Spatiotemporal sampling trade-off for inverse diffusion source problems
We consider the spatiotemporal sampling of diffusion fields induced by M point sources, and study the associated inverse problem of recovering the initial parameters of the unknown sources. In particular, we focus on characterising qualitatively the error of the obtained source estimates. To achieve this, we obtain an expression with which we can trade the sensor density for performance accuracy. In other words, by evaluating the optimal sampling instant for a given sensor density—and using the corresponding field samples at that instant—we can expect to obtain an improvement in the estimation performance when compared to an arbitrary sampling instant. Finally, several numerical simulations are presented, to support the theoretical results obtained.