平面张量场的傅立叶断层重建方法

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-10-04 DOI:10.1016/j.jmaa.2024.128928

David Omogbhe

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引用次数: 0

摘要

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。

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

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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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

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: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.