Research Activities
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Variational Image Processing Research Results Demo:            
                (1) Salt-Pepper To first detect which are noisy ones and then fix such pixels by relying on the `correct' pixels (left), result: right[Impulse noise]     (2) Denoising To remove the environmental noise (left) without damaging the
               image by a variational model, result: right [Gaussian noise]
                Total variation model for Poisson noise High order model for Gaussian noise removal (where kappa is the curvature)
                (3) Denoising video MG solution   (4) Segmentation video    Variational Chan-Vese segmentation model - PC Mumford/Shah
                (5) Image segmentation by multigrids     (6) Image inpainting by MG
                (7) Image registration by optimisation a)                                 b)
    System of PDEs for quality (deformable) registration System of Curvature PDEs for quality (deformable) registration
                (8) Image selective segmentation and reconstruction 2D image and 3D image (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.)

Ke's Research Related Activities:
Journal Editorial Boards
Member of the EPSRC peer review college
Referee for more than 50 applied and computational maths journals including
Other information:
General research interests (including tutorials)
External visitors,
Some Recent Talks,
Who cares about Ax=b?
What is Applied Mathematics?

BACK to Ke Chen's home page

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: