Learning Preconditioners in Gates-controlled Deep Unfolding Networks based on Quasi-Newton Methods For Accelerated MRI Reconstruction

Deep unfolding networks (DUNs) have made significant progress in MRI reconstruction, successfully tackling the problem of prolonged imaging time. However, the ill-conditioned nature of MRI reconstruction often causes slow convergence in iterative optimization, potentially compromising the performance of DUNs. In this study we propose a preconditioned and gates-controlled DUN (PGDUN) to address these challenges. Our approach starts with optimizing the step size of proximal gradient descent (PGD) through a preconditioner. To improve flexibility and adaptability, we relax the constrains on quasi-newton-based optimization procedure. We design ConvLSTM-based modules, where the gate units automatically preserve necessary long- and short-term information, facilitating the learning of optimized variables and their combinations. Furthermore, we design gate units to modulate the features fed to regularizers across different iterations, boosting their robustness against potential accumulated errors. Evaluations using PSNR and SSIM metrics reveal that our approach outperforms existing state-of-the-art methods, achieving superior reconstruction results across various sequences.