Minimax signal detection in ill-posed inverse problems

Abstract

Saint Petersburg Electrotechnical University, University of Cyprus and Saint Petersburg University of Information Technologies, Mechanics and Optics Ill-posed inverse problems arise in various scientific fields. We consider the signal detection problem for mildly, severely and extremely ill-posed inverse problems with lq -ellipsoids (bodies), q ε (0, 2], for Sobolev, analytic and generalized analytic classes of functions under the Gaussian white noise model. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived tests are, often, nonadaptive. Minimax rate-optimal adaptive tests of rather simple structure are also constructed. © Institute of Mathematical Statistics, 2012.