Convergence Rates for Linear Inverse Problems in the Presence of an Additive Normal Noise

被引：13
|
作者：
Hofinger, Andreas [1 ]
Pikkarainen, Hanna K. [1 ]
机构：
[1] Austrian Acad Sci, Johann Radon Inst Computat & Appl Math, A-4040 Linz, Austria
来源：
STOCHASTIC ANALYSIS AND APPLICATIONS | 2009年 / 27卷 / 02期
基金：
美国国家科学基金会;
关键词：
Convergence rates; Linear inverse problems; Parameter choice rules; Statistical inversion theories; OPERATOR-EQUATIONS;
D O I：
10.1080/07362990802558295
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we examine a finite-dimensional linear inverse problem where the measurements are disturbed by an additive normal noise. The problem is solved both in the frequentist and in the Bayesian frameworks. Convergence of the used methods when the noise tends to zero is studied in the Ky Fan metric. The obtained convergence rate results and parameter choice rules are of a similar structure for both approaches.
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页码：240 / 257
页数：18
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