Maxiset point of view for signal detection in inverse problems

TL;DR

This paper extends the maxiset paradigm from function estimation to signal detection in inverse problems, introducing a robustified version that allows for tail condition analysis and comparison of testing procedures.

Contribution

It develops a new maxiset framework for signal detection in inverse problems, including tail conditions and comparison of direct and indirect tests.

Findings

Introduction of a robustified maxiset framework

Comparison of direct and indirect testing procedures

Tail conditions characterization for signals

Abstract

This paper extends the successful maxiset paradigm from function estimation to signal detection in inverse problems. In this context, the maxisets do not have the same shape compared to the classical estimation framework. Nevertheless, we introduce a robustified version of these maxisets, allowing to exhibit tail conditions on the signals of interest. Under this novel paradigm we are able to compare direct and indirect testing procedures.