Learned Soft-Thresholding for Streaming Sparse Signal Recovery in Nuclear Instrumentation

Abstract

Experiments in High Energy Physics, such as those conducted at the Large Hadron Collider (LHC), use calorimeters for particle detection and energy measurement. Under high-luminosity conditions, these systems face the pile-up effect, where overlapping signals distort energy estimation and reduce trigger efficiency. Sparse representation (SR)-based methods have been widely explored for signal deconvolution and pile-up mitigation in calorimeters. This paper proposes a novel deconvolution method that combines a finite impulse response (FIR) filter with sparse representation using a dynamic threshold estimated by a neural network. Unlike conventional SR approaches that rely on iterative algorithms—often unsuitable for real-time applications—the proposed method operates in a non-iterative, feed-forward manner, making it compatible with online data acquisition (DAQ) systems. Performance evaluations against traditional least squares (LS) techniques and SR methods with fixed thresholds demonstrate improved accuracy and resolution. Simulated datasets validate the effectiveness of the proposed approach, showing enhanced signal reconstruction while maintaining feasibility for hardware implementation.