Comptes Rendus
no. 11
Partial differential equations/Numerical analysis
Localization of extended current source with finite frequencies
[Localisation de sources étendues à partir d'un nombre fini de fréquences]

Présenté par : Philippe G. Ciarlet

Abdul Wahab1 ; Amer Rasheed1 ; Rab Nawaz2 ; Saman Anjum1
1 COMSATS Institute of Information Technology, G. T. Road, 47040, Wah Cantt., Pakistan
2 COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 44000, Islamabad, Pakistan
Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 917-921.

Dans cette note, nous présentons un algorithme de conjugaison de phase pour la reconstruction d'une source étendue à partir de mesures de champ électrique obtenues pour un ensemble fini de fréquences. Nous commençons par introduire et analyser une fonctionnelle d'imagerie à partir de mesures obtenues pour un intervalle de fréquences. Ensuite, nous proposons une régularisation l1 d'une telle fonctionnelle d'imagerie afin d'éliminer les artefacts dus à l'aspect discret et limité des fréquences utilisées.

A phase conjugation algorithm for localizing the spatial support of an extended radiating current source from boundary measurements of the electric field over a finite set of frequencies is presented. An imaging function using a full frequency bandwidth is established and analyzed. It is subsequently adopted to the case of finite frequency measurements. Finally, the algorithm is blended with l1-regularization in order to deal with the artifacts associated with finite frequency data.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.009
Abdul Wahab 1 ; Amer Rasheed 1 ; Rab Nawaz 2 ; Saman Anjum 1

1 COMSATS Institute of Information Technology, G. T. Road, 47040, Wah Cantt., Pakistan
2 COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 44000, Islamabad, Pakistan 
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Abdul Wahab; Amer Rasheed; Rab Nawaz; Saman Anjum. Localization of extended current source with finite frequencies. Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 917-921. doi : 10.1016/j.crma.2014.09.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.009/

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