Consistency conditions for approximating attenuation distributions in positron emission tomography
Attenuation correction by measurement of the transmission properties of the field of view with and without the object has some drawbacks. It will take extra time to produce transmission scans, which then can not be used for processing more patients and may be uncomfortable for the patient being scanned. The search is on then for a replacement for transmission scanning that may be used in clinical practice and many suggestions have been put forward for this purpose. Attenuation correction of this sort must be as accurate as the measured attenuation correction but without placing time dependencies on the scanner. We introduce many of these suggestions in this thesis and then move on to the theory behind the method that we have tested for this purpose. Our aim is to remove these artifacts from images and reproduce as accurately as possible the emission image without attenuation. This is important for image interpretation and quantitative analysis of images. The method developed in this thesis revolves around the consistency conditions of the Radon transform. We test an algorithm based on these consistency conditions for its ability to approximate attenuation distributions in conjunction with a parameterised model of the attenuation and a search algorithm. The model has been a uniform ellipse, an elliptical cylinder, and finally an out of position attenuation distribution. In each case we have found solutions that do not correspond to better PET images mainly because of the unpredictability in the solutions found. However these solutions are limited by the amount of information given to the search, increasing things like the similarity of the model and the actual attenuation, reducing the amounts of transformation allowed increase the chances of a predictable useful solution being found by this method. Finally we remark on the usefulness of the current technique and its dependence on the acuity of the model plus the possibility of its use in future PET scanning.