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