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Positron Emission Tomography is a very useful form of functional imaging. It allows physiology to be examined in vivo, and so provides a useful complement to anatomical imaging modalities like CT or MRI. Motion poses serious problems to PET, especially in quantitative studies. The first effect of motion is blurring, especially as changes due to motion are confounded with mose from the physiology. The second effect is CO do wi(h the corrections for attenuation and scatter required for quantitative studies, nowadays based on a CT scan acquired before the PET acquisition. A change of position means that corrections introduce artefacts. Lastly, modern reconS(fllcrion algorithms are nonlinear, meaning the overall image is nOt simply a combination of images corresponding to the different positions. This thesis concerns a particular class of motions that often cause PET scans to be unusable, namely twitches, transient motion between comparatively stable positions. These modons can be corrected. by registration. One registration method for rigid body motions, e.g. of the brain, is presented. here. This method does not require the data to be reconstructed prior to reconstruction, saving computation, the need to choose reconstruction parameters, and avoiding any artefacts that result from the modon. Registradon to correct the motion is not possible without knowledge of when the position changes. A method to localise when twitches occur during a scan is considered to ~ the major conrribution of the thesis. The novel method presented here is a Significant improvement on exisdng approaches as it automated and does not require any additional equipment or steps to the imaging procedure. It too is performed before reconstruction as this allows performance that exceeds real-time and allows the unusually strong statistical properties of raw PET data to be used. Combined cogether, the work presented in this thesis allows twitches to be located and corrected.