Selective minimum-norm solution of the biomagnetic inverse problem

A new multidipole estimation method which gives a sparse solution of the biomagnetic inverse problem is proposed. This solution is extracted from the basic feasible solutions of linearly independent data equations. These feasible solutions are obtained by selecting exactly as many dipole-moments as the number of magnetic sensors. By changing the selection, the authors search for the minimum-norm vector of selected moments. As a result, a practically sparse solution is obtained; computer-simulated solutions for L _p-norm (p=2, 1, 0.5, 0.2) have a small number of significant moments around the real source-dipoles. In particular, the solution for L ₁-norm is equivalent to the minimum-L ₁-norm solution of the original inverse problem. This solution can be uniquely computed by using linear programming.