Diffusion Models for Large-Scale and 3D Image Reconstruction Problems
Abstract
We live in a world where imaging systems are ubiquitous. From the cell phones in our pockets to our cars and doorbells and on to telescopes and medical scanners, imaging has changed how we share, document, and understand our world. There is an increasing demand to make these systems more efficient by producing higher-quality images with fewer and fewer resources. When we need an image that is of higher quality than can be directly constructed from its measurements, we have an inverse problem and must rely on reconstruction schemes. These reconstruction algorithms fill the gap between the measured samples and the desired high-quality images by leveraging a model that attempts to recover image contents while reducing artifacts. Diffusion models are trained on large image datasets to learn an underlying prior. This iterative process, which starts with pure noise and is gradually denoised to eventually obtain a clean image, can be modified to generate or restore the clean image that is also enforced to be consistent with the measurement, thereby solving an inverse problem. However, diffusion models are computationally expensive to train and require large, clean training datasets. To tackle these challenges, this thesis develops methods of using diffusion models to solve inverse problems. In particular, we develop a novel patch-based diffusion prior that allows for image generation and reconstruction using a memory efficient network trained on small patches of an image. We later…
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