| This work is concerned with the reconstruction of motion-corrected images of the thorax from respiratory gated Positron Emission Tomography (PET) measurements. In scans of the thorax, image intensity in the region of a lung lesion can be used as an indicator of malignancy and the progress of treatment. Quantifying this intensity accurately is therefore desirable. However, blur associated with motion of the lungs can degrade quantification accuracy, unless effective motion-corrected image reconstruction measures are employed. This leads to questions about which reconstruction method, among various candidates, performs best, as well as how these methods can be implemented efficiently.; In the first part of our work, we experiment with several motion-corrected image re-construction methods on simulated measurements. In these experiments, we compare the average percent error with which each method recovers the intensity of a synthetic lung lesion. One of these methods, introduced by us, is based on joint penalized likelihood estimation of both image intensity and motion parameters. The other methods are based on more ad hoc gate-wise processing strategies. In our experiments, the joint estimation method exhibited the highest quantification accuracy, very near to the performance bound where motion was fully known.; The different reconstruction methods considered involve time consuming cost function minimization steps. In the subsequent parts of our work, we look at two ways to facilitate these minimizations. One way is to accelerate interpolation operations that are associated with the motion model. We show that appreciable speed-up of these operations can be obtained by approximating and pre-tabulating certain intermediate quantities. The second way is to employ Majorize-Minimize (MM) algorithms, wherein the cost function minimization steps are reduced to the minimization of computationally simpler functions. The practical aspect of this branch of work is ongoing. However, we have, in the course of this work, accomplished a comprehensive theoretical analysis of the asymptotic behavior of MM, generalizing the analyses of previous literature. We also give an original region of convergence analysis for MM algorithms based on connected motorizing functions. |
