Heuristic algorithm for 1D and 2D unfolding

TL;DR

This paper presents a simple iterative heuristic algorithm for unfolding 1D and 2D distributions, which converges to the true distribution after a few hundred iterations using a combination of chi-squared testing and regularization.

Contribution

It introduces a new straightforward heuristic iterative method for unfolding that combines chi-squared testing and regularization, demonstrating effective convergence.

Findings

Converges to the true distribution after 500-1000 iterations

Uses a combination of chi-squared test and regularization

Effective for 1D and 2D unfolding problems

Abstract

A very simple heuristic approach to the unfolding problem will be described. An iterative algorithm starts with an empty histogram and every iteration aims to add one entry to this histogram. The entry to be added is selected according to a criteria which includes a $\chi^2$ test and a regularization. After a relatively small number of iterations (500 - 1000) the growing reconstructed distribution converges to the true distribution.