Combined Correction and Reconstruction Methods - Correction Techniques in Emission Tomography - page 196

prior to reconstruction, has demonstrated that although this approach leads
to significant improvements in lesion contrast and position in the lung fields, it
is impossible to use such a model to account at the same time for respiratory
motion effects in both the lung fields and organs under the diaphragm. These
limitations are due to the application of a common set of ane transformation
parameters across the entire emission imaging field of view, whereas the organs
have independent movements due to respiration. In oncologic applications for
instance, the parameters appropriate for the lungs do not significantly correct
the respiratory effects for organs situated below the diaphragm, as well as the
heart and the mediastinum [29].
Numerous applications have been developed for the movement correction
of the head in SPECT [15] and TEP [39, 14, 16, 10]. In all these methods the
movement was known through the use of an infrared camera tracking in real
time the position of reflecting captors attached to the head of the patient.
Moreover, as the skull is not compressible, the movement of the head is then
reduced to a rotation and translation and a six-parameters transformation is
therefore enough to describe the movement of the head in this type of study.
An important effort has also been carried out in studying the respiratory
movement in cardiac applications in TEP. The movement of the heart due to
respiration is more complex than of the head. In addition to the rotation and
translation, a dilation has to be considered, leading to a transformation with
nine parameters. Different authors have attempted to correct for the effects
of respiratory motion in cardiac emission tomography imaging through the
use of either a rigid body transformation of list mode PET datasets [36] or
through tracking of the center of mass in single photon emission tomography
(SPECT) projections [9].

9.3.2.2 Approaches based on a non-rigid motion model

Although the application of a rigid or ane transformation in the raw
data domain is feasible considering individual lines of response [36, 29], a sim-
ilar approach for elastic transformation poses obvious challenges. The elastic
transformation is not applied to the raw PET emission data prior to recon-
struction as in the case of a rigid or ane motion model, but the iterative
reconstruction algorithm has to be adapted to account for the elastic motion
model. In the past, different approaches for the incorporation of transfor-
mations in the system matrix during the reconstruction process have been
described [43, 24, 45, 44, 35, 30]. While the work of Qi and Huesman as well
as Rahmim et al. considered only rigid body transformations, Jacobson and
Fessler described the theoretical framework of incorporating non-rigid trans-
formations in the reconstruction algorithm without evaluating the proposed
methodology. In addition, Qiao et al. and Li et al. evaluated their proposed
algorithm on a phantom study simulating only rigid body motion, therefore
not allowing the evaluation of elastic transformations in the performance of
their algorithm implementation. Finally, the patient study included in Li et al.