A Convex Compressibility-Inspired Unsupervised Loss Function for Physics-Driven Deep Learning Reconstruction

Physics-driven deep learning (PD-DL) methods have gained popularity for improved reconstruction of fast MRI scans. Though supervised learning has been used in early works, there has been a recent interest in unsupervised learning methods for training PD-DL. In this work, we take inspiration from statistical image processing and compressed sensing (CS), and propose a novel convex loss function as an alternative learning strategy. Our loss function evaluates the compressibility of the output image while ensuring data fidelity to assess the quality of reconstruction in versatile settings, including supervised, unsupervised, and zero-shot scenarios. In particular, we leverage the reweighted ℓ1 norm that has been shown to approximate the ℓ0 norm for quality evaluation. Results show that the PD-DL networks trained with the proposed loss formulation outperform conventional methods, while maintaining similar quality to PD-DL models trained using existing supervised and unsupervised techniques.