Noise Level Free Regularization of General Linear Inverse Problems under Unconstrained White Noise

Tim Jahn

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Noise Level Free Regularization of General Linear Inverse Problems under Unconstrained White Noise

机译：无约束白噪声下一般线性逆问题的无噪声级正则化

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In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian) noise is controlled via introducing an auxiliary discretization dimension and choosing it in an adaptive fashion. We first show convergence for completely arbitrary compact forward operator and ground solution. Then the uncertainty of reaching the optimal convergence rate is quantified in a specific Bayesian-like environment. We conclude with numerical experiments.

机译：在这个报告中我们解决一个通用的统计反问题在缺乏的知识噪声和噪声分布通过应用启发式(修改)差异原则。(非高斯噪声)是通过控制的引入一个辅助离散化维度并以一种自适应的方式选择。显示收敛完全任意的紧凑运营商和地面的解决方案。不确定性达到最优的收敛率是在特定Bayesian-like量化环境。实验。

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来源
《SIAM/ASA Journal on Uncertainty Quantification》 |2023年第2期|591-615|共25页
作者
Tim Jahn;
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作者单位

Institute for Numerical Simulation, University of Bonn, 53115 Bonn, Germany;

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原文格式 PDF
正文语种英语
中图分类计量学;
关键词
statistical inverse problems; heuristic discrepancy principle; unknown noise level; convergence;

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Noise Level Free Regularization of General Linear Inverse Problems under Unconstrained White Noise

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