# The empirical process of residuals from an inverse regression

## TL;DR

This paper studies an inverse regression model using Radon transformation for medical imaging, proposing a spectral cut-off estimator and analyzing the residuals' empirical process, which follows a functional central limit theorem.

## Contribution

It introduces a series estimator based on spectral cut-off for inverse regression and establishes the asymptotic behavior of residuals in this context.

## Key findings

- Residuals' empirical process satisfies a functional central limit theorem.
- Proposes a spectral cut-off series estimator for inverse Radon regression.
- Provides theoretical foundation for residual analysis in medical imaging models.

## Abstract

In this paper we investigate an indirect regression model characterized by the Radon transformation. This model is useful for recovery of medical images obtained by computed tomography scans. The indirect regression function is estimated using a series estimator motivated by a spectral cut-off technique. Further, we investigate the empirical process of residuals from this regression, and show that it satsifies a functional central limit theorem.