Advancing Scientific Computational Imaging Through Data-Driven and Physics-Based Priors

The core idea of computational imaging is to supplement limited observable data with human-imposed assumptions, or priors. One could formulate a prior as a statistical model or physics model of the object being imaged. However, incorporating such assumptions in the imaging process poses computational challenges, including efficiently expressing sophisticated priors, appropriately balancing priors with observations, and gently enforcing physics constraints. This thesis addresses such challenges with principled methods for bringing informative assumptions into computational imaging. We emphasize applications in scientific imaging, and we focus on two categories of priors as well as the intersection between them: data-driven statistics and physics knowledge. On the data-driven side, this thesis presents work on score-based priors, including a posterior-estimation method and results of re-imagining the famous M87* black hole from real data with score-based priors. On the physics-based side, we have been able to tackle extremely under-determined imaging problems by enforcing physics constraints, including performing single-viewpoint dynamic tomography of emission near a black hole and characterizing interior material properties from video. As a means towards integrating data-driven and physics-based assumptions, we have developed a method to enforce physics constraints on generative models. In this thesis, we explore each aforementioned project with an emphasis on technical novelty and experimental validation on simulated and real data. By opening new routes for bringing in both data-driven and physics-based assumptions, the methods presented in this thesis enable visualizing scientific phenomena beyond the reach of conventional sensors.