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. FEI reformulates the EI objective through an inexact variable-splitting scheme, decoupling network training from an auxiliary restoration step implemented with a plug-and-play denoiser, this novel unsupervised scheme shows superior efficiency and performance compared to the standard 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. Beyond offline training, the proposed scheme also 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.

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