阈值
操作员(生物学)
数学
趋同(经济学)
希尔伯特空间
应用数学
投影(关系代数)
迭代法
线性地图
收敛速度
算法
常量(计算机编程)
数学优化
计算机科学
图像(数学)
数学分析
人工智能
纯数学
基因
频道(广播)
抑制因子
转录因子
经济
化学
生物化学
程序设计语言
经济增长
计算机网络
作者
Kristian Bredies,Dirk A. Lorenz
摘要
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized gradient methods and present a new convergence analysis. As main result we show that the algorithm converges with linear rate as soon as the underlying operator satisfies the so-called finite basis injectivity property or the minimizer possesses a so-called strict sparsity pattern. Moreover it is shown that the constants can be calculated explicitly in special cases (i.e. for compact operators). Furthermore, the techniques also can be used to establish linear convergence for related methods such as the iterative thresholding algorithm for joint sparsity and the accelerated gradient projection method.
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