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:以模型为基础的方法广泛用于重建压缩遥感磁共振成像(MRI),使用前缀来描述感兴趣的图像。重建过程相当于解决一个复合优化问题。加速准方法(APMs)是处理这类问题的非常普遍的办法。本文件建议对波子采用复杂的准牛顿准准成像法(CQNPM)和基于总变异的CS磁共振成像(CS MRI)重建。与杀伤人员地雷相比,CQNPM需要较少的迭代来聚合,但需要计算出更具有挑战性的准成像图,称为加权准成像图(WPM)。为了使CQNPM更实用,我们提出了解决相关WPM的有效方法。数字实验显示了CQNPM的效益和效率。</s>