Compressibility-Based Unsupervised Loss for Physics-Driven MRI Reconstruction Networks

Motivation: Alternative unsupervised training methods are needed for training physics-driven deep learning reconstruction without fully-sampled data. Goal(s): We propose a novel loss formulation, inspired by compressibility, to evaluate reconstruction quality in supervised, unsupervised and zero-shot settings. Approach: We leverage reweighted $$$\ell_1$$$-norm, which corresponds to $$$\ell_0$$$-norm of a sparse signal, to evaluate reconstruction quality. In supervised setting, reference weights are used for reweighting, while in unsupervised case, they are updated after each reweighting. Results: Our findings demonstrate that the networks trained with this loss outperform conventional compressed sensing, while performing similarly to deep learning methods trained using established supervised and unsupervised techniques. Impact: This work proposes an alternative compressibility-inspired loss formulation that is applicable to supervised, unsupervised and zero-shot learning problems for the training of physics-driven reconstruction neural networks. This approach utilizes compressibility and convexity for learning.