Solving physics-driven inverse problems via structured least squares

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Title: Solving physics-driven inverse problems via structured least squares
Authors: Dragotti, P
Murray-Bruce, M
Item Type: Conference Paper
Abstract: Numerous physical phenomena are well modeled by partial differential equations (PDEs); they describe a wide range of phenomena across many application domains, from model- ing 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 some sparse sensor measurements of it. This will be the main task of this work. Specifically, we will show that finding the sources of such PDE-driven fields can be turned into solving a class of well-known multi-dimensional structured least squares prob- lems. This link is achieved by leveraging from recent results in modern sampling theory – in particular, the approximate Strang-Fix theory. Subsequently, numerical simulation re- sults are provided in order to demonstrate the validity and robustness of the proposed framework.
Issue Date: 1-Dec-2016
Date of Acceptance: 10-May-2016
ISSN: 2076-1465
Publisher: IEEE
Start Page: 331
End Page: 335
Journal / Book Title: Signal Processing Conference (EUSIPCO), 2016 24th European
Copyright Statement: © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Sponsor/Funder: Commission of the European Communities
Funder's Grant Number: 277800
Conference Name: EUSIPCO 2016
Publication Status: Published
Start Date: 2016-08-29
Finish Date: 2016-09-02
Conference Place: Budapest, Hungary
Appears in Collections:Electrical and Electronic Engineering

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