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

• Published in: IEEE transactions on nuclear science 1997-06, Vol.44 (3), p.1140-1145
• Main Authors: King, M.A., deVries, D.J., Pan, T.-S., Pretorius, P.H., Case, J.A.
• Format: Article
• Language: English
• Subjects: Cutoff frequency; Digital filters; Filtering; Frequency estimation; Image reconstruction; Interpolation; Low pass filters; Monte Carlo methods; Scattering; Wiener filter
• ISSN: 0018-9499; 1558-1578
• DOI: 10.1109/23.596978

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.