Alexandra Koulouri

Imperial College London
Communications and Signal Processing - EEE
London

alexandra.koulouri07@imperial.ac.uk

Room: 805 EEE Department
Phone no: +44 7964922728

I am a PhD student at Communications and Signals Processing group at Imperial College under the supervision of Mike Brookes (my former supervisor was Prof. Maria Petrou). At the moment I am at the writing up stage.

Area of Research: Vector field tomography (VFT), Inverse EEG problem, Regularization techniques, Large scale sparse problems, Non-linear Optimizations and Bayesian Approximation Error Approach.
I am currently working on: Focal Source reconstruction problem penalized with sparsity contraints (mixed l1/l2 norms) and the Bayesian Approximation Error Approach (AEA) the inverse EEG Problem, introduced by Prof. J. Kaipio. Particularly, the modeling errors (e.g. unknown geometry and conductivities uncertainties) caused by the use of standard models (e.g three Layers concentric model) are compensated using the AEA. In the following picture, I present the results for a focal source recovery when (a) we know the actual geometry (head structure) of the individual and when (b) we employ a 3 layers standard geometry (unknown geometry) in the inverse modeling.

With blue x we denote the projected actual source location. Further results will be presented when this work is published.
With my previous supervisor M. Petrou, we worked on an alternative brain imaging method compared to the dipole source localization problem. We computed the underlying quasi-static electric field of a bounded domain from boundary potentials employing longitudinal line integrals (also called X-Ray Integrals) and simple regularization techniques.
Previous Homepage: Between 2007-2009, I worked in two different medical image segmentation problems. I used Level-set method (e.g. Chan-Vese algorithm) and other image processing thechniques. Further details, code and documentations can be found in my old homepage .


Research articles

  • Vector Field Tomography: Reconstruction of an Irrotational Field in the Discrete Domain.
    DOI: 10.2316/P.2012.778-021
    Proceeding (778) Signal Processing, Pattern Recognition and Applications / 779: Computer Graphics and Imaging - 2012

    Abstract
    We revisit the problem of the reconstruction of an irrotational vector field by solving a set of line integral equations in the discrete domain. We show that the continuous inverse Radon formulation fails to reconstruct an irrotational vector field while the approximate solution of the problem in the digital domain is feasible, overcoming the intrinsic ill-posedness of the problem. In particular, we show that the discretization of the problem is an efficient way of regularising the continuous ill posedness since it ensures an upper bound to the solution error. We demonstrate the effectiveness of the method with simulations.

  • Stable Reconstruction of Irrotational Vector Fields based on the Discrete Longitudinal Ray Transform. (To appear)

    Abstact
    In this paper, we show that the estimation of an irrotational smooth vector field employing the longitudinal ray transform in the discrete domain is tractable, despite the fact that this problem cannot be solved in the continuous domain using the same formulation. We derive a set of algebraic equations and solve the ill conditioned inverse problem by directly inverting the produced ray projection matrix. In particular, we prove that the problem is regularized via discretization and we provide an upper bound for the numerical error of the approximation, ensuring the stability of our formulation. We validate our theoretical results by performing simple simulations reconstructing irrotational fields based solely on boundary measurements without the need of any prior information.


    Presentations
    Presentations in Vector Field Tomography Download and Download


    Teaching

    Maths tutor at EEE department (2010-2012)
    I teach small groups of undergraduate students on a weekly basis. Course includes Calculus, Differential Equations, Linear Algebra and introduction to Discrete Mathematics.

    GTA demonstrator in C/C++ (first and second years lab and quizzes author).

    Research visit
    Maths Dept, University of Auckland (2013-Apr. 2014), work with Dr. Viller Rimpilainen and J. Kaipio.