Explicit network noise amplification penalty in loss function for k-space interpolation networks through fast backpropagation

Motivation: GRAPPA and RAKI optimize purely for data consistency, completely lacking physics-driven or model-based loss terms. Goal(s): Recurrently feed noise amplification information into k-space interpolation networks by penalizing the online computed g-factor. Approach: JAX-implemented GRAPPA and RAKI g-factors were estimated online in each training iteration and incorporated into the optimization as an inherent network noise amplification penalty. Results: Networks including g-factor loss outperformed implementations optimizing only for the data consistency term. Inclusion of g-factor loss terms manifested Tikhonov regularization-like effects on image noise distribution, as revealed by difference maps to the fully sampled gold standard. Impact: Incorporating the penalty of inherent noise amplification into k-space interpolation networks reduces reconstruction noise levels compared to implementation that optimize only for data consistency. G-factor-informed reconstructions manifest Tikhonov regularization-like effects, as revealed by noise distribution on difference maps.