Reconstructing non-point sources of diffusion fields using sensor measurements

We present a framework for estimating non-localized sources of diffusion fields using spatiotemporal measurements of the field. Specifically in this contribution, we consider two non-localized source types: straight line and polygonal sources and assume that the induced field is monitored using a sensor network. Given the sensor measurements, we demonstrate, for each non-point source parameterization, how to reduce the source estimation problem to a system governed by a power series expansion that can then be efficiently solved using Prony's method, in order to reconstruct the source. We then evaluate the proposed algorithms by performing some numerical simulations using both noiseless and noisy spatiotemporal sensor measurements of the field.