Injectivity and weak*-to-weak continuity suffice for convergence rates in l1-regularization

被引：11

作者：

Flemming, Jens ^{[1
]}

Gerth, Daniel ^{[1
]}

机构：

[1] Tech Univ Chemnitz, Fac Math, D-09107 Chemnitz, Germany

来源：

JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2018年 / 26卷 / 01期

关键词：

Linear ill-posed problem; sparsity promoting regularization; Tikhonov regularization; source condition; variational source condition; convergence rates; REGULARIZATION;

D O I：

10.1515/jiip-2017-0008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the convergence rate of l(1)-regularization for linear ill-posed equations is always O(delta) if the exact solution is sparse and if the considered operator is injective and weak*-to-weak continuous. Under the same assumptions convergence rates in case of non-sparse solutions are proven. The results base on the fact that certain source-type conditions used in the literature for proving convergence rates are automatically satisfied.

引用

页码：85 / 94

页数：10

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