无约束白噪声下一般线性逆问题的无噪声正则化

IF 2.1 3区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-05-25 DOI:10.1137/22m1506675

Tim Jahn

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引用次数: 0

摘要

在本文中，我们通过应用(改进的)启发式差异原理解决了在不知道噪声水平和噪声分布的情况下的一般统计逆问题。在此基础上，通过引入辅助离散维数并自适应选择辅助离散维数来控制无界(非高斯)噪声。首先给出了完全任意紧正算子的收敛性和地面解。然后在一个特定的类贝叶斯环境中量化了达到最优收敛速率的不确定性。最后进行了数值实验。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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.

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来源期刊

Siam-Asa Journal on Uncertainty Quantification Mathematics-Statistics and Probability

CiteScore

3.70

自引率

0.00%

发文量

期刊介绍： SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.