具有平移几何的康普顿散射层析成像模态的有效实现解析重建公式

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2021-12-28 DOI:10.3934/ipi.2021075

Cécilia Tarpau, Javier Cebeiro, Geneviève Rollet, Maï K. Nguyen, Laurent Dumas

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引用次数: 0

摘要

在本文中，我们讨论了Webber和Miller (inverse Problems(36)， 2025007, 2020)提出的平移几何中康普顿散射层析成像模态中圆弧上Radon变换的精确逆公式的替代公式。最初的研究提出了第一种重建方法，使用Volterra积分方程理论。这类逆公式的数值实现可能会遇到一些困难，主要是由于稳定性问题。在这里，我们提供了一个合适的精确反演公式，可以直接在傅里叶域中实现。仿真结果验证了所提重构算法的有效性。

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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Analytical reconstruction formula with efficient implementation for a modality of Compton scattering tomography with translational geometry

In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory of Volterra integral equations. The numerical realization of such a type of inverse formula may exhibit some difficulties, mainly due to stability issues. Here, we provide a suitable formulation for exact inversion that can be straightforwardly implemented in the Fourier domain. Simulations are carried out to illustrate the efficiency of the proposed reconstruction algorithm.

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.