Publication: Parallel minimum p-norm solution of the neuromagnetic inverse problem for realistic signals using exact Hessian-vector products
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Parallel minimum p-norm solution of the neuromagnetic inverse problem for realistic signals using exact Hessian-vector products

- Article in a journal -
 

Area
Biomedicine

Author(s)
H. M. Bücker , R. Beucker , A. Rupp

Published in
SIAM Journal on Scientific Computing

Year
2008

Abstract
In the neuromagnetic inverse problem, one is interested in determining the current density inside the human brain from measurements of the magnetic field recorded outside the head. From a numerical point of view, the solution of this inverse problem is challenging not only in terms of non-uniqueness and time complexity but also with respect to numerical stability. An efficient and robust computational technique is presented that finds the minimum p-norm solution of the neuromagnetic inverse problem. The approach is based on carefully combining a subspace trust-region algorithm for the solution of an unconstrained nonlinear optimization problem, automatic differentiation for the truncation-error free evaluation of first- and second order derivatives, and shared-memory parallelization using the OpenMP programming paradigm. Using actual measurements obtained from a head phantom model as well as realistic data sets of middle-latency auditory evoked field data (MAEF), it is demonstrated that a valid reconstruction of neuromagnetic activity is achieved for values of p less than 2.

AD Tools
TAF

AD Theory and Techniques
Hessian

Related Applications
- Solution of the Biomagnetic Inverse Problem

BibTeX
@ARTICLE{
         Bucker2008Pmp,
       author = "H. M. B{\"u}cker and R. Beucker and A. Rupp",
       title = "Parallel minimum $p$-norm solution of the neuromagnetic inverse problem for realistic
         signals using exact {H}essian-vector products",
       journal = "{SIAM} Journal on Scientific Computing",
       pages = "2905--2921",
       doi = "10.1137/07069198X",
       abstract = "In the neuromagnetic inverse problem, one is interested in determining the current
         density inside the human brain from measurements of the magnetic field recorded outside the head.
         From a numerical point of view, the solution of this inverse problem is challenging not only in
         terms of non-uniqueness and time complexity but also with respect to numerical stability. An
         efficient and robust computational technique is presented that finds the minimum $p$-norm solution
         of the neuromagnetic inverse problem. The approach is based on carefully combining a subspace
         trust-region algorithm for the solution of an unconstrained nonlinear optimization problem,
         automatic differentiation for the truncation-error free evaluation of first- and second order
         derivatives, and shared-memory parallelization using the OpenMP programming paradigm. Using actual
         measurements obtained from a head phantom model as well as realistic data sets of middle-latency
         auditory evoked field data (MAEF), it is demonstrated that a valid reconstruction of neuromagnetic
         activity is achieved for values of $p$ less than 2.",
       year = "2008",
       volume = "30",
       number = "6",
       ad_area = "Biomedicine",
       ad_tools = "TAF",
       ad_theotech = "Hessian"
}


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