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Minimax detection of localized signals in statistical inverse problems

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Munk,  Axel
Research Group of Statistical Inverse Problems in Biophysics, Max Planck Institute for Multidisciplinary Sciences, Max Planck Society;

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Citation

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.


Cite as: https://hdl.handle.net/21.11116/0000-000D-BC16-7
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.