Sampling and reconstruction of time-varying atmospheric emissions

Abstract

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 lowdimensional 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.

Estimating Localized Sources of Diffusion Fields Using Spatiotemporal Sensor Measurements

“…Specifically: (9) for and . Then it follows that, hence substituting the expressions and into the above immediately gives the Vandermonde system: (10) Now (10) allows us to uniquely and simultaneously retrieve and as follows: For joint location and intensity recovery given instantaneous sources, notice that the sequence obtained by setting (or equivalently ) in (10) for is governed by the following Vandermonde system: (11) where (12) and…”

“…In the rest of this section, we establish a novel scheme for directly recovering the remaining source parameters: and from the generalized energy . Remark 2: It is easy to show, from (8), that given any arbitrary temporal parameterization of sources, it is possible to recover their locations by evaluating the integral expression (12), for and applying Prony's method on the resulting sequence , as long as all sources are localized in space. Specifically, one can show that will always take the form , where is the generalized energy given by for the generic source with parameterization .…”

Solving inverse source problems for linear PDEs using sparse sensor measurements

“…In majority of these applications, a collection of sensor nodes are deployed over a region of interest to collect sparse spatiotemporal measurements of the phenomena (signal), such as: neuronal currents in brain source imaging, thermal fields in server clusters/multi-core processors and the concentration of toxic substances/releases into the environment. Hence, given these sensor measurements of the phenomena, one might be interested in locating cortical avalanches for epilepsy management/diagnosis [1], localizing hot spots in servers/processors for load balancing [2] or plume sources/leakages [3], [4] respectively. This class of estimation problems are more commonly referred to as inverse source problems (ISPs).…”

Sampling and reconstructing diffusion fields in presence of aliasing

“…Lu and Vetterli introduced two different approaches to the reconstruction of a sparse source distributions driving the diffusion field based on spatial super-resolution [9], and on an adaptive spatio-temporal sampling scheme [10]. An approach using compressed sensing on a discrete grid was proposed by Ranieri et al [11] and it was generalized to the real line by Dokmanić et al [12].…”