Increasing the precision in the estimates of noise power spectrum in digital x-ray imaging systems

Abstract

The noise power spectrum (NPS) of a digital x-ray imaging device is usually estimated from the average of periodograms of ROIs in images obtained with uniform radiation fields. The purpose of this work was developing a new estimator for calculating the NPS and comparing its uncertainties with those of the smoothed periodogram.The new estimator is built by removing those addends in the summation of the periodogram that do not contain information on stochastic noise. This was carried out by applying a short-length lag window to the autocorrelation function of noise. The length of the window was obtained from the support of this function. It has to be large enough not to eliminate information on noise autocorrelation and it has be as short as possible to minimize uncertainty. In this work, this length was set to three times the support of the autocorrelation function of noise.The new truncated sum (TS) estimator is shown to be unbiased and to have a much higher precision than that of the periodogram. The combined process of applying lag windows to the autocorrelation function of noise and removing addends with null expected values from the periodogram summation has a double effect on NPS curves. On the one hand, the curves are smoothed and, on the other hand, the uncertainties in the calculated values are highly reduced.