Minimax nonparametric testing in a problem related to the Radon transform

TL;DR

This paper investigates the problem of detecting a 2D function from noisy line integral observations, deriving minimax error bounds and proposing both non-adaptive and adaptive optimal tests.

Contribution

It introduces a new minimax framework for the Radon transform detection problem and constructs a simple, adaptive test achieving optimal rates.

Findings

Derived minimax error asymptotics for the detection problem.

Constructed a non-adaptive test with optimal error rates.

Developed a simple, adaptive test that is rate-optimal.

Abstract

We consider the detection problem of a two-dimensional function from noisy observations of its integrals over lines. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived tests are non-adaptive. We also construct a minimax rate-optimal adaptive test of rather simple structure.