Singh, Imraj Ravi Devia; (2025) Advanced Medical Image Reconstruction: Deep Generative and Functional Approaches. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Medical imaging is pivotal in diagnosis and treatment planning, with modalities such as Positron Emission Tomography (PET) and Magnetic Resonance Imaging (MRI) providing critical insights into physiological and anatomical structures. The process of reconstructing images from raw scanner measurements, known as medical image reconstruction, is essential for producing clinically useful images. This thesis develops advanced methods for medical image reconstruction using deep generative and functional approaches, focusing primarily on PET and MRI. First, we developed a Deep Image Prior (DIP) method for PET image reconstruction. DIP is an untrained deep generative model that leverages the inductive bias of network architectures to regularise the reconstruction process. Applied to fully three-dimensional problems, the DIP method demonstrated strong performance in moderate noise settings but encountered challenges at higher noise levels. To address this, we incorporated additional traditional regularisation techniques to stabilise the reconstruction and improve performance compared to traditional methods alone. The second study investigates normalisation techniques for supervised PET image reconstruction. These supervised methods directly predict the reconstruction from raw measurements or an approximate reconstruction. We proposed and compared a range of normalisation techniques to handle the widely varying dynamic range of PET images. The normalisation strategies improved clinically relevant image assessment methods as compared with unnormalised models. In the third study, we adapted Score-Based Generative Models (SGMs), a trained deep generative model, for PET image reconstruction. This method utilised a learned prior, sampled while ensuring consistency with PET measurements, which necessitated careful handling of PET data-consistency. We also developed normalisation strategies and extensions for fully 3D imaging. For paired PET and MRI images, we developed a guided reconstruction method that enforced consistency with both PET measurements and the corresponding MRI image. The results were compared with state-of-the-art methods, demonstrating improved performance. Finally, we developed Adaptable-Blobs (AB), a continuous functional image representation, for parallel MRI reconstruction. AB represents the image as a summation of Gaussians with parameterised locations, shapes, and intensities. Exploiting the properties of Gaussians, we derived an analytical forward model for parallel MRI, termed MR-Blob. This method exhibited favourable properties, including noise robustness and dense representational capacity. Collectively, these studies expand the scope of medical image reconstruction and demonstrate the potential of deep generative and functional approaches to significantly advance the field.

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