Inversion of the elliptical Radon transform arising in migration imaging using the regular Radon transform

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• 作者：Sunghwan Moon^a ; ^{shmoon@unist.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Joonghyeok Heo^b
• 关键词：Radon transform ; Tomography ; Elliptical ; Migration ; Seismic reflection
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 April 2016
• 年：2016
• 卷：436
• 期：1
• 页码：138-148
• 全文大小：797 K

文摘

In recent years, many types of elliptical Radon transforms that integrate functions over various sets of ellipses/ellipsoids have been considered, relating to studies in bistatic synthetic aperture radar, ultrasound reflection tomography, radio tomography, and migration imaging. In this article, we consider the transform that integrates a given function in Rⁿ${\mathbb{R}}^n$ over a set of ellipses (when n=2$n=2$) or ellipsoids of rotation (when 4d6d789c10b4f2e69" title="Click to view the MathML source">n≥3$n\ge 3$) with foci restricted to a hyperplane. We show a relation between this elliptical Radon transform and the regular Radon transform, and provide the inversion formula for the elliptical Radon transform using this relation. Numerical simulations are performed to demonstrate the suggested algorithms in two dimensions, and these simulations are also provided in this article.