPSRC CASE/QinetiQ supported, Iterative solution of coupled 3D fluid structure interaction problems. Completed Jun 2004. (see papers: 1, 2, 3)

2003: Dr Kamal Shaanazari, New methods for numerical PDE's, (completed Jul 03 -- see related papers: 1, 2, 3 (to add))
2002: Miss Qun Xie (M.Phil completed Dec). Parallel computation methods for nonlinear power systems.
2002: Dr Anwar Hussein, (PhD, now in UAE), --- Fast bifurcation methods for nonlinear systems
, UK EPSRC support. (see related papers: 1, 2, 3, 4, 5, 6) (completed Nov 02)
2001 : Dr Judith Ford, UK EPSRC supported --- PhD Thesis title: Wavelets and preconditioned iterative solvers
(see related papers: 1, 2, 3, 4, 5, 6)
2000: Dr Andy Sunderland --- PhD Thesis: Large-scale applications in distributed-memory parallel computers using efficient numerical methods. (see related papers: here)
1999 : Dr Jonathan Gibson, UK EPSRC supported PhD: Application and analysis of dissipative particle dynamics.
(see related papers: 1, 2, 3)

Past co-workers:

Dr Stuart Hawkins (postdoc) -- now Teaching at Macquarie University, Australia
Dr Bob Blundall (Postdoc) -- joined University of Edinburgh
Dr Bartur Jumahon (Postdoc) -- joined Nottingham Trent University
Prof S. P. Zhu (UK EPSRC visiting fellow) -- University of Wollongong
Prof G. Piliposian (RS visiting fellow) -- joined University of Liverpool
Prof Wei-Guo Li (Visiting professor from Petrolium University of China).

External visitors / students: If you or people you know of intend to do a M.Sc and/or Ph.D in Numerical Analysis, Computational Mathematics or Scientific Computing, please contact me. If you like to cooperate in any of the above areas or simply visit Liverpool, I'd like to hear from you.

Recent talks: 1998, University of Manchester, ``Discrete wavelet transforms based sparse preconditioners''. 1998, University of Coventry, ``Sparse preconditioners for boundary elements''. 1998, Institute of Computational Physics, Beijing, ``Iterative methods for boundary elements''. 1998, Institute of Computational Mathematics and Scientific Computing, Chinese Academy of Sciences (CAS), Beijing. ``Preconditioned iterative methods''. 1999, University of Strathclyde, Wavelet accelerated preconditioners. 1999, Stanford University, USA. Wavelets and sparse preconditioners. 2000, University of Oxford, `Fast wavelet transforms, sparse approximation and preconditioners''. 2001, Institute of Computational Mathematics and Scientific Computing, Chinese Academy of Sciences (CAS), Beijing. ``On some analytical bifurcation methods''. 2004 Jan, Maths, University of Reading, 2004 Jan, SCCM, Manchester University, ``On a multigrid method for solving the total variation minimization''. 2004 Sep, Liverpool University, Multilevel methods for an inverse problem form image restoration" 2005 Mar, BICOM, Brunel University, " Fast multilevel methods for variational formulations from image processing and inverse problems" 2005 Oct, Dept of Maths, Ohio State University 2005 Oct, CAM, University of California, at LA 2005 Dec, Dept of Maths, Chinese University of Hong Kong 2006 Jan, Dept of Maths, University of Macau 2006 Mar, School of Maths, University of Birmingham 2006 Aug, Institute of Applied Mathematics, CAS On Multilevel Methods for Image Restoration, Academy of Mathematics and Systems Science. 2006 Nov, Department of Com[uter Science, Chu Hai College ``Variational Image Restoration and Segmentation Problems: Models and Fast Algorithms". 2006 Nov, Department of Mathematics, HK Baptist University Optimisation-based Multilevel Methods for Image Restoration, Centre for Mathematical Imaging and Vision. 2006 Dec, Department of Mathematics, South China Normal University ``Fast Multilevel Algorithms for Variational Imaging Models". 2006 Dec, Department of Mathematics, Hong Kong University ``Multilevel Methods for Variational Image Processing Models". 2006 Dec, Institute of Mathematical Sciences, The Chinese University of Hong Kong Fast Multilevel Algorithms for Nonlinear Varitional Imaging Models 2007 Jun, Academy of Mathematics and Systems Science, Chinese Academy Sciences Iterative Solution Methods for Some Variational Model 2007 Oct, Dept of Mathematics, University of Sussex On fast algorithms for variational models from image processing 2008 Dec, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences On fast multilevel algorithms for nonlinear variational imaging models 2009 Jan, University of Graz, Austria Fast Multilevel Algorithms For Nonlinear Variational Imaging Models 2009 Mar, University of Oxford, RAL and Oxford NA colloquium On fast multilevel algorithms for nonlinear variational imaging models 2009 Apr, Nanyang Technological University On Fast Multilevel Algorithms For Nonlinear Variational Imaging Models 2009 Nov, Institute of Computational Maths and Applied Physics On fast multilevel algorithms for High Order Denoising Models 2009 Dec, Warwick Mathematics Institute Variational Imaging Models And Fast Algorithms 2010 Jun, Dalian University of Technology Image registration Algorithms 2010 Jul, Beijing - Institute of Applied Phys and Computational Math Image High order models 2010 Aug, Guang Zhou - SYS University Image Selection models 2010 Oct, London - Brunel University Variational Image selection models and Fast algorithms 2011 Aug, University of Cambridge Invited Talk at Isaac Newton Institute for Mathematical Sciences, Inverse Problem and Medical Imagining workshop. 2011 Nov, Shandong University Image segmentation and registration (link) 2011 Dec, University of Macau Invited Talk at Sci Cpmput Workshop. 2012 Jan, Chinese University of Hong Kong Plenary Talk at Int Conf on Sci Comput. 2012 Nov, University of Cambridge Invited Colloquium on Applied and Computational Analysis series. 2013 Jan and Oct, University of Liverpool Invited Talks at Institute of Translational Medicine Workshop in Medical Imaging and 7th Int Conf AKU Society. 2013 Dec, Chinese Academy of Maths and System Sci and Xian JT University. Invited Talks. 2014 Jan, Beijing University of Aeronautical and Astronautics 2014 Feb, University of Cambridge Invited Talk at LMS Inverse Day on Sparse Regularisation. 2014 Feb, Singapore 3rd CMCGS 2014 conference Plenary Talk.