Minimax detection of localized signals in statistical inverse problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-04-27 DOI:10.1093/imaiai/iaad026

Markus Pohlmann, Frank Werner, Axel Munk

引用次数: 0

Abstract

Abstract We investigate minimax testing for detecting local signals or linear combinations of such signals when only indirect data are available. Naturally, in the presence of noise, signals that are too small cannot be reliably detected. In a Gaussian white noise model, we discuss upper and lower bounds for the minimal size of the signal such that testing with small error probabilities is possible. In certain situations we are able to characterize the asymptotic minimax detection boundary. Our results are applied to inverse problems such as numerical differentiation, deconvolution and the inversion of the Radon transform.

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统计逆问题中局域信号的极大极小检测

摘要:我们研究了在只有间接数据可用的情况下检测局部信号或这些信号的线性组合的极大极小检验。当然，在噪声存在的情况下，太小的信号不能被可靠地检测到。在高斯白噪声模型中，我们讨论了信号最小尺寸的上界和下界，使小误差概率的测试成为可能。在某些情况下，我们能够描述渐近极大极小检测边界。我们的结果应用于数值微分、反卷积和Radon变换反演等反问题。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.