Exploring Statistical Independence for Energy Reconstruction in Calorimeter Systems Operating in Signal Pile-up Conditions

Abstract In high event rate detection systems, signal processing must simultaneously provide fast response and robustness against noise. This requirement is particularly critical in high-energy calorimeters operating in modern collider experiments such as those at the LHC. In such condition, the presence of pile-up introduces non-Gaussian components into the noise, degrading the performance of conventional reconstruction algorithms that assume Gaussian statistics. For the non-Gaussian case, an optimal estimation can be obtained using a Maximum Likelihood Estimator (MLE) based on the joint probability distribution of the multivariate noise. However, in practical systems the correct joint distribution is generally unknown and difficult to model. In this work, we propose an approach that circumvents this difficulty by first applying Independent Component Analysis (ICA) as a pre-processing step to pursuit a representation in which the noise mutual information is minimized. In this transformed basis, the joint probability can be factorized into a product of marginal probability density functions, enabling a tractable MLE formulation. The proposed ICA + MLE framework allows the implementation of likelihood-based estimators even in the presence of strongly non-Gaussian noise. Simulation results using calorimeter-like signals show that the pre-processing step effectively reduces the noise mutual information, leading to performance improvements up to approximately 10% and 50% in terms of estimation error and KL divergence, respectively, with respect to the typical Gaussian MLE approach.