4-D Tomographic Inference: Application to SPECT and MR-driven PET

Emission tomographic imaging is framed in the Bayesian and information theoretic framework. The first part of the thesis is inspired by the new possibilities offered by PET-MR systems, formulating models and algorithms for 4-D tomography and for the integration of information from multiple imaging modalities. The second part of the thesis extends the models described in the first part, focusing on the imaging hardware. Three key aspects for the design of new imaging systems are investigated: criteria and efficient algorithms for the optimisation and real-time adaptation of the parameters of the imaging hardware; learning the characteristics of the imaging hardware; exploiting the rich information provided by depthof- interaction (DOI) and energy resolving devices. The document concludes with the description of the NiftyRec software toolkit, developed to enable 4-D multi-modal tomographic inference

Spatio-temporal reconstruction of dPET data using complex wavelet regularisation.

Traditionally, dynamic PET studies reconstruct temporally contiguous PET images using algorithms which ignore the inherent consistency between frames. We present a method which imposes a regularisation constraint based on wavelet denoising. This is achieved efficiently using the Dual Tree Complex Wavelet Transform (DT-CWT) of Kingsbury, which has many important advantages over the traditional discrete wavelet transform: shift invariance, implicit measure of local phase, and directional selectivity. In this paper, we apply the decomposition to the full spatio-temporal volume and use it for the reconstruction of dynamic (spatio-temporal) PET data. Instead of using traditional wavelet thresholding schemes we introduce a locally defined and empirically-determined Cross Scale regularisation technique. We show that wavelet based regularisation has the potential to produce superior reconstructions and examine the effect various levels of boundary enhancement have on the overall images. We demonstrate that wavelet-based spatio-temporally regularised reconstructions have superior performance over conventional Gaussian smoothing in simulated and clinical experiments. We find that our method outperforms conventional methods in terms of signal-to-noise ratio (SNR) and Mean Square Error (MSE), and removes the need to post-smooth the reconstruction