Superresolution Rates in Prokhorov Metric

Abstract

Consider the problem of recovering a probability measure supported by a compact subsetUof ℝ^mwhen the available measurements concern only some of its Ф-moments (Ф being an ℝ^kvalued continuous function onU). When thetrueФ-momentclies on the boundary of the convex hull of Ф(U), generalizing the results of [10], we construct asmallsetR_α,δ(∊)such that any probability measureμsatisfyingisalmostconcentrated onR_α,δ(∊). When Ф is a pointwiseT-system (extension ofT-systems), the study of the setR_α,δ(∊)leads to the evaluation of the Prokhorov radius of the set.