October 1991 – Diploma in Physics, Ludwig-Maximilian Universität München
December 1994 – Ph.D. Department of Medical Physics, University College London
1995 – 2000 Research Fellow, Department of Medical Physics, University College London
2001 – date Senior Research Fellow, Department of Computer Science, University College London
Numerical solutions to partial differential equations are required to solve many real-world problems. We have developed a finite element solver package that provides the building blocks for solving a variety of problems, including diffusion processes and linear elasticity problems. The package is implemented in an object-oriented framework that is both versatile and efficient. It contains a variety of element classes, basis functions and solver methods. The hierarchical class structure of the numerical and FEM libraries allows easy extension with new element types or solver methods.
The solution of nonlinear inverse problems generally requires iterative approaches that find the parameters of a differential equation by minimising a norm of the data difference. Optimisation stategies include methods that make use of the first derivative of the forward model (e.g. nonlinear steepest descent or conjugate gradient methods), the second derivative (e.g. Gauss-Newton, truncated Newton or Levenberg-Marquardt methods). Other methods use a statistical approach to describe the solution by the mean and standard deviation of a distribution of samples (Markov Chain Monte-Carlo method).
The numerical, modelling and inversion techniques described above are all applied to the problem of image reconstruction in diffuse optical tomography. Optical tomography is a medical imaging modality that seeks to recover the optical parameters of tissue from boundary measurements of infrared light transmission. The applications are in imaging of brain and muscle activity, monitoring of oxygen uptake and consumption, and breast tumour screening. Infrared light is strongly scattered in most biological tissues, making the propagation a highly nonlinear process, and the reconstruction is an ill-posed inverse problem.
The finite element solver routines, as well as its application to the problem of image reconstruction in optical tomography, have been integrated into a complete imaging suite. The suite contains the core numerical and FEM libraries, application programs for the solution of the forward and inverse problems, and an interface to Matlab that allows users to rapidly build modelling and reconstruction scripts tailored to their specific applications. The TOAST software suite is published online and can be downloaded under http://web4.cs.ucl.ac.uk/research/vis/toast/
Funded under EPSRC Grant EP/E034950/1. The aim of this project is the improvement of performance, accuracy and robustness of image reconstruction in optical tomography. The strategies invstigated in this project are (i) model reduction – statistical characterisation of a computationally efficient model allows to combine high performance with high accuracy; (ii) prior knowledge – incorporation of generic or anatmoical priors in a Bayesian framework, and combination with data from other imaging modalities; (iii) combined analysis and reconstruction – integration of segmentation and classification tasks directly into the reconstruction process.
Funded by the Seventh Framework Health (Grant agreement no. 201076). Home page: http://www.neuropt.eu/. The objective of this project is the development of novel imaging technieques for optical imaging of the brain from time-resolved measurements. The UCL-CS contribution to the project includes improvements to the modelling and reconstruction methods, such as efficient modelling of temporal point spread functions, multispectral and multimodality reconstruction methods.
M. Schweiger, S. R. Arridge, O. Dorn, A. Zacharopoulos and V. Kolehmainen, Reconstructing absorption and diffusion shape profiles in optical tomography by a level set technique, Opt. Lett. 21(4), 471-473 (2006).
M. Schweiger, I. Nissila, D. A. Boas and S. R. Arridge, Image reconstruction in optical tomography in the presence of coupling errors, Appl. Opt. 46(14), 2743-2756 (2007).
S. Wright, M. Schweiger and S. R. Arridge, Reconstruction in optical tomography using the PN approximations, Meas. Sci. Technol. 18(1), 79-86 (2007).
M. Schweiger, O. Dorn and S. R. Arridge, 3-D shape and contrast reconstruction in optical tomography with level sets, in Applied Inverse Problems 2007: Theoretical and Computational Aspects, J. Phys.: Conf. Ser. 124, paper 012043 (2008).
M. Schweiger, O. Dorn, A. Zacharopoulos, I. Nissila and S. R. Arridge, 3D level set reconstruction of model and experimental data in Diffuse Optical Tomography, Optics Express 18(1), 150-164 (2010).