Fast Equivariant Imaging: Acceleration for Unsupervised Learning via Augmented Lagrangian and Auxiliary PnP Denoisers

TL;DR

Fast Equivariant Imaging (FEI) introduces an unsupervised learning framework that accelerates training and enhances performance of deep imaging networks by reformulating optimization with Lagrange multipliers and plug-and-play denoisers, enabling rapid training and test-time adaptation.

Contribution

The paper presents FEI, a novel unsupervised imaging method that significantly speeds up training and improves generalization by integrating Lagrangian optimization and auxiliary denoisers.

Findings

Achieves 10x faster training than standard Equivariant Imaging.

Improves image reconstruction and inpainting quality.

Enables efficient test-time adaptation for individual samples.

Abstract

In this work, we propose Fast Equivariant Imaging (FEI), a novel unsupervised learning framework to rapidly and efficiently train deep imaging networks without ground-truth data. From the perspective of reformulating the Equivariant Imaging based optimization problem via the method of Lagrange multipliers and utilizing plug-and-play denoisers, this novel unsupervised scheme shows superior efficiency and performance compared to the vanilla Equivariant Imaging paradigm. In particular, our FEI schemes achieve an order-of-magnitude (10x) acceleration over standard EI on training U-Net for X-ray CT reconstruction and image inpainting, with improved generalization performance. In addition, the proposed scheme enables efficient test-time adaptation of a pretrained model to individual samples to secure further performance improvements. Extensive experiments show that the proposed approach provides a noticeable efficiency and performance gain over existing unsupervised methods and model adaptation techniques.