Abstract
The application of neural network is considered in solving the inverse problem at high speed in producing maps of neuron current densities, resulting from brain activity, with magnetic field data measured by superconducting quantum interference device (SQUID) sensors. Neuron activity in the brain is modeled as current dipoles. The dipoles are located in a 2-dimensional reconstruction plane which is separate but parallel with the sampling plane. Each coordinate component of a vector dipole is assigned to a neuron.
If zero is selected as the initial state of each neuron, and if the distance (=Dd) between the reconstruction plane and the sampling plane is short, the location of dipoles is obtained correctly by a Hopfield type neural network after a small number of iterations. For the assurance of the spontaneous energy minimization process, coefficients of energy function are selected to cancel out the diagonal elements of connectivity matrix.
Boltzmann machine makes it possible to obtain the correct location with no relation to Dd and the initial state of each neuron under a priori information about the true number of dipoles.
