Almost Sure Convergence of the Kaczmarz Algorithm with Random Measurements

被引：36
|
作者：
Chen, Xuemei [1 ]
Powell, Alexander M. [1 ]
机构：
[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2012年 / 18卷 / 06期
基金：
美国国家科学基金会;
关键词：
Almost sure convergence; Convergence rates; Kaczmarz algorithm; EXPONENTIAL CONVERGENCE; HILBERT-SPACE; SYSTEMS;
D O I：
10.1007/s00041-012-9237-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Kaczmarz algorithm is an iterative method for reconstructing a signal xaa"e (d) from an overcomplete collection of linear measurements y (n) =aOE (c) x,phi (n) >, na parts per thousand yen1. We prove quantitative bounds on the rate of almost sure exponential convergence in the Kaczmarz algorithm for suitable classes of random measurement vectors . Refined convergence results are given for the special case when each phi (n) has i.i.d. Gaussian entries and, more generally, when each phi (n) /ayen phi (n) ayen is uniformly distributed on . This work on almost sure convergence complements the mean squared error analysis of Strohmer and Vershynin for randomized versions of the Kaczmarz algorithm.
引用
收藏
页码：1195 / 1214
页数：20
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