Robust plug-and-play methods for highly accelerated non-Cartesian MRI reconstruction

Achieving high-quality Magnetic Resonance Imaging (MRI) reconstruction at accelerated acquisition rates remains challenging due to the inherent ill-posed nature of the inverse problem. Traditional Compressed Sensing (CS) methods, while robust across varying acquisition settings, struggle to maintain good reconstruction quality at high acceleration factors ($\ge$ 8). Recent advances in deep learning have improved reconstruction quality, but purely data-driven methods are prone to overfitting and hallucination effects, notably when the acquisition setting is varying. Plug-and-Play (PnP) approaches have been proposed to mitigate the pitfalls of both frameworks. In a nutshell, PnP algorithms amount to replacing suboptimal handcrafted CS priors with powerful denoising deep neural network (DNNs). However, in MRI reconstruction, existing PnP methods often yield suboptimal results due to instabilities in the proximal gradient descent (PGD) schemes and the lack of curated, noiseless datasets for training robust denoisers. In this work, we propose a fully unsupervised preprocessing pipeline to generate clean, noiseless complex MRI signals from multicoil data, enabling training of a high-performance denoising DNN. Furthermore, we introduce an annealed Half-Quadratic Splitting (HQS) algorithm to address the instability issues, leading to significant improvements over existing PnP algorithms. When combined with preconditioning techniques, our approach achieves state-of-the-art results, providing a robust and efficient solution for high-quality MRI reconstruction.