In this paper, we deal with the problem of reconstruction from Radon random samples in local shift-invariant signal space. Different from sampling after Radon transform, we consider sampling before Radon transform, where the sample set is randomly selected from a square domain with a general probability distribution. First, we prove that the sampling set is stable with high probability under a sufficiently large sample size. Second, we address the problem of signal reconstruction in two-dimensional computed tomography. We demonstrate that the sample values used for this reconstruction process can be determined completely from its Radon transform data. Consequently, we develop an explicit formula to reconstruct the signal using Radon random samples.

翻译：本文研究局部平移不变信号空间中基于Radon随机采样的重建问题。与Radon变换后采样不同，我们考虑在Radon变换前进行采样，其中采样点集依据一般概率分布从方形区域中随机选取。首先，我们证明在足够大的采样规模下，采样集以高概率保持稳定性。其次，我们针对二维计算机断层成像中的信号重建问题展开分析。我们证明用于重建过程的采样值可完全由其Radon变换数据确定。基于此，我们推导出利用Radon随机采样重建信号的显式公式。