Superresolution Rates in Prokhorov Metric
- 1 April 1996
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 48 (2) , 316-329
- https://doi.org/10.4153/cjm-1996-017-9
Abstract
Consider 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.Keywords
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