Model-based methods are widely used for reconstruction in compressed sensing (CS) magnetic resonance imaging (MRI), using priors to describe the images of interest. The reconstruction process is equivalent to solving a composite optimization problem. Accelerated proximal methods (APMs) are very popular approaches for such problems. This paper proposes a complex quasi-Newton proximal method (CQNPM) for the wavelet and total variation based CS MRI reconstruction. Compared with APMs, CQNPM requires fewer iterations to converge but needs to compute a more challenging proximal mapping called weighted proximal mapping (WPM). To make CQNPM more practical, we propose efficient methods to solve the related WPM. Numerical experiments demonstrate the effectiveness and efficiency of CQNPM.

翻译：基于模型的方法广泛用于压缩感知（CS）磁共振成像（MRI）中的图像重建，通过先验知识描述感兴趣图像。重建过程等价于求解复合优化问题。加速近端法（APMs）是处理此类问题的常用方法。本文提出一种基于小波和全变分的复数拟牛顿近端法（CQNPM）用于CS MRI重建。与APMs相比，CQNPM只需较少迭代次数即可收敛，但需计算更具挑战性的近端映射——加权近端映射（WPM）。为使CQNPM更具实用性，我们提出了求解相关WPM的高效方法。数值实验验证了CQNPM的有效性和高效性。