论文标题
通过重球kaczmarz在线信号恢复
Online Signal Recovery via Heavy Ball Kaczmarz
论文作者
论文摘要
从一系列线性测量中恢复信号$ x^\ ast \ in \ mathbb {r}^n $，在计算机断层扫描和压缩传感等领域中是一个重要的问题。在这项工作中，我们考虑了一个在线环境，其中测量是从某些来源分布中逐一采样的。我们建议使用Kaczmarz方法的变体和其他重球动量术语来解决此问题。最近的工作是解决线性方程式系统的流行技术，最近的工作表明，当应用于随机测量模型时，Kaczmarz方法也享有线性收敛性，但是当连续测量高度相干时，收敛可能会减慢。我们证明，当数据连贯时，加重球动量的添加可能会加速Kaczmarz方法的收敛性，并提供对该方法的理论分析，最终在线性收敛保证中为广泛的源分布提供了线性保证。
Recovering a signal $x^\ast \in \mathbb{R}^n$ from a sequence of linear measurements is an important problem in areas such as computerized tomography and compressed sensing. In this work, we consider an online setting in which measurements are sampled one-by-one from some source distribution. We propose solving this problem with a variant of the Kaczmarz method with an additional heavy ball momentum term. A popular technique for solving systems of linear equations, recent work has shown that the Kaczmarz method also enjoys linear convergence when applied to random measurement models, however convergence may be slowed when successive measurements are highly coherent. We demonstrate that the addition of heavy ball momentum may accelerate the convergence of the Kaczmarz method when data is coherent, and provide a theoretical analysis of the method culminating in a linear convergence guarantee for a wide class of source distributions.
