In recent years, many types of elliptical Radon transforms that integratefunctions over various sets of ellipses/ellipsoids have been considered,relating to studies in bistatic synthetic aperture radar, ultrasound reflectiontomography, radio tomography, and migration imaging. In this article, weconsider the transform that integrates a given function in $\mathbf R^n$ over aset of ellipses (when $n=2$) or ellipsoids of rotation (when $n\geq 3$) withfoci restricted to a hyperplane. We show a relation between this ellipticalRadon transform and the regular Radon transform, and provide the inversionformula for the elliptical Radon transform using this relation. Numericalsimulations are performed to demonstrate the suggested algorithms in twodimensions, and these simulations are also provided in this article.
展开▼
机译：近年来，已经考虑了在各种椭圆/椭球集上集成功能的多种椭圆Radon变换，涉及双基地合成孔径雷达，超声反射层析成像，放射线层析成像和迁移成像的研究。在本文中，我们将考虑将$ \ mathbf R ^ n $中的给定函数集成到一组椭圆（当$ n = 2 $时）或旋转椭球体（当$ n \ geq 3 $时）时，焦点仅限于超平面的变换。我们展示了此椭圆Radon变换与常规Radon变换之间的关系，并使用此关系为椭圆Radon变换提供了反演公式。进行了数值模拟，以二维方式论证了建议的算法，本文还提供了这些模拟。
展开▼
