Radiation detection with non-parametric decompounding of pulse pile-up

A method of estimating count rate of individual quanta of radiation received in a radiation detector, the method comprising the steps of:

• (1) obtaining a time series of digital observations from the radiation detector comprising pulses corresponding to the detection of the individual quanta;
• (2) computing spectrum sensitive statistics from the detector signal, based on a sum of the digital observations over a plurality of time intervals, the spectrum sensitive statistics defining a mapping from a density of amplitudes of the pulses to the spectrum sensitive statistics using an approximate compound Poisson process, the plurality of time intervals including:
• a first set of nonoverlapping time intervals of constant length L selected without regard to entirety of clusters of the pulses;
• and a second set of nonoverlapping time intervals of constant length L1 less than L also selected without regard to entirety of clusters of the pulses;
• wherein L is at least as long as a duration of the pulses;
• (3) determining an estimate of a characteristic function of the approximate compound Poisson process using:
• ∅
• ^
• y
• =
• G
• ⁢
• ∅
• ^
• ⁢
• x
• ∅
• z
• ⁢
• ∅
• ^
• x
• where G is a windowing function, {circumflex over (Ø)}x is an estimate of a characteristic function of a sum of the digital observations over each nonoverlapping time interval in the first set, {circumflex over (Ø)}z is a characteristic function of a modelled noise process and {circumflex over (Ø)}x1 is an estimate of a characteristic function of a sum of the digital observations over each nonoverlapping time interval in the second set;
• (4) estimating the count rate from the estimate of the characteristic function.