Kernel based unfolding of data obtained from detectors with finite resolution and limited acceptance

TL;DR

This paper introduces a kernel-based method for correcting experimental data distortions caused by finite resolution and limited acceptance, using regularization and cross-validation to improve unfolding accuracy.

Contribution

The paper presents a novel kernel-based unfolding method that incorporates regularization and cross-validation to effectively correct for detector effects in experimental data.

Findings

Successfully estimates true distributions from distorted data

Demonstrates robustness against systematic and statistical errors

Provides an effective regularization parameter selection method

Abstract

A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without some a priori information about solution such as, for example, smoothness or positivity. In the approach presented here the true distribution is estimated by a weighted sum of kernels, with the width of the kernels acting as a regularization parameter responsible for the smoothness of the result. Cross-validation is used to determine an optimal value for this parameter. A numerical example with a simulation study of systematical and statistical errors is presented to illustrate the procedure.