In this paper, we consider the conical Radon transform on all one-sided circular cones in \(\mathbf{R}^3\) with horizontal central axis whose vertices are on a vertical line. We derive an explicit inversion formula for such transform. The inversion makes use of the vertical slice transform on a sphere and V-line transform on a plane.

中文翻译：

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水平圆锥Radon变换的反演公式

在本文中，我们考虑\（\ mathbf {R} ^ 3 \）中所有单侧圆锥的圆锥Radon变换，其水平中心轴的顶点在垂直线上。我们为这种变换导出了一个明确的反演公式。反演利用球体上的垂直切片变换和平面上的V线变换。