An investigation of the filtering of TEW scatter estimates used to compensate for scatter with ordered subset reconstructions

With the triple energy window (TEW) scatter correction method, scatter is estimated by interpolation between narrow energy windows placed on either side (or from a single window just below) the photopeak window. The use of narrow windows results in a noisy estimate which requires filtering to prevent significant amplification of noise in the corrected images. Using Monte Carlo simulated projections of a digital model of the anatomy of the torso, we investigated two-dimensional pre-reconstruction filtering of the scatter estimate by the Wiener low-pass filter, and Butterworth low-pass filters with various cutoff frequencies. The scatter estimate was either subtracted from the photopeak window projection or used directly in ordered-subset maximum-likelihood (OS-ML) reconstruction. Using the normalized mean square error (NMSE) between the estimated and true slices as the criterion, it was observed that: 1) low-pass filtering of the TEW scatter estimate dramatically decreases the NMSE compared to that of no filtering of this estimate; 2) the cutoff frequency of the Butterworth filter used to filter the scatter estimate is lower than that typically used for photopeak window images; 3) the cutoff frequency of the Butterworth filter has a broad range of values over which the MMSE is near its minimum value; 4) the cutoff frequency at which the Butterworth reaches its minimum value depends on the number of counts in the TEW window(s), and source distribution; 5) the Wiener low-pass filter adapts to produce a low, but not necessarily the minimum, NMSE; and 6) the inclusion of the scatter estimate directly into OS-ML reconstruction results in a lower NMSE than subtraction of the scatter estimate from the photopeak window prior to reconstruction