Exact Solutions to Super Resolution on Semi-Algebraic Domains in Higher Dimensions

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Exact Solutions to Super Resolution on Semi-Algebraic Domains in Higher Dimensions

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Exact Solutions to Super Resolution on Semi-Algebraic Domains in Higher Dimensions

Popis výsledku anglicky

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.

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

2017

Kód důvěrnosti údajů

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

Název periodika

IEEE Transactions on Information Theory

ISSN

0018-9448

e-ISSN

1557-9654

Svazek periodika

63

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

621-630

Kód UT WoS článku

000391740000036

EID výsledku v databázi Scopus

2-s2.0-85008477501