Combined Correction and Reconstruction Methods - Correction Techniques in Emission Tomography - page 186

9.1 Introduction
In the beginning of PET reconstruction in the middle of the 1970s the
well-known reconstruction algorithms for CT were applied since both imaging
techniques rely on the ecient recovery of a function from its line integrals
[40]. It turned out that the resulting images were good enough that these algo-
rithms were use over years until new algorithms especially designed for PET
were introduced [54]. As presented in Chapter 3 the filtered-backprojection
type algorithms (FBP) were more and more replaced by new model-based,
iterative algorithms that take into account the Poisson statistical proper-
ties [57, 22]. The new algorithms|mainly originating from the maximum-
likelihood expectation-maximization (ML-EM) algorithm|show good perfor-
mance even in the case of low statistic measurements where the old reconstruc-
tion algorithms may fail. Next to the statistical properties, these algorithms
can easily be extended with any other corrections, such as resolution model-
ing, the use of different forward and backward projectors, or even higher di-
mensional reconstruction approaches with the use of suitable basis functions.
These extensions are possible since the model-based reconstruction algorithms
are not limited to the X-ray projection geometry of the FBP type algorithms.
We mention that there are, as well, approaches to extend the analytical algo-
rithms, such as the motion compensated local tomography of Katsevich [26],
but usually the ML-EM-type algorithms are used for extensive modeling. In
general the statistical model is used and extended for the necessary correction,
whereas the resulting linear (in some cases even non-linear) equation system
is solved afterwards. Due to the enormous speed increase of CPUs and port-
ing of reconstruction algorithms to clusters or even GPUs [52] we are now
able to work with extensive PET models. In this chapter we will focus on two
interesting, recently growing approaches:

• Parameter estimation during 4D reconstructions using compartment

models to investigate physiological parameters.

• Incorporation of motion information in the reconstruction algorithm to

correct for reconstruction artifacts due to patient movement or intrinsi-
cal motion (like heart beat, breathing).

We will present both approaches in detail giving an overview of recent pub-
lications. In the end one may recognize that both approaches are multi-
dimensional reconstructions using different types of basis functions. Hence
both approaches can be combined to create an even more complex recon-
struction model.