Generative Models for Uncertainty of Medical and Seismic Imaging
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Orozco, Rafael
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Abstract
This thesis develops scalable algorithms for solving high-dimensional, ill-posed inverse problems, particularly in imaging applications such as medical imaging and seismic exploration. These problems involve inferring unknown parameters from indirect measurements via a forward operator, typically requiring computationally expensive solutions of partial differential equations (PDEs).
To address the ill-posed nature of these problems, characterized by non-unique solutions, we adopt a Bayesian framework. This framework integrates prior knowledge and observational data, resulting in a posterior distribution that characterizes the range of plausible solutions. Such uncertainty quantification is critical in applications where decisions rely not only on the most likely solution but also on an understanding of its associated confidence, such as in risk-aware subsurface modeling or medical diagnostics.
Given the high computational cost of traditional sampling methods like Markov Chain Monte Carlo (MCMC), this thesis focuses on developing scalable algorithms that reduce the reliance on repeated forward and adjoint PDE computations. By leveraging advanced generative models (Normalizing Flows + Diffusion), we aim to make Bayesian uncertainty quantification computationally feasible for large-scale imaging problems. The thesis includes theoretical advancements and experiments demonstrating the practical use of a suite of algorithms developed (WISE, ASPIRE, WISER) on a variety of applications ranging from MRI to field data seismic imaging. Finally, we discuss some additional modules to the inference framework including Bayesian optimal experimental design and an application toward digital twins.
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2024-12-09
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Dissertation