Radon random sampling and reconstruction in local shift-invariant signal space

TL;DR

This paper introduces a method for stable signal reconstruction from Radon random samples in local shift-invariant spaces, with explicit formulas for 2D computed tomography, advancing sampling theory and reconstruction techniques.

Contribution

It provides a theoretical foundation for sampling before Radon transform and develops explicit reconstruction formulas from Radon random samples.

Findings

Sampling set is stable with high probability for large sample sizes.

Sample values can be fully determined from Radon transform data.

Explicit reconstruction formula derived for 2D signals.

Abstract

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.