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

2025-07-09

AI Summary

To address the low training efficiency and poor generalization of deep imaging networks in the absence of ground-truth labels, this paper proposes an equivariant imaging framework integrating augmented Lagrangian optimization with plug-and-play (PnP) denoisers. For the first time, it couples the method of Lagrange multipliers with PnP priors within an equivariance-constrained formulation, enabling end-to-end unsupervised reconstruction without ground-truth supervision. Evaluated on the CT100 dataset for X-ray computed tomography reconstruction using a U-Net backbone, the method achieves a 10× speedup in training compared to conventional unsupervised approaches, while significantly improving reconstruction fidelity and cross-domain generalization. The core contributions are: (1) a differentiable augmented Lagrangian–PnP joint optimization paradigm; and (2) an efficient, stable, and ground-truth-free training strategy for deep imaging models.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

We propose Fast Equivariant Imaging (FEI), a novel unsupervised learning framework to 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 vanilla Equivariant Imaging paradigm. In particular, our PnP-FEI scheme achieves an order-of-magnitude (10x) acceleration over standard EI on training U-Net with CT100 dataset for X-ray CT reconstruction, with improved generalization performance.

Problem

• Efficient unsupervised training of deep imaging networks
• Accelerating Equivariant Imaging via Lagrange multipliers
• Improving performance with plug-and-play denoisers

Innovation

• Unsupervised learning with augmented Lagrangian
• Plug-and-play denoisers for efficiency
• Order-of-magnitude acceleration in training