Data-driven Image Reconstruction in Computed Tomography
Time: Mon 2025-03-17 13.00
Location: Lecture Hall F3, Lindstedtsvägen 22
Language: English
Subject area: Applied and Computational Mathematics
Doctoral student: Jevgenija Rudzusika , Matematik (Inst.)
Opponent: Professor Tristan van Leeuwen, Universiteit Utrecht: Utrecht, Utrecht, NL
Supervisor: Ozan Öktem, Strategiskt centrum för industriell och tillämpad matematik, CIAM, Matematik (Avd.)
QC 2025-02-19
Abstract
This thesis focuses mainly on improving the quality of reconstruction in computed tomography (CT), which is an imaging techniquethat aims to reconstruct the interior of an object from a set of X-ray projections obtained from different viewpoints. Mathematically, this is an inverse problem that is often ill-posed and, therefore, requires some sort of regularization. Recently, this research field has been dominated by data-driven approaches, and this thesis is not an exception. In contrast to model-based methods that assume that a reconstructed object possesses certain predefined properties, data-driven methods use the statistical information obtained from a set of similar objects to improve reconstruction of a new object from the same class. The recent development of computer hardware has allowed us to extract and store this statistical information from a large set of samples, and thereforeis responsible for the increased popularity of these methods. However, the problem with these approaches is that the most efficient of them, such as deep neural networks, lack interpretability, and their extraordinary empirical performance is not fully justified from the theoretical perspective. Another big challenge concerning CT in particular is to move from methods that perform very well on toy experiments conducted on simulated low-dimensional data to methods that could be used in real-life applications, such as medical imaging.
This thesis explores several directions that could potentially address the above issues. The first is data-driven optimization that can be used to reduce the number of iterations needed to obtain the final reconstruction when it is defined as a solution to an optimization problem. Such optimization problems appear within a classic regularization framework.
Next, we revisit dictionary learning, which can be seen as a predecessor to data-driven methods that go under the caption “deep learn-ing”. The advantage of dictionary learning is in its relative mathematical simplicity and interpretability. We see this as a bridge between well-understood but somewhat limited model-based approaches and a black-box paradigm of deep learning. Since reconstruction using learned dictionaries is defined as an optimization problem, data-driven optimization comes in useful here as well.
Finally, this thesis addresses the problem of upscaling state-of-the-art deep learning architectures so that they can be applied to clinical CT data. We show that certain modifications in the architecture combined with engineering techniques allow us to do that without relyingon super-computing resources.