English

A simple shearlet-based reconstruction for computer tomography

Functional Analysis 2018-05-09 v2

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.

Keywords

Cite

@article{arxiv.1707.08185,
  title  = {A simple shearlet-based reconstruction for computer tomography},
  author = {Santiago Córdova and Daniel Vera},
  journal= {arXiv preprint arXiv:1707.08185},
  year   = {2018}
}

Comments

First author added. Includes numerical simulations and 5 figures

R2 v1 2026-06-22T20:57:22.864Z