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"
}