Multiple Energy Window Methods

The triple energy window (TEW) method is a straightforward extension of DEW which introduces a modification factor that accounts for source size and distribution dependencies in Rsc [45].Under the assumption that Rsc >> Runsc, the TEW method can be written pUW _ pUW _ JUT

Robj

y calib y

Robj and Rcalib are the ratios of counts in the two lower energy windows for the object being imaged and a calibration phantom respectively. The parameter b is a relaxation factor that controls the amount of feedback of the modification term into the correction and when b = 0, the TEW technique becomes the DEW technique. The energy window used in the Clw/Rsc term may be either of the two lower energy windows (Fig. 5.15c). In the implementation of Shao et al., the lower energy windows spanned the energies 385-450 keV and 350-450 keV, the calibration phantom was a 20 cm diameter uniform cylinder and the relaxation factor was 0.5 [45]. As in the DEW technique, the ratios Robj and Rcalib and the modification factor M are calculated for each sino-gram element. The TEW method has many of the same advantages and drawbacks of the dual energy methods. However, it improves on the DEW method in particular by reducing the sensitivty of the scatter correction to variations in source distribution and size.

In the methods discussed so far, a relatively narrow energy window is set over the photopeak and events recorded below the lower energy threshold are assumed to be unwanted events, mainly due to scatter in the object being imaged. However, when small discrete detectors are used in high resolution tomographs, such as those designed for animal imaging studies, a large proportion of events recorded in the low energy range are due to scattering in the detectors and these are potentially useful events.

Bentourkia et al demonstrated that with careful characterisation and correction of scatter in multiple energy windows, it is possible to extend the useful energy range for acceptance of coincidences without degrading the image [46]. Specifically, they showed by Monte Carlo simulation and measurements on a PET simulator that up to 80% of events recorded above a threshold of 129 keV are either trues or detector scatters and, therefore, potentially useful for image formation. The approach developed was to correct for object scatter using position-dependent convolution subtraction while detector scatter is handled by nonstationary restoration. First, they carefully characterised the slope and amplitude of scatter components as a function of energy and position by measuring coincidence data in 16 x 16 energy window pairs. They summed the coincidence data into energy windows which had a common upper energy threshold of 645 keV and a variable lower energy threshold spanning the range 129 keV to 516 keV (Fig. 5.15d). Count profiles derived from these energy windows were fitted with multi-exponential functions. During imaging, coincidence data are recorded in the same energy windows and the scatter subtraction-restoration is effected using:

where Pobs are the measured projection data, F0 is the nonstationary object scatter kernel and Rd is the non-stationary restoration kernel that corrects for detector scatter. Rd is defined as:

where fg and fd are the fractions of geometric and detector scatter components and 3 and 3-1 are the forward and inverse Fourier transforms respectively.

The multiple energy window approach is not straightforward to implement as it requires specialised hardware and extensive measurements to characterise the scatter components. However, the technique makes better use of coincidence data measured over a wider energy range than in conventional imaging, resulting in an effective increase in sensitivity of approximately 60%. The method is particularly well suited to high resolution tomographs with small discrete detectors.

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