Local models and local convergence for maximum likelihood iterative reconstruction

Iterative methods are being increasingly used for
reconstruction of tomographic data as in computed tomography (CT) and positron
emission tomography (PET). These methods often yield better reconstructions
compared to analytical methods. An important reason for this is that iterative
reconstruction has a more flexible data acquisition model which allows for a
more accurate simulation of the true acquisition during the reconstruction.
Moreover, a noise model can be included in the reconstruction algorithm.</></>

This thesis investigated several remaining problems
for iterative reconstruction in CT and PET based on the principles of local
modeling andlocal convergence improvements.</></>

For CT, iterative metal artifact reduction was
studied. Metalsattenuate the majority of the photons which makes that small
deviations in the reconstruction model can have a large influence and introduce
severe artifacts. In the current state of the art methods, data points with low
photons are removed and replaced with artificial data points that do not cause
artifacts. This reduces the most severe artifacts but by the removal of the
data points also contrast in the regionsaround and between the metals is
removed. Alternatively, iterative methods can be used. These methods model the
effects that cause the artifacts and do not remove data points. The existing
iterative methodsdo not reduce the artifacts sufficiently and they are often
too slowfor possible clinical usage. </></>

To reduce computation time, a local model scheme
was introduced. This approach uses the most accurate (and computation
intensive)model for the metals in the image and a simpler model elsewhere.
This local model structure is called the patchwork structure and was able to
reduce the computation time without losing image quality. With the patchwork
structure it was also possible to improve the convergence of the metal regions
locally, leading to an improved artifact reduction. This method has been
applied on simulated and measured phantom andpatient scans. The artifacts in
the reconstructed images were clearly reduced without loss of contrast around
the metals. Some artifacts,however reduced, are still present. The origin of
these artifacts remains unclear.</></>

The local convergence improvements that can be
obtained by the patchwork structure were also evaluated for convergence
improvements for the entire image volume. Hence, the volume was divided in a
set of equal smallimage blocks that are separately updated. This alternative
patchworkstructure has been applied on both CT and PET data. For both
applications, a considerable increase in convergence rate was obtained,
yielding the same image quality in a shorter time, which is important for
clinical application of iterative methods.</></>

In clinical environments, PET is usually
reconstructed with iterative reconstruction. A problem of the applied iterative
method is that it tends to produce bias when the data are very noisy and in
cold regions. This bias may cause problems for tracer kinetic analysis. Origins
of this bias are the strong asymmetry of the employedPoisson distribution in
case of low count data and the inherent nonnegativity constraint of the algorithm.
A modified algorithm has been developed that switches from the Poisson
distribution to the Gaussiandistribution for low count data points. This new
method lowers the bias significantly and gives results comparable to other bias
reduction methods. An advantage of this new method is that the distribution is
locally changed and that it has only a single parameter, the value of which is
easily determined.</>



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