Date of Award
7-22-2024
Degree Name
Doctor of Philosophy (PhD)
Degree Type
Dissertation
Abstract
This dissertation addresses the integration of physical models with learning-based artifact removal priors for computational imaging. The motivation for our work stems from the growing interest in combining imaging models, which ensure data consistency with observed measurements, with deep learning, which provides advanced data-driven prior modeling. Following this approach, we adopt classic statistical inference as the foundational framework and integrate deep artifact removal models as image priors. This allows our framework to simultaneously leverage both physical models and learning-based priors. Furthermore, the increasing size of images and measurements in modern computational imaging systems imposes significant computational and memory burdens. Another objective of this dissertation is to extend our framework to these scenarios by incorporating large-scale optimization techniques. We have developed multiple algorithms to achieve efficient and reliable imaging. We validate the performance of our algorithms through rigorous theoretical analysis and by demonstrating their effectiveness in various imaging applications. The dissertation significantly extends three algorithmic frameworks—that is, plug-and-play priors (PnP, Part II), deep model-based architectures (DMBA, Part III), and diffusion probabilistic models (DPM, Part IV)—with multiple contributions including the design of novel algorithms, establishment of unified theory, and applications to real imaging problems. Specifically, in Part II, we present in-depth discussions of two popular PnP algorithms: the proximal gradient method PnP (PnP-PGM) and Regularization by Denoising (RED). Our contributions include the introduction of Regularization by Artifact Removal (RARE), which broadens the current denoiser-centric view of PnP methods by considering priors corresponding to networks trained for more general artifact removal. We provide recovery analysis under both deep denoising priors and artifact removal priors for compressive sensing scenarios. Additionally, we propose scalable PnP variants that efficiently infer large images using block coordinate computing techniques. Finally, we introduce a new method called Calibrated RED (Cal-RED), which enables the joint calibration of the measurement operator along with the reconstruction of the unknown image. In Part III, we conduct both empirical and theoretical investigations on DMBA. Building on existing variants of DMBA—Deep Unfolding (DU) and Deep Equilibrium Model (DEQ)—which interpret the iterations of a model-based algorithm as layers of a deep neural network and train it end-to-end in a supervised fashion, we propose scalable DMBA variants for processing a large set of measurements using online gradients. Our analysis framework, based on monotone operator theory and stochastic gradient descent in machine learning, is unified for online DMBA and represents a novel contribution to the existing literature. Finally, we develop a new DMBA for learning explicit regularization functionals, extending the existing implicit prior-centric approaches of PnP and DMBA. In Part IV, we extend DPM—a novel probabilistic prior—to computational imaging by developing a conditional diffusion posterior sampling method. Our method, DOLCE, explores the regularization capability of conditional DPM specifically for the extremely ill-posed inverse problem of limited-angle computed tomography (LACT).
Language
English (en)
Chair
Ulugbek Kamilov