Hybrid tomographic reconstruction in grating interferometry breast CT: combining physics-based likelihoods with data-driven priors

Breast cancer is the most prevalent malignancy among the female population. To fight this public health burden, early detection is crucial. Unfortunately, currently available breast imaging technologies suffer from limitations ranging from insufficient resolution to low soft-tissue contrast, from costly and long scans to painful breast compression. This all negatively impacts the sensitivity and specificity of these methods, thus leading to overdiagnosis and missed tumors. X-ray phase contrast CT has the potential to overcome these limitations and enable painless fast scans with high three-dimensional resolution and high soft-tissue contrast. The method has been successfully used on synchrotron facilities for two decades but its translation into clinical practice has not happened yet. Grating Interferometry CT (GI-CT) is arguably the phase-contrast technique which has the highest chances of making this transition. Thanks to its relatively high mechanical robustness, its modest requirements in terms of spatial and temporal beam coherence and the possibility to operate with a large field-of-view (FOV), the method is in fact compatible with clinical X-ray sources and human-sized subjects. In an attempt to translate Grating Interferometry Breast CT (GI-BCT) to the clinics, our group has developed prototype scanners to test the compatibility of the technology with clinical requirements (large FOV and low-dose) and to investigate the added value phase contrast can offer to breast CT. Owing to the peculiar signal acquisition scheme in GI-CT and the current limitations in hardware fabrication, it is an arduous task to reconstruct high-quality tomographies under clinically compatible conditions. This dissertation aimed at solving this problem. It first discusses the main challenges in GI-CT reconstruction, namely high and heterogeneous noise and high problem ill-conditioning. To tackle these problems, the combination of state-of-the-art classical iterative reconstruction algorithms with data-driven regularization was then investigated. After evaluating many approaches, a hybrid tomographic reconstruction framework is presented which combines a physics-based likelihood with a data-driven prior. Specifically, the high problem ill-conditioning was addressed by developing better conditioned forward operators and by imposing a relation between the absorption and phase-contrast channels which allows to iteratively fuse the two and leverage the strengths of each channel. The noise problem was tackled by deep learning algorithms which remove the unwanted noise and artefacts introduced by the physics-based likelihood, thus allowing for nearly noise-free reconstructions. Thanks to the developed reconstruction method, first ex-vivo studies suggest that GI-BCT could outperform attenuation-based breast CT in a clinical-dose regime, thus bringing the technology a step closer to first in-vivo studies. In particular, the results in this dissertation indicate that with GI-BCT it might be possible to reduce the dose and/or to increase the spatial resolution compared to clinical breast CT. The added value that phase contrast can bring to the clinics thus lies in its higher contrast for high-frequency details compared to absorption