In this chapter, classical filtered backprojection and statistical maximum likelihood expectation
maximization image reconstruction algorithms are evaluated in terms of image quality and processing
delay. Image files were taken from a concurrent study investigating the use of SPECT as
a diagnostic tool for the early onset of Alzheimer-type dementia. Filtered backprojection (FBP)
image reconstruction needs a careful control of the noise since it tends to amplify high frequency
noise. Pre- and post-filtering improves the quality of FBP reconstruction by removing the huge
high frequency noise present in Single Photon Emission Computed Tomography (SPECT) data
and the residual noise after reconstruction. Maximum likelihood expectation maximization (MLEM)
yields better image quality when compared to FBP since a precise statistical model of the
emission is used. However, the processing delay is considerable due to its slow convergence.
On the other hand, the ordered subsets expectation maximization (OS-EM) method is also explained.
OS-EM is found to be a good trade-off between image quality and processing delay
since it converges in a single iteration by partitioning the set off detection elements into about 15-
20 subsets. Furthermore, in this chapter, the performance of five different nonlinear least-square
optimization algorithms is compared in the context of the affine registration of SPECT images.
The Levenberg-Marquardt algorithm is shown to be very robust but the convergence rate is considerably
lower than for Gauss-Newton algorithms. Two existing Gauss-Newton procedures are
compared to two GN algorithms which include an additional parameter. This parameter allows
to adaptively change the descent direction and it improves the performance upon most used brain
registration algorithms in the literature.
Keywords: Image reconstruction, SPECT, Spatial normalization, Gauss-Newton method, Optimization algorithms.
