AmbientFlow: Invertible generative models from incomplete, noisy measurements

Varun A. Kelkar, Rucha Deshpande, Arindam Banerjee, Mark Anastasio

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.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

We have made changes to the manuscript based on the feedback from reviewers. We have also added additional numerical studies that include the following:
1. Evaluation of the conditional posterior model:
- Evaluating whether our learned models satisfy $p_\phi(\mathbf{f} | \mathbf{g}) \propto q_{\mathbf{n}}(\mathbf{g} - H\mathbf{f}) p_\theta(\mathbf{f})$, and
- Comparing the samples from the posterior network with the samples obtained by Langevin dynamics using the unconditional prior.
2. Evaluation of the first- and second-order statistics learned by the unconditional model.
3. Additional ablation studies: FID score for different undersampling ratios used to simulate the measurements that constitute the AmbientFlow training data.
4. Face image inpainting case study: Evaluating how well an AmbientFlow trained on noisy images can serve as a prior for an image inpainting task.

Code: https://github.com/comp-imaging-sci/ambientflow

Assigned Action Editor: ~Laurent_Dinh1

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Submission Number: 1549