A simple shearlet-based reconstruction for computer tomography

TL;DR

This paper introduces a shearlet-based inversion formula for the Radon transform that enables stable, fast, and edge-preserving image reconstruction from noisy data without increasing noise, simplifying the process and improving computational efficiency.

Contribution

The authors develop a new shearlet-based inversion method for the Radon transform that simplifies the reconstruction process and enhances stability and edge preservation.

Findings

Provides a new inversion formula using shearlets and Radon properties

Yields a fast, stable, and computable algorithm for image reconstruction

Introduces natural density-compensation weights for ShearLab

Abstract

We find a new and simple inversion formula of the Radon transform RT with the only use of the shearlet system and of well-known properties of RT. No intertwining relation of differential operators in Euclidean space and Radon domain is used. As a consequence, an additive noise is not incremented. Since the continuum theory of shearlets has a straight translation to the discrete theory, we find a fast, stable and computable algorithm that recovers a digital image from noisy samples of the Radon transform preserving edges. In the process, we find a more natural and easier-to-construct density-compensation weight functions for the ShearLab toolbox.