Imperial College London
Alternate

Mr Mike Brookes

Faculty of Engineering, Department of Electrical and Electronic Engineering

Emeritus Reader
 
 
 
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Contact

 

+44 (0)20 7594 6165mike.brookes Website

 
 
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Assistant

 

Miss Vanessa Rodriguez-Gonzalez +44 (0)20 7594 6267

 
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Location

 

807aElectrical EngineeringSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Koulouri:2016:10.1016/j.jcp.2016.10.037,
author = {Koulouri, A and Brookes, DM and Rimpiläinen, V},
doi = {10.1016/j.jcp.2016.10.037},
journal = {Journal of Computational Physics},
pages = {73--90},
title = {Vector tomography for reconstructing electric  elds with non-zero divergence in bounded domains},
url = {http://dx.doi.org/10.1016/j.jcp.2016.10.037},
volume = {329},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are called the longitudinal and transverse measurements, respectively. In most cases, however, the transverse measurements cannot be physically acquired. Therefore, the VT methods are typically used to reconstruct divergence-free (or source-free) velocity and flow fields that can be reconstructed solely from the longitudinal measurements. In this paper, we show how vector fields with non-zero divergence in a bounded domain can also be reconstructed from the longitudinal measurements without the need of explicitly evaluating the transverse measurements. To the best of our knowledge, VT has not previously been used for this purpose. In particular, we study low-frequency, time-harmonic electric fields generated by dipole sources in convex bounded domains which arise, for example, in electroencephalography (EEG) source imaging. We explain in detail the theoretical background, the derivation of the electric field inverse problem and the numerical approximation of the line integrals. We show that fields with non-zero divergence can be reconstructed from the longitudinal measurements with the help of two sparsity constraints that are constructed from the transverse measurements and the vector Laplace operator. As a comparison to EEG source imaging, we note that VT does not require mathematical modeling of the sources. By numerical simulations, we show that the pattern of the electric field can be correctly estimated using VT and the location of the source activity can be determined accurately from the reconstructed magnitudes of the field.
AU  - Koulouri,A
AU  - Brookes,DM
AU  - Rimpiläinen,V
DO  - 10.1016/j.jcp.2016.10.037
EP  - 90
PY  - 2016///
SN  - 0021-9991
SP  - 73
TI  - Vector tomography for reconstructing electric  elds with non-zero divergence in bounded domains
T2  - Journal of Computational Physics
UR  - http://dx.doi.org/10.1016/j.jcp.2016.10.037
UR  - http://hdl.handle.net/10044/1/41519
VL  - 329
ER  -
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