Bandlimited field reconstruction from samples obtained on a discrete grid with unknown random locations

Abstract

Sampling spatial fields using sensors which are location unaware is an exciting topic. Due to symmetry and shift-invariance of bandlimited fields, it is known that uniformly distributed location-unaware sensors cannot infer the field. This work studies asymmetric (nonuniform) distributions on location-unaware sensors that will enable bandlimited field inference. In this first exposition, to facilitate analysis, location-unaware sensors are restricted to a discrete grid. Oversampling is used to overcome the lack of location information. The samples obtained from location-unaware sensors are clustered together to infer the field using the probability distribution that governs sensor placement on the grid. Based on this clustering algorithm, the main result of this work is to find the optimal probability distribution on sensor locations that minimizes the detection error-probability of the underlying spatial field.