In compressed sensing (CS) MRI, model-based methods are pivotal to achieving accurate reconstruction. One of the main challenges in model-based methods is finding an effective prior to describe the statistical distribution of the target image. Plug-and-Play (PnP) and REgularization by Denoising (RED) are two general frameworks that use denoisers as the prior. While PnP/RED methods with convolutional neural networks (CNNs) based denoisers outperform classical hand-crafted priors in CS MRI, their convergence theory relies on assumptions that do not hold for practical CNNs. The recently developed gradient-driven denoisers offer a framework that bridges the gap between practical performance and theoretical guarantees. However, the numerical solvers for the associated minimization problem remain slow for CS MRI reconstruction. This paper proposes a complex quasi-Newton proximal method that achieves faster convergence than existing approaches. To address the complex domain in CS MRI, we propose a modified Hessian estimation method that guarantees Hermitian positive definiteness. Furthermore, we provide a rigorous convergence analysis of the proposed method for nonconvex settings. Numerical experiments on both Cartesian and non-Cartesian sampling trajectories demonstrate the effectiveness and efficiency of our approach.

翻译：在压缩感知(CS)MRI中，基于模型的方法对于实现精确重建至关重要。基于模型方法的主要挑战之一在于寻找有效的先验来描述目标图像的统计分布。即插即用(PnP)和降噪正则化(RED)是两种使用降噪器作为先验的通用框架。虽然采用基于卷积神经网络(CNN)降噪器的PnP/RED方法在CS MRI中优于经典手工设计的先验方法，但其收敛理论依赖于对实际CNN不成立的假设。最近发展的梯度驱动降噪器提供了一个弥合实际性能与理论保证之间差距的框架。然而，对于CS MRI重建，相关最小化问题的数值求解器仍然较慢。本文提出了一种复拟牛顿近端方法，其收敛速度优于现有方法。针对CS MRI中的复数域问题，我们提出了一种改进的Hessian估计方法，确保埃尔米特正定性。此外，我们对所提方法在非凸设置下进行了严格的收敛性分析。在笛卡尔和非笛卡尔采样轨迹上的数值实验证明了我们方法的有效性和高效性。