Limitations of Decision Based Pile-Up Correction Algorithms

Nuclear spectroscopy attempts to infer elemental composition by estimating the energy distribution of X-ray/gamma-ray photons. Performance at high count rates is limited by pulse pile-up. Numerous approaches attempt to estimate the properties of individual photons in the time domain. This work provides an asymptotic description of pile-up for the Neyman Pearson detector, showing that any algorithm that makes decisions regarding individual pulses will eventually suffer and be limited by pile-up.