Exact Solutions to Super Resolution on Semi-Algebraic Domains in Higher Dimensions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F17%3A00306534" target="_blank" >RIV/68407700:21230/17:00306534 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1109/TIT.2016.2619368" target="_blank" >http://dx.doi.org/10.1109/TIT.2016.2619368</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1109/TIT.2016.2619368" target="_blank" >10.1109/TIT.2016.2619368</a>
Alternative languages
Result language
angličtina
Original language name
Exact Solutions to Super Resolution on Semi-Algebraic Domains in Higher Dimensions
Original language description
We investigate the multi-dimensional super resolution problem on closed semi-algebraic domains for various sampling schemes such as Fourier or moments. We present a new semidefinite programming (SDP) formulation of the ℓ1-minimization in the space of Radon measures in the multi-dimensional frame on semi-algebraic sets. While standard approaches have focused on SDP relaxations of the dual program (a popular approach is based on Gram matrix representations), this paper introduces an exact formulation of the primal ℓ1-minimization exact recovery problem of super resolution that unleashes standard techniques (such as moment-sum-of-squares hierarchies) to overcome intrinsic limitations of previous works in the literature. Notably, we show that one can exactly solve the super resolution problem in dimension greater than 2 and for a large family of domains described by semi-algebraic sets.
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE Transactions on Information Theory
ISSN
0018-9448
e-ISSN
1557-9654
Volume of the periodical
63
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
621-630
UT code for WoS article
000391740000036
EID of the result in the Scopus database
2-s2.0-85008477501