Tomographic Approach for Parametric Estimation of Local Diffusive Sources and Application to Heat Diffusion

We consider localized instantaneous sources that reside in a 2D diffusive environment. Our goal is to reconstruct the induced field from the measurements obtained by distributed sensors. Although the field is non-bandlimited, we capitalize on the fact that it is completely determined by a finite number of parameters to develop a method that allows perfect reconstruction. We demonstrate how these results can be applied in practice in the particular case of heat diffusion. Simulation results confirm the effectiveness of the method.