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- Title
Minimax detection of localized signals in statistical inverse problems.
- Authors
Pohlmann, Markus; Werner, Frank; Munk, Axel
- 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.
- Subjects
INVERSE problems; SIGNAL detection; DECONVOLUTION (Mathematics); NUMERICAL differentiation; WHITE noise; RANDOM noise theory; RADON transforms
- Publication
Information & Inference: A Journal of the IMA, 2023, Vol 12, Issue 3, p2160
- ISSN
2049-8764
- Publication type
Article
- DOI
10.1093/imaiai/iaad026