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 on reconstructing non-Cartesian MRI data demonstrate the effectiveness and efficiency of CQNPM.

翻译：基于模型的方法广泛应用于压缩感知（CS）磁共振成像（MRI）的重建，通过正则化项描述感兴趣图像。重建过程等价于求解一个复合优化问题。加速近端方法（APMs）是处理此类问题的常用方法。本文提出一种基于小波和总变差的复拟牛顿近端方法（CQNPM），用于CS MRI重建。与APMs相比，CQNPM需要更少的迭代次数即可收敛，但需计算难度更大的近端映射——加权近端映射（WPM）。为提升CQNPM的实用性，我们提出了求解相关WPM的高效方法。针对非笛卡尔MRI数据重建的数值实验验证了CQNPM的有效性与高效性。