AmbientFlow: Invertible generative models from incomplete, noisy measurements

TL;DR

AmbientFlow is a novel framework that learns flow-based generative models directly from incomplete and noisy measurements, enabling improved image reconstruction in applications where high-quality data is hard to acquire.

Contribution

It introduces a variational Bayesian approach to train flow-based generative models from noisy, incomplete data, addressing a key challenge in imaging science.

Findings

Effective learning of object distribution from noisy data

Improved image reconstruction performance

Demonstrated robustness in numerical studies

Abstract

Generative models have gained popularity for their potential applications in imaging science, such as image reconstruction, posterior sampling and data sharing. Flow-based generative models are particularly attractive due to their ability to tractably provide exact density estimates along with fast, inexpensive and diverse samples. Training such models, however, requires a large, high quality dataset of objects. In applications such as computed imaging, it is often difficult to acquire such data due to requirements such as long acquisition time or high radiation dose, while acquiring noisy or partially observed measurements of these objects is more feasible. In this work, we propose AmbientFlow, a framework for learning flow-based generative models directly from noisy and incomplete data. Using variational Bayesian methods, a novel framework for establishing flow-based generative models from noisy, incomplete data is proposed. Extensive numerical studies demonstrate the effectiveness of AmbientFlow in learning the object distribution. The utility of AmbientFlow in a downstream inference task of image reconstruction is demonstrated.