Graph Recovery from Incomplete Moment Information
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Graph Recovery from Incomplete Moment Information
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Constructive Approximation
ISSN
0176-4276
e-ISSN
1432-0940
Volume of the periodical
56
Issue of the periodical within the volume
1
Country of publishing house
CH - SWITZERLAND
Number of pages
23
Pages from-to
165-187
UT code for WoS article
000761894400001
EID of the result in the Scopus database
2-s2.0-85125241284