Mobile sampling of bandlimited fields

We investigate a new method for the acquisition of bandlimited functions, which we call mobile sampling. A field is sampled by a mobile sensor that moves along a continuous path. In this context, it is possible to increase the spatial sampling rate along the sensor´s path with marginal additional cost. Hence we assume that the sensors acquire the field values on its path at an arbitrarily high resolution. While in classical sampling theory the relevant performance metric is the average number of samples per unit area, in mobile sampling the main acquisition cost comes from the total distance that needs to be traveled by the moving sensor. We consider a performance metric tailored to mobile acquisition and study the mobile sampling problem with respect to this metric. The introduction of this metric completely changes the mathematical nature of the sampling problem. We present in a brief and simplified form recent results that show to which extent the classical Nyquist sampling theory admits a parallel in the context of mobile acquisition. We also provide a brief account of the main technical tools.