Spatio-temporal sampling and reconstruction of diffusion fields induced by point sources

In this paper we consider a diffusion field induced by multiple point sources and address the problem of reconstructing the field from its spatio-temporal samples obtained using a sensor network. We begin by formulating the problem as a multi-source estimation problem - so estimating source locations, activation times and intensities given samples of the induced field. Next a two-step algorithm is proposed for the single (localized and instantaneous) source field. First, the source location and intensity are estimated by applying the “reciprocity gap” principle; we show that this step can also reveal locations of multiple non-instantaneous sources. In the second step, we use an iterative method, based on Cauchy-Schwarz inequality, to find the activation time given the estimated location and intensity. Finally we extend this algorithm to the multi-source field and present simulation results to validate our findings.