Exact sinogram: an analytical approach to the Radon transform of phantoms

TL;DR

This paper introduces analytical formulas for computing exact sinograms of specific phantoms, enabling precise validation of MRI numerical methods by comparing analytical and approximate Radon transforms.

Contribution

It provides the first explicit analytical expressions for the Radon transform of three classes of phantoms, enhancing accuracy in image reconstruction validation.

Findings

Analytical sinograms match closely with discrete Radon transform results.

Exact formulas improve validation accuracy for MRI phantom reconstructions.

Comparison shows advantages of analytical over numerical methods.

Abstract

Phantoms can serve as a gold standard for the validation of MRI numerical methods. In some special cases, it is possible to compute analytically the Radon transform, or sinogram, of a phantom. In this work, we present analytical formulae to compute the exact sinograms of three classes of phantoms. We compare the use of the discrete Radon transform, that yields an approximate sinogram, and the correspondent analytical sinogram for image reconstruction.