Genetic algorithms for minimal source reconstructions

Under-determined linear inverse problems arise in applications in which signals must be estimated from insufficient data. In these problems the number of potentially active sources is greater than the number of observations. In many situations, it is desirable to find a minimal source solution. This can be accomplished by minimizing a cost function that accounts for both the compatibility of the solution with the observations and for its "sparseness". Minimizing functions of this form can be a difficult optimization problem. Genetic algorithms are a relatively new and robust approach to the solution of difficult optimization problems, providing a global framework that is not dependent on local continuity or on explicit starting values. We describe the use of genetic algorithms to find minimal source solutions, using as an example a simulation inspired by the reconstruction of neural currents in the human brain from magnetoencephalographic (MEG) measurements.>