由椭圆Radon变换求函数
On the Determination of a Function from an Elliptical Radon Transform
摘要：
近年来，Radon型变换，集成功能的各种集合的椭圆/椭球体已被认为是在SAR，超声反射层析成像，和无线电层析成像。在本文中，我们考虑的变换，积分一个给定的功能在$\RR^n$上的一组固体旋转椭球与一个固定的偏心率和焦点限制在一个超平面。对于关于超平面为偶数的函数类，得到了相应的反演公式。还提供了稳定性估计，范围描述和局部唯一性结果。
英文摘要：
In recent years, Radon type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in SAR, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that integrates a given function in $\RR^n$ over a set of solid ellipsoids of rotation with a fixed eccentricity and foci restricted to a hyperplane. Inversion formulas are obtained for appropriate classes of functions that are even with respect to the hyperplane. Stability estimates, range description, and local uniqueness results are also provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
