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Partial differential equations are central to describing many physical phenomena. In many applications, these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain results in sampling and approximation theory, we present a new framework for solving a class of inverse source problems for physical fields governed by linear partial...
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....
Many physical phenomena across several applications can be described by partial differential equations (PDEs). In these applications, sensors collect sparse samples of the resulting phenomena with the aim of detecting its cause/source, using some intelligent data analysis tools on the samples. These problems are commonly referred to as inverse source problems. This work presents a novel framework...
Numerous physical phenomena are well modeled by partial differential equations (PDEs); they describe a wide range of phenomena across many application domains, from modeling EEG signals in electroencephalography to, modeling the release and propagation of toxic substances in environmental monitoring. In these applications it is often of interest to find the sources of the resulting phenomena, given...
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