Theoretical Lower Error Bound for Comparative Evaluation of Sensor Arrays in Magnetostatic Linear Inverse Problems

We introduce a theoretical lower error bound for solutions to magnetostatic linear inverse problems and we propose it as a figure of merit for the comparative evaluation of sensor arrays. With the help of the proposed error bound, we demonstrate the superiority of three-axial biomagnetic sensor arrays applying truncated singular value decomposition analysis to a kernel matrix computed from boundary-element-method (BEM) models of the human torso for a biomagnetic application. In simulations, we found that, for a more complex five-compartment BEM model, the advantage of using three-axial measurements is more pronounced, compared to a three-compartment BEM model