一类锥体上radon变换的解析反演公式

IF 0.6 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Eurasian Journal of Mathematical and Computer Applications Pub Date : 2022-09-27 DOI:10.32523/2306-6172-2022-10-3-73-83

Cebeiro Javier, Nguyen Mai K., Rollet Genevi`eve, Dumas Laurent

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引用次数: 0

摘要

自Radon和Cormack关于直线上经典Radon变换的工作以来，研究了几种涉及圆锥曲面上积分的推广。本文通过原点引入了一种新的具有空间任意顶点和轴的圆锥曲面族，并研究了相应的Radon变换。我们推导了它在二维和三维的解析反演。对二维情况进行了数值模拟。

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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AN ANALYTIC INVERSION FORMULA FOR A RADON TRANSFORM ON A CLASS OF CONES

Since the works of Radon and Cormack on the classical Radon transform on straight lines, several generalizations involving integrations on conical surfaces have been studied. In this article, we introduce a new family of conical surfaces with arbitrary vertices of the space and axes through the origin and study the corresponding Radon transform. We derive its analytical inversion in two and three dimensions. Numerical simulations are carried out for the two-dimensional case.

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来源期刊

Eurasian Journal of Mathematical and Computer Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： Eurasian Journal of Mathematical and Computer Applications (EJMCA) publishes carefully selected original research papers in all areas of Applied mathematics first of all from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time Eurasian Journal of Mathematical and Computer Applications (EJMCA) will also publish survey papers. Eurasian Mathematical Journal publishes 4 issues in a year. A working language of the journal is English. Main topics are: - Mathematical methods and modeling in mechanics, mining, biology, geophysics, electrodynamics, acoustics, industry. - Inverse problems of mathematical physics: theory and computational approaches. - Medical and industry tomography. - Computer applications: distributed information systems, decision-making systems, embedded systems, information security, graphics.