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Reconstructing gas distribution maps via an adaptive sparse regularization algorithm
Örebro University, School of Science and Technology. (Mathematics)ORCID iD: 0000-0003-4023-6352
Örebro University, School of Science and Technology.ORCID iD: 0000-0003-0332-2315
Örebro University, School of Science and Technology. (AASS)ORCID iD: 0000-0001-5061-5474
Örebro University, School of Science and Technology. (AASS)ORCID iD: 0000-0002-0804-8637
2016 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 24, no 7, 1186-1204 p.Article in journal (Refereed) Published
Abstract [en]

In this paper, we present an algorithm to be used by an inspectionrobot to produce a gas distribution map and localize gas sources ina large complex environment. The robot, equipped with a remotegas sensor, measures the total absorption of a tuned laser beam andreturns integral gas concentrations. A mathematical formulation ofsuch measurement facility is a sequence of Radon transforms,which isa typical ill-posed problem. To tackle the ill-posedness, we developa new regularization method based on the sparse representationproperty of gas sources and the adaptive finite-element method. Inpractice, only a discrete model can be applied, and the quality ofthe gas distributionmap depends on a detailed 3-D world model thatallows us to accurately localize the robot and estimate the paths of thelaser beam. In this work, using the positivity ofmeasurements and theprocess of concentration, we estimate the lower and upper boundsof measurements and the exact continuous model (mapping fromgas distribution to measurements), and then create a more accuratediscrete model of the continuous tomography problem. Based onadaptive sparse regularization, we introduce a new algorithm thatgives us not only a solution map but also a mesh map. The solutionmap more accurately locates gas sources, and the mesh map providesthe real gas distribution map. Moreover, the error estimation of theproposed model is discussed. Numerical tests for both the syntheticproblem and practical problem are given to show the efficiency andfeasibility of the proposed algorithm.

Place, publisher, year, edition, pages
Taylor & Francis, 2016. Vol. 24, no 7, 1186-1204 p.
Keyword [en]
Gas distribution map, source localization, Radon transform, ill-posed inverse problem, adaptive sparse regularization
National Category
Computational Mathematics Other Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-47923DOI: 10.1080/17415977.2015.1130039ISI: 000381017200004Scopus ID: 2-s2.0-84953226224OAI: oai:DiVA.org:oru-47923DiVA: diva2:900402
Note

Funding Agency:

Gasbot project 8140

Available from: 2016-02-04 Created: 2016-02-04 Last updated: 2017-10-17Bibliographically approved

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