Learning to Sample in Computational Imaging: Measurement Acquisition and Posterior Estimation

Many problems in science and engineering require visualizing objects that are not directly observable—such as black holes that are millions of light-years away from the Earth or internal anatomical structures hidden within the human body. Computational imaging is a powerful paradigm that combines sensor design with advanced computational algorithms to make the invisible visible. The typical computational imaging pipeline involves first collecting indirect measurements of the target object and then solving a reconstruction problem. This thesis focuses on two core challenges about sampling along this pipeline: (1) optimizing the sampling process for measurement acquisition, and (2) sampling the posterior distribution of possible reconstructions given noisy measurements. The first part of the thesis investigates how to design adaptive and task-specific acquisition strategies for computational imaging systems, with a focus on compressed sensing magnetic resonance imaging (CS-MRI). We propose a sequential sampling method that learns to select measurements in multiple stages, and an approach that tailors sampling patterns for specific downstream tasks such as region-of-interest reconstruction, segmentation, and classification. These methods enable a better selection of measurements taken during acquisition, leading to improved performance compared to conventional baselines. We have also implemented our learned sequences on a real MRI scanner and verified their improvement in practice. The second part of the thesis develops a principled framework for posterior sampling using diffusion models (DMs)—a state-of-the-art class of generative models. By revealing a key connection between DMs and the Split Gibbs Sampling, we introduce a posterior sampling method that rigorously incorporates pre-trained DMs as image priors for solving inverse problems, which exhibits strong performance on a variety of applications. We then show that this framework can be naturally extended into a series of instantiations for solving more general inverse problems, addressing topics like text conditioning, video inverse problems, non-differentiable forward models, and discrete-space sampling. We also present a comprehensive benchmark for systematically evaluating state-of-the-art DM-based posterior estimation methods. By leveraging machine learning to address challenges in both data acquisition and posterior estimation, this thesis provides new possibilities for building more intelligent and reliable imaging systems across science and engineering.