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}essianvector products",
journal = "{SIAM} Journal on Scientific Computing",
pages = "29052921",
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 nonuniqueness 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
trustregion algorithm for the solution of an unconstrained nonlinear optimization problem,
automatic differentiation for the truncationerror free evaluation of first and second order
derivatives, and sharedmemory parallelization using the OpenMP programming paradigm. Using actual
measurements obtained from a head phantom model as well as realistic data sets of middlelatency
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"
}
