Superresolution Rates in Prokhorov Metric

Abstract

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