Sparse Representation for Signal Reconstruction in Calorimeters Operating in High Luminosity

Abstract

A calorimeter signal reconstruction method based on sparse representation (SR) of redundant data is proposed for energy reconstruction in particle colliders operating under high-luminosity conditions. Signal overlapping is initially modeled as an underdetermined linear system, leading to a convex set of feasible solutions. The solution with the smallest number of superimposed signals (i.e., the sparse representation) that best represents the recorded data is obtained using an interior-point (IP) optimization procedure. From a signal processing perspective, this procedure performs source separation, enabling the estimation of the amplitude of each convoluted signal. Simulation results include a comparison between the proposed method and a standard signal reconstruction approach. For this purpose, a toy Monte Carlo simulation was developed, focusing exclusively on calorimeter front-end signal generation, where different levels of pile-up and signal-to-noise ratio were considered to evaluate the method. The results indicate that the proposed approach can be competitive in high-luminosity environments.