Graph Recovery from Incomplete Moment Information

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00359324" target="_blank" >RIV/68407700:21230/22:00359324 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00365-022-09563-8" target="_blank" >https://doi.org/10.1007/s00365-022-09563-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00365-022-09563-8" target="_blank" >10.1007/s00365-022-09563-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Graph Recovery from Incomplete Moment Information

Popis výsledku v původním jazyce

We investigate a class of moment problems, namely recovering a measure supported on the graph of a function from partial knowledge of its moments, as, for instance, in some problems of optimal transport or density estimation. We show that the sole knowledge of first degree moments of the function, namely linear measurements, is sufficient to obtain asymptotically all the other moments by solving a hierarchy of semidefinite relaxations (viewed as moment matrix completion problems) with a specific sparsity-inducing criterion related to a weighted l(1)-norm of the moment sequence of the measure. The resulting sequence of optimal solutions converges to the whole moment sequence of the measure which is shown to be the unique optimal solution of a certain infinite-dimensional linear optimization problem (LP). Then one may recover the function by a recent extraction algorithm based on the Christoffel-Darboux kernel associated with the measure. Finally, the support of such a measure supported on a graph is a meager, very thin (hence sparse) set. Therefore, the LP on measures with this sparsity-inducing criterion can be interpreted as an analogue for infinite-dimensional signals of the LP in super-resolution for (sparse) atomic signals.

Název v anglickém jazyce

Graph Recovery from Incomplete Moment Information

Popis výsledku anglicky

We investigate a class of moment problems, namely recovering a measure supported on the graph of a function from partial knowledge of its moments, as, for instance, in some problems of optimal transport or density estimation. We show that the sole knowledge of first degree moments of the function, namely linear measurements, is sufficient to obtain asymptotically all the other moments by solving a hierarchy of semidefinite relaxations (viewed as moment matrix completion problems) with a specific sparsity-inducing criterion related to a weighted l(1)-norm of the moment sequence of the measure. The resulting sequence of optimal solutions converges to the whole moment sequence of the measure which is shown to be the unique optimal solution of a certain infinite-dimensional linear optimization problem (LP). Then one may recover the function by a recent extraction algorithm based on the Christoffel-Darboux kernel associated with the measure. Finally, the support of such a measure supported on a graph is a meager, very thin (hence sparse) set. Therefore, the LP on measures with this sparsity-inducing criterion can be interpreted as an analogue for infinite-dimensional signals of the LP in super-resolution for (sparse) atomic signals.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Constructive Approximation

ISSN

0176-4276

e-ISSN

1432-0940

Svazek periodika

56

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

23

Strana od-do

165-187

Kód UT WoS článku

000761894400001

EID výsledku v databázi Scopus

2-s2.0-85125241284