Publication: Using Automatic Differentiation for the Minimal p-Norm Solution of the Biomagnetic Inverse Problem
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Using Automatic Differentiation for the Minimal p-Norm 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 26--29, 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 minimum-norm 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 least-squares algorithms with their potential numerical instabilities, a gradient-based optimization algorithm is investigated. More precisely, a Newton-type 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 so-called 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~26--29, 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 minimum-norm 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 least-squares algorithms with their
         potential numerical instabilities, a gradient-based optimization algorithm is investigated. More
         precisely, a Newton-type 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 so-called
         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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