Tomography is a powerful technique to non-destructively determine the interior structure of an object.Usually, a series of projection images (e.g.\ X-ray images) is acquired from a range of... Show moreTomography is a powerful technique to non-destructively determine the interior structure of an object.Usually, a series of projection images (e.g.\ X-ray images) is acquired from a range of different positions.from these projection images, a reconstruction of the object's interior is computed. Many advanced applications require fast acquisition, effectively limiting the number of projection images and imposing a level of noise on these images. These limitations result in artifacts (deficiencies) in the reconstructed images. Recently, deep neural networks have emerged as a powerful technique to remove these limited-data artifacts from reconstructed images, often outperformingconventional state-of-the-art techniques. To perform this task, the networks are typically trained on a dataset of paired low-quality and high-quality images of similar objects. This is a major obstacle to their use in many practical applications. In this thesis, we explore techniques to employ deep learning in advanced experiments where measuring additional objects is not possible. Show less
Gibbs measures, as used in Statistical Mechanics, have a definition that is remarkably similar to the definition ofg-measures, used in dynamical systems. For both types of measures the continuity... Show moreGibbs measures, as used in Statistical Mechanics, have a definition that is remarkably similar to the definition ofg-measures, used in dynamical systems. For both types of measures the continuity of conditional probabilities play a central role.In this thesis we give necessary and sufficient conditions for when a g-measure is a Gibbs measure. We relate this result to well known uniqueness conditions and briefly consider the related question: when is a g-measure reversible.Subsequently we consider an application in information theory by considering whether one-sided models can be used for two-sided modeling.Finally, we apply a technique called measure disintegration to give very general conditions for when the conditional probabilities of factors of Markov processesare g-measures and factors of Gibbs measure are Gibbs measures. Show less
