Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

Minimax detection of localized signals in statistical inverse problems


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

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available

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
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.