A Fourier approach to tomographic reconstruction of tensor fields in the plane

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-04 DOI:10.1016/j.jmaa.2024.128928

David Omogbhe

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.

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平面张量场的傅立叶断层重建方法

我们考虑的是 1 形式和对称 2 张量场的 X 射线变换的反演问题。这个问题是在相关的旅行时间断层扫描问题线性化之后产生的，该问题通过磁流能级 1/2 的马内作用势来描述。在欧几里得平面的严格凸有界域中，我们展示了何时以及如何通过测量边界的辐射通量同时唯一地恢复未知的 1 张量场和对称 2 张量场。重建方法基于与 A 分析映射相关的贝尔特拉米方程的考奇问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.