2025/11/04 by Deng, Zhanpeng, Li, Jiao, Xian, Jun
Computer Science · Mathematics · Medicine · #Digital Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2511.02261
openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28
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.