We consider the X-ray transform in a projective space over a finite field. It is well known (after Bolker) that this transform is injective. We formulate an analog of Gelfand’s admissibility problem for the Radon transform, which asks for a classification of all minimal sets of lines for which the restricted Radon transform is injective. The solution involves doubly ruled quadric surfaces.

中文翻译：

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有限域上射影 X 射线变换的可容许复形

我们考虑在有限域上的投影空间中的 X 射线变换。众所周知（在 Bolker 之后）这种变换是单射的。我们为 Radon 变换制定了 Gelfand 可接受性问题的模拟，它要求对受限 Radon 变换是单射的所有最小线集进行分类。该解决方案涉及双规则二次曲面。