{"title":"A Fourier approach to tomographic reconstruction of tensor fields in the plane","authors":"David Omogbhe","doi":"10.1016/j.jmaa.2024.128928","DOIUrl":null,"url":null,"abstract":"<div><div>We consider the problem of inversion of the X-ray transform for sums of 1-forms and symmetric 2-tensor fields. Such a problem arises after linearization of a related travel time tomography problem, described via Mañé's action potential of the energy level 1/2 for a magnetic flow. In a strictly convex bounded domain in the Euclidean plane, we show when and how to recover simultaneously both unknown 1-tensor and symmetric 2-tensor field uniquely from measurement of radiating flux at the boundary. The approach to reconstruction is based on the Cauchy problem for a Beltrami-like equation associated with <em>A</em>-analytic maps.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128928"},"PeriodicalIF":1.2000,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24008503","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the problem of inversion of the X-ray transform for sums of 1-forms and symmetric 2-tensor fields. Such a problem arises after linearization of a related travel time tomography problem, described via Mañé's action potential of the energy level 1/2 for a magnetic flow. In a strictly convex bounded domain in the Euclidean plane, we show when and how to recover simultaneously both unknown 1-tensor and symmetric 2-tensor field uniquely from measurement of radiating flux at the boundary. The approach to reconstruction is based on the Cauchy problem for a Beltrami-like equation associated with A-analytic maps.
期刊介绍：
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
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• Real and harmonic analysis
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