Solving inverse source problems for linear PDEs using sparse sensor measurements

Murray-Bruce, John; Dragotti, Pier Luigi

doi:10.1109/acssc.2016.7869094

Cited by 1 publication

(2 citation statements)

References 27 publications

(29 reference statements)

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“…where {w n,l (k, r)} n,l ∈ C denote the specific sequence of weights we wish to compute 2 . In particular if we require this weighted sum of the sensor data to yield the exact multidimensional measurements, i.e.…”

Section: Multidimensional Generalised Measurements From Sensor Samplesmentioning

confidence: 99%

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A Sampling Framework for Solving Physics-Driven Inverse Source Problems

Murray-Bruce

Dragotti

2017

IEEE Trans. Signal Process.

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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 differential equations. Specifically, we demonstrate that the unknown field sources can be recovered from a sequence of, so called, generalised measurements by using multidimensional frequency estimation techniques. Next we show that-for physics-driven fields-this sequence of generalised measurements can be estimated by computing a linear weighted-sum of the sensor measurements; whereby the exact weights (of the sums) correspond to those that reproduce multidimensional exponentials, when used to linearly combine translates of a particular prototype function related to the Green's function of our underlying field. Explicit formulae are then derived for the sequence of weights, that map sensor samples to the exact sequence of generalised measurements when the Green's function satisfies the generalised Strang-Fix condition. Otherwise, the same mapping yields a close approximation of the generalised measurements. Based on this new framework we develop practical, noise robust, sensor network strategies for solving the inverse source problem, and then present numerical simulation results to verify their performance.

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Section: Multidimensional Generalised Measurements From Sensor Samplesmentioning

confidence: 99%

“…iii) M vs = 1: Estimate the source parameters from the measurements {ϕ n (t l )} L l=0 using Algorithm 1. (e) Synthesise the field due to this source using equation(2) and adjust the sensor measurements by removing the contribution of this source. Increment L and return to step (a).…”

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confidence: 99%