Radon transform intertwines shearlets and wavelets

TL;DR

This paper demonstrates how the affine Radon transform connects shearlet and wavelet representations, providing a new formula for shearlet coefficients that could improve Radon transform inversion techniques.

Contribution

It establishes a mathematical intertwining between shearlet and wavelet representations via the Radon transform, offering novel insights for signal analysis and Radon inversion.

Findings

Radon transform intertwines shearlet and wavelet representations

New formula for shearlet coefficients involving Radon transform

Potential for improved Radon transform inversion methods

Abstract

We prove that the unitary affine Radon transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation with a wavelet-like representation. This yields a formula for shearlet coefficients that involves only integral transforms applied to the affine Radon transform of the signal, thereby opening new perspectives in the inversion of the Radon transform.