Effect of noise, order and range in fitting the photopeak region of local, Anger-camera energy spectra

Abstract

In order to estimate and correct Compton scattering in nuclear-medicine Anger-camera imaging, we have previously required the least-mean-square error between the locally measured energy spectrum and one dependent on a model. The model assumes a fixed-order polynomial for the spectrum of scatter and fits the data over a specified energy range. In this study, a Monte Carlo simulation program produces spectra at specified locations in a projection image of a 99mTc “hot” sphere in a “cold” cylinder. Poisson noise is subsequently added to each spectral channel, modelling a given count level within the acceptance window. Tests were done at two pixel locations, one at the center of the sphere and the other near the edge. Without noise, we find that the calculated-to-true ratio for unscattered counts is reasonably close to 1.0 (average 1.03, range 0.85 to 1.16) for all of the 16 order-range combinations that were tested. Tests on experimental data yield comparable results. For comparison, without any Compton-scatter correction the average ratio is 1.39. Optimizing the fitting parameters is difficult because, for example, the best set for location 1 is the worst for location 2. With noisy data, the relative standard deviation, and sometimes the bias for the estimate of direct (i.e. unscattered) counts, increases as the statistical noise increases. The average relative error for the estimate is 10% for the 3 cases measured with about 5000 unscattered counts but increases to 20% if that number decreases to 700.