论文标题
关于随机原始二元算法的收敛和采样及其在平行MRI重建中的应用
On the convergence and sampling of randomized primal-dual algorithms and their application to parallel MRI reconstruction
论文作者
论文摘要
随机原始双重杂交梯度（SPDHG）是Chambolle等人提出的算法。 （2018）有效地解决了一系列非平滑大规模优化问题。在本文中，我们为其理论基础做出了贡献，并证明了其几乎确定的凸照，但既不一定强烈凸面也不是光滑的功能，也不是任何随机采样。此外，我们研究了SPDHG用于并行磁共振成像重建，其中每次迭代中都会随机选择来自不同线圈的数据。我们使用广泛的随机采样方法应用SPDHG，并比较其在各种设置中的性能，包括迷你批量大小和步长参数。我们表明，采样可以显着影响SPDHG的收敛速度，并且在许多情况下，可以确定最佳抽样。
Stochastic Primal-Dual Hybrid Gradient (SPDHG) is an algorithm proposed by Chambolle et al. (2018) to efficiently solve a wide class of nonsmooth large-scale optimization problems. In this paper we contribute to its theoretical foundations and prove its almost sure convergence for convex but neither necessarily strongly convex nor smooth functionals, as well as for any random sampling. In addition, we study SPDHG for parallel Magnetic Resonance Imaging reconstruction, where data from different coils are randomly selected at each iteration. We apply SPDHG using a wide range of random sampling methods and compare its performance across a range of settings, including mini-batch size and step size parameters. We show that the sampling can significantly affect the convergence speed of SPDHG and for many cases an optimal sampling can be identified.
