Inversion of noisy Radon transform by SVD based needlet

TL;DR

This paper introduces a linear inversion method for noisy Radon transform data using needlet decomposition based on the SVD basis, providing theoretical risk bounds and practical examples.

Contribution

It develops a novel SVD-based needlet approach for Radon transform inversion, with proven risk bounds and practical implementation.

Findings

Risk bounds established in $L^p$ norms for Besov smooth functions

Method successfully applied in practical examples

Provides a new linear inversion technique for noisy Radon data

Abstract

A linear method for inverting noisy observations of the Radon transform is developed based on decomposition systems (needlets) with rapidly decaying elements induced by the Radon transform SVD basis. Upper bounds of the risk of the estimator are established in $L^p$ ($1\le p\le \infty$) norms for functions with Besov space smoothness. A practical implementation of the method is given and several examples are discussed.