Altmetric

A Sampling Framework for Solving Physics-driven Inverse Source Problems

File Description SizeFormat 
08014505.pdfPublished version1.54 MBAdobe PDFView/Open
Title: A Sampling Framework for Solving Physics-driven Inverse Source Problems
Authors: Dragotti, P
Murray-Bruce, J
Item Type: Journal Article
Abstract: 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 its 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.
Issue Date: 22-Aug-2017
Date of Acceptance: 27-Jul-2017
URI: http://hdl.handle.net/10044/1/50271
DOI: https://dx.doi.org/10.1109/TSP.2017.2742983
ISSN: 1053-587X
Publisher: IEEE
Start Page: 6365
End Page: 6380
Journal / Book Title: IEEE Transactions on Signal Processing
Volume: 65
Issue: 24
Copyright Statement: This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/.
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: 277800
Keywords: Science & Technology
Technology
Engineering, Electrical & Electronic
Engineering
Partial differential equations (PDEs)
inverse problems
universal sampling
sensor networks
diffusion equation
wave equation
Strang-Fix conditions
Prony's method
WIRELESS SENSOR NETWORKS
DISTRIBUTED ESTIMATION
SOURCE LOCALIZATION
DIFFUSION FIELDS
RECONSTRUCTION
APPROXIMATION
INTERPOLATORS
ADVECTION
ALGORITHM
SIGNAL
MD Multidisciplinary
Networking & Telecommunications
Publication Status: Published
Appears in Collections:Faculty of Engineering
Electrical and Electronic Engineering



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Creative Commons