Recovery of spectral information from an imperfect detector using the expectation maximization algorithm

A gamma-ray detector can be modeled as a linear system which maps a photon flux with a given energy distribution to a pulse-height spectrum. In a perfect detector, the response to a monoenergetic beam would be a delta function. In any real detector, carrier trapping, escape of K x-rays, Compton scattering, and instrument noise will produce a broadened response function. We develop a model of the response function of a ZnCdTe detector and use it to recover the incident energy spectrum from a measured pulse height spectrum using the Expectation-Maximization (EM) algorithm. This technique can be applied to any type of nuclear detector, using any combination of modeled and measured response functions. An analysis of the noise cost incurred in the reconstruction algorithm shows that the technique can be used to advantage even with relatively few counts in the measured spectrum.