Smooth operators: exploring B-splines as learnable non-linear activation functions for complex-valued MRI reconstruction

Motivation: Complex-valued neural networks have shown remarkable results in MR image reconstruction. However, these approaches have relied on extensions of real-valued activation functions to perform these activations, which might not be optimal. Goal(s): To explore the effect of learning data-driven non-linear activation functions on the performance of complex-valued neural networks for MR image reconstruction. Approach: We train networks using spline-based activations and compare them to networks using conventional complex-valued activation functions. Finally, we evaluate the effects of the new hyperparameters that learnable activation functions offer. Results: Spline-based activation functions are superior to conventional activation functions while maintaining model robustness. Impact: Spline-based complex-valued neural networks might improve image quality and enable further acceleration of MRI acquisitions. These results can better help to diagnose patients based on MRI exams while improving patient comfort by reducing the MRI acquisition time.