Muckley Matthew J, Noll Douglas C, Fessler Jeffrey A
IEEE Trans Med Imaging. 2015 Feb;34(2):578-88. doi: 10.1109/TMI.2014.2363034. Epub 2014 Oct 14.
Sparsity-promoting regularization is useful for combining compressed sensing assumptions with parallel MRI for reducing scan time while preserving image quality. Variable splitting algorithms are the current state-of-the-art algorithms for SENSE-type MR image reconstruction with sparsity-promoting regularization. These methods are very general and have been observed to work with almost any regularizer; however, the tuning of associated convergence parameters is a commonly-cited hindrance in their adoption. Conversely, majorize-minimize algorithms based on a single Lipschitz constant have been observed to be slow in shift-variant applications such as SENSE-type MR image reconstruction since the associated Lipschitz constants are loose bounds for the shift-variant behavior. This paper bridges the gap between the Lipschitz constant and the shift-variant aspects of SENSE-type MR imaging by introducing majorizing matrices in the range of the regularizer matrix. The proposed majorize-minimize methods (called BARISTA) converge faster than state-of-the-art variable splitting algorithms when combined with momentum acceleration and adaptive momentum restarting. Furthermore, the tuning parameters associated with the proposed methods are unitless convergence tolerances that are easier to choose than the constraint penalty parameters required by variable splitting algorithms.
促进稀疏性的正则化对于将压缩感知假设与并行MRI相结合以减少扫描时间同时保持图像质量很有用。变量分裂算法是用于具有促进稀疏性正则化的SENSE型MR图像重建的当前最先进算法。这些方法非常通用，并且已观察到几乎可以与任何正则化器一起使用；然而，相关收敛参数的调整是其应用中经常提到的障碍。相反，基于单个Lipschitz常数的最大化-最小化算法在诸如SENSE型MR图像重建等移位变体应用中被观察到速度较慢，因为相关的Lipschitz常数对于移位变体行为是宽松的界限。本文通过在正则化矩阵的范围内引入主化矩阵，弥合了SENSE型MR成像的Lipschitz常数和移位变体方面之间的差距。当与动量加速和自适应动量重启相结合时，所提出的最大化-最小化方法（称为BARISTA）比当前最先进的变量分裂算法收敛得更快。此外，与所提出方法相关的调整参数是无量纲的收敛容差，比变量分裂算法所需的约束惩罚参数更容易选择。
