Source function from two-particle correlation function through entropy-regularized Richardson-Lucy deblurring

TL;DR

This paper introduces a novel maximum-entropy regularized Richardson-Lucy deblurring method for extracting source functions from particle correlation data, effectively handling noise and normalization issues in both simulated and experimental cases.

Contribution

The paper develops and demonstrates a new MEM-RL algorithm that combines entropy regularization with RL deblurring to improve source function extraction from correlation functions.

Findings

Effective noise suppression in source function extraction

Ensures proper normalization of source functions

Validated on both simulated and experimental data

Abstract

Source functions are obtained from $p$-$p$ and $d$--$\alpha$ correlation functions by applying the Richardson-Lucy (RL) deblurring to the Koonin-Pratt (KP) equation. To prevent fitting of noise in the correlation function, total-variation (TV) regularization is employed that has been effective in ordinary image restoration. TV alone cannot ensure normalization of the source functions. To ensure the latter, we propose a maximum-entropy regularized RL algorithm (MEM-RL). We outline the MEM-RL formalism and optimization strategy for the KP equation, demonstrating its effectiveness on both simulated and experimental data, including the $p$-$p$ and $d$-$\alpha$ correlation functions.