Osg

Noise Free

Noisy

Figure 14. Reconstructed images from analytically-simulated projections of a cylinder obtained using LEGP and LEHR collimators. Only the GRF was modelled in the projections. Images were reconstructed from projection data with and without the addition of Poisson noise. Five iterations of OSEM were used with 64 subsets per iteration (4 angles per subset) with no compensation (OS-N) and compensation for the GRF (OS-G).

Figure 14. Reconstructed images from analytically-simulated projections of a cylinder obtained using LEGP and LEHR collimators. Only the GRF was modelled in the projections. Images were reconstructed from projection data with and without the addition of Poisson noise. Five iterations of OSEM were used with 64 subsets per iteration (4 angles per subset) with no compensation (OS-N) and compensation for the GRF (OS-G).

are nonlinear, the PSF cannot be estimated by simply reconstructing the projections of a point source. Instead, the point source projections are treated as a perturbation to a background image. After reconstruction of the perturbed image, the reconstruction of the background image is subtracted providing a local PSF; the magnitude of the FT of this local PSF provides the local MTF. The local NPS is computed from the covariance matrix for the point of interest. It was found that iterative reconstruction with CDRF compensation produces local MTFs with improved response at mid-frequencies. Subsequent unpublished work has demonstrated that, with large numbers of iterations, all frequencies up to approximately the first zero in the MTF obtained by filtered backprojection can be restored. This is illustrated by Figures 15 and 16, which show the local MTF for a point source reconstructed with FBP and iterative reconstruction with CDRF compensation. Note that for the iterative method, there is some overcompensation at mid-frequencies (MTF > 1) and that there is some artifactual increase at frequencies above the point where the MTF for FBP goes to zero.

The noise properties are also an important factor in evaluating CDRF compensation. It has been found that the local NPS increases at the frequencies that are restored, similar to what is found with restoration filtering. This gives rise to the lumpy noise texture seen in the images in Figure 14.39 In fact, the boosting of the noise is such that the NEQ is not greatly improved by CDRF compensation. In recent work using these measures, Wilson

Figure 15. Images of local MTF in transaxial plane for a point source located 15 cm from the center of rotation. The projections were generated analytically and simulated a LEGP collimator. The image on the left is from FBP with no low pass filter and the one on the right is from 20 iterations of OSEM with 64 subsets per iteration (4 angles per subset) with GRF compensation.

Figure 15. Images of local MTF in transaxial plane for a point source located 15 cm from the center of rotation. The projections were generated analytically and simulated a LEGP collimator. The image on the left is from FBP with no low pass filter and the one on the right is from 20 iterations of OSEM with 64 subsets per iteration (4 angles per subset) with GRF compensation.

Figure 16. Profiles through the MTF images in Fig. 15. The tangential direction is along the vertical axis and the radial direction along the horizontal one in Fig. 15.

et al.41 have pointed out that improper modelling of the CDRF can result in poorer MTFs and noise spectra, while the NEQ was relatively insensitive to these modelling errors.

Several studies have demonstrated an improvement in performance on estimation tasks with CDRF compensation. In the context of myocardial perfusion imaging, both analytic and iterative CDRF compensation were found to provide improved uniformity in the myocardial wall and improved estimates of wall thickness compared to no compensation. Iterative reconstruction-based compensation provided better results than analytic compensation based on the FDR.43 Pretorius et al.42 evaluated iterative and analytic FDR-based CDRF compensation in terms of recovery of the maximum and total counts in a volume. They found that iterative methods provided better recovery and reduced variance in estimates compared to the analytic methods, but that recovery coefficients were more spatially variant for the iterative methods.

Iterations: Method: os-as Cutoff (pixel-1)

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