Model-Based Pileup Events Correction via Kalman-Filter Tunnels

A Kalman-filter-based method is proposed to address challenges in nuclear signal processing, including pileup events and noise cancelation. The state-transition equation is established on the basis of suitable pulse shape models. By regarding the output signal of particle detectors as a measurable variable, the measurement equation is also introduced to correct dynamic processes of the state transition. A linear Kalman filter with $n$ tunnels is constructed to separate pileup events and maintain the original waveforms of pulses. In addition, two terms are defined and addressed for separation operations, namely, Availability , which is used to prepare for upcoming events, and Clearance Mechanism , which is given to remove thumbnail information from the previous events and make occupied tunnels available to subsequent nuclear events. Simulation and field experiments demonstrate that the proposed method can handle critical situations of pulse pileup and minimize count loss and dead time in the X-ray energy spectrum while maintaining the original pulse shapes.