Model-based methods are widely used for reconstruction in compressed sensing (CS) magnetic resonance imaging (MRI), using regularizers 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磁共振成像中的图像重建，通过正则化项描述感兴趣图像的先验特征。该重建过程等价于求解一个复合优化问题。加速近端法是解决此类问题的常用方法。本文提出了一种基于小波变换与全变分的复拟牛顿近端法用于压缩感知磁共振成像重建。与加速近端法相比，复拟牛顿近端法收敛所需迭代次数更少，但需要计算更复杂的加权近端映射。为使复拟牛顿近端法更具实用性，我们提出了求解相关加权近端映射的高效方法。数值实验验证了复拟牛顿近端法的有效性与高效性。