A Deconvolutional Technique Based on Pseudoinverse for Online Energy Reconstruction

Abstract

Modern High-Energy Physics (HEP) experiments face significant challenges in data processing due to high-luminosity environments where the overlapping of signals, known as pile-up, degrades detector resolution. Traditionally, the Optimal Filter (OF) algorithm is employed for amplitude estimation. However, its performance is limited in high-occupancy scenarios because the filter weights must be specifically recalculated for different pile-up levels to maintain accuracy. This paper proposes an alternative online energy reconstruction technique based on deconvolutional filtering using the Moore-Penrose pseudoinverse. By treating the signal reconstruction as an inverse problem, the proposed method relies solely on the knowledge of the system’s impulse response to effectively separate overlapping pulses across varying pile-up conditions. Unlike the OF approach, which typically requires an additional peak detection stage combined with a phase filter, the deconvolution output directly provides the energy values at the precise time of the collision. The approach was validated using the Lorenzetti Showers framework, simulating Liquid Argon (LArg) calorimeter responses under severe multi-hit conditions. Results demonstrate that the deconvolution method significantly reduces the Root Mean Square Error (RMSE) from approximately 200 MeV in the conventional OF to values between 50 and 100 MeV, representing a reduction of up to 62.5% in reconstruction error. Also, it maintains high detection efficiency compared to the conventional OF. The proposed architecture is suitable for low-latency implementation in Field Programmable Gate Arrays (FPGAs), offering a streamlined and robust solution for real-time trigger systems.