On Optimal Sampling Trajectories for Mobile Sensing

We study the design of sampling trajectories for stable sampling and reconstruction of bandlimited spatial fields using mobile sensors. As a performance metric we use the path density of a set of sampling trajectories, defined as the total distance traveled by the moving sensors per unit spatial volume of the spatial region being monitored. We obtain new results for the problem of designing stable sampling trajectories with minimal path density, that admit perfect reconstruction of bandlimited fields. In particular, we identify the set of parallel lines with minimal path density that contains a set of stable sampling for isotropic fields.