Sampling and Reconstruction of Time-Varying Atmospheric Emissions

We study the spatio-temporal sampling of physical fields representing the dispersion of a substance in the atmosphere. We consider the following setup: N sensors are deployed at ground level and measure the concentration of a particular substance, while M smokestacks are located in the same area and emit a time-varying amount of the substance. To recover the emission rates of the smokestacks with a limited number of spatio-temporal samples, we consider time varying emissions rates lying in two specific low-dimensional subspaces. We propose efficient algorithms and sufficient conditions to recover the emission rates of the smokestacks from the local measurements collected by the sensor network.