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

We introduce a theoretical lower error bound for magnetostatic linear inverse problem solutions 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 out of 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 the advantage of using three-axial measurements is more pronounced as compared to a three compartment BEM.