

Using Automatic Differentiation for the Minimal pNorm Solution of the Biomagnetic Inverse Problem
Part of a collection
  

Area Biomedicine 
Author(s)
H. M. Bücker
, R. Beucker
, C. H. Bischof

Published in Shaping Future with Simulation, Proceedings of the 4th International Eurosim 2001 Congress, Delft, The Netherlands, June 2629, 2001

Editor(s) A. W. Heemink, L. Dekker, H. de Swaan Arons, I. Smit, T. L. van Stijn 
Year 2001 
Publisher Dutch Benelux Simulation Society 
Abstract Given the measurements of a magnetic field induced by the electrical activity of the brain, the mathematical model to localize the electrical activity on the human cortex is given by an inverse problem. The minimumnorm approach is among the common reconstruction techniques to localize the brain activity. Here, the standard approach is to minimize the Euclidean norm of the current distribution of the underlying dipole moments. A generalization from the Euclidean norm to general pnorms with 1 < p <= 2 is attractive because the reconstructions appear more focal as p approaches 1. Rather than using reweighted leastsquares algorithms with their potential numerical instabilities, a gradientbased optimization algorithm is investigated. More precisely, a Newtontype algorithm is used where the required gradient of the cost function is either accurately computed by automatic differentiation or approximated by finite differences. Numerical results are reported illustrating that accurate gradients computed by the socalled reverse mode of automatic differentiation are more efficient than approximations based on finite differences. 
AD Tools ADIFOR 
Related Applications
 Solution of the Biomagnetic Inverse Problem

BibTeX
@INPROCEEDINGS{
Bucker2001UAD,
author = "H. M. B{\"u}cker and R. Beucker and C. H. Bischof",
title = "Using Automatic Differentiation for the Minimal $p$Norm Solution of the Biomagnetic
Inverse Problem",
booktitle = "Shaping Future with Simulation, Proceedings of the 4th International Eurosim 2001
Congress, Delft, The Netherlands, June~2629, 2001",
editor = "A. W. Heemink and L. Dekker and H. {de~Swaan Arons} and I. Smit and T. L. van~Stijn",
publisher = "Dutch Benelux Simulation Society",
abstract = "Given the measurements of a magnetic field induced by the electrical activity of
the brain, the mathematical model to localize the electrical activity on the human cortex is given
by an inverse problem. The minimumnorm approach is among the common reconstruction techniques to
localize the brain activity. Here, the standard approach is to minimize the Euclidean norm of the
current distribution of the underlying dipole moments. A generalization from the Euclidean norm to
general $p$norms with~$1 < p <= 2$ is attractive because the reconstructions appear more
focal as~$p$ approaches~$1$. Rather than using reweighted leastsquares algorithms with their
potential numerical instabilities, a gradientbased optimization algorithm is investigated. More
precisely, a Newtontype algorithm is used where the required gradient of the cost function is
either accurately computed by automatic differentiation or approximated by finite differences.
Numerical results are reported illustrating that accurate gradients computed by the socalled
reverse mode of automatic differentiation are more efficient than approximations based on finite
differences.",
ad_area = "Biomedicine",
ad_tools = "ADIFOR",
year = "2001"
}
 
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