Abstract This article deals with characterizations of a function in terms of its circular mean Radon transform. We present a new approach (the consistency method) showing how to describe the class of real-valued, planar functions f which have the given circular mean Radon transform M f over circles centered on the unit circle. Also, expressions are derived for the geometric moments of an unknown function in terms of its circular mean Radon transform.

中文翻译：

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从球面平均 Radon 变换中恢复矩

摘要 本文根据函数的圆形平均 Radon 变换处理函数的表征。我们提出了一种新方法（一致性方法），展示了如何描述在以单位圆为中心的圆上具有给定圆形平均 Radon 变换 M f 的实值平面函数 f 类。此外，根据圆形平均 Radon 变换导出未知函数的几何矩的表达式。