Safeguarded Deep Unfolding Network for Parallel MR Imaging

This study proposes a safeguarded methodology for network unrolling. Specifically, focusing on parallel MR imaging, we unroll a zeroth-order algorithm, of which the network module represents a regularizer itself so that the network output can still be covered by a regularization model. Furthermore, inspired by the idea of deep equilibrium models, before backpropagation, we carry out the unrolled network to converge to a fixed point and then prove that it can tightly approximate the real MR image. In a case where the measurement data contain noise, we prove that the proposed network is robust against noisy interferences.