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  Minimax detection of localized signals in statistical inverse problems

Pohlmann, M., Werner, F., & Munk, A. (2023). Minimax detection of localized signals in statistical inverse problems. Information and Inference, 12(3), 2160-2196. doi:10.1093/imaiai/iaad026.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000D-BC16-7 Version Permalink: https://hdl.handle.net/21.11116/0000-000D-BC17-6
Genre: Journal Article

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iaad026.pdf (Publisher version), 985KB
 
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 Creators:
Pohlmann, Markus, Author
Werner, Frank, Author
Munk, Axel1, Author           
Affiliations:
1Research Group of Statistical Inverse Problems in Biophysics, Max Planck Institute for Multidisciplinary Sciences, Max Planck Society, ou_3350280              

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 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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Language(s): eng - English
 Dates: 2023-07-182023-09
 Publication Status: Issued
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 Rev. Type: Peer
 Identifiers: DOI: 10.1093/imaiai/iaad026
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Project name : This work was supported by the German Research Foundation [Research Training Group 2088 to M. P., Cluster of Excellence 2067 to A.M., WE 6204/4-1 to F.W.].
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Title: Information and Inference
  Other : Information and Inference: A Journal of the IMA
Source Genre: Journal
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Publ. Info: Oxford : Oxford University Press
Pages: - Volume / Issue: 12 (3) Sequence Number: - Start / End Page: 2160 - 2196 Identifier: Other: ISSN
CoNE: https://pure.mpg.de/cone/journals/resource/2049-8772