Sensing physical fields: Inverse problems for the diffusion equation and beyond (2016)
Abstract / truncated to 115 words
Due to significant advances made over the last few decades in the areas of (wireless) networking, communications and microprocessor fabrication, the use of sensor networks to observe physical phenomena is rapidly becoming commonplace. Over this period, many aspects of sensor networks have been explored, yet a thorough understanding of how to analyse and process the vast amounts of sensor data collected remains an open area of research. This work, therefore, aims to provide theoretical, as well as practical, advances this area. In particular, we consider the problem of inferring certain underlying properties of the monitored phenomena, from our sensor measurements. Within mathematics, this is commonly formulated as an inverse problem; whereas in signal processing, it ... toggle 10 keywordsinverse problems – sampling theory – finite rate of innovation – prony's method – matrix pencil method – pdes – diffusion fields – sensor networks – wave phenomena – spatiotemporal phenomena
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