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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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