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

Wahab, Abdul1 ; Rasheed, Amer1 ; Nawaz, Rab2 ; Anjum, Saman1
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, Tome 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
Wahab, Abdul 1 ; Rasheed, Amer 1 ; Nawaz, Rab 2 ; Anjum, Saman 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 
@article{CRMATH_2014__352_11_917_0,
     author = {Wahab, Abdul and Rasheed, Amer and Nawaz, Rab and Anjum, Saman},
     title = {Localization of extended current source with finite frequencies},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {917--921},
     publisher = {Elsevier},
     volume = {352},
     number = {11},
     year = {2014},
     doi = {10.1016/j.crma.2014.09.009},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2014.09.009/}
}
TY  - JOUR
AU  - Wahab, Abdul
AU  - Rasheed, Amer
AU  - Nawaz, Rab
AU  - Anjum, Saman
TI  - Localization of extended current source with finite frequencies
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 917
EP  - 921
VL  - 352
IS  - 11
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2014.09.009/
DO  - 10.1016/j.crma.2014.09.009
LA  - en
ID  - CRMATH_2014__352_11_917_0
ER  - 
%0 Journal Article
%A Wahab, Abdul
%A Rasheed, Amer
%A Nawaz, Rab
%A Anjum, Saman
%T Localization of extended current source with finite frequencies
%J Comptes Rendus. Mathématique
%D 2014
%P 917-921
%V 352
%N 11
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2014.09.009/
%R 10.1016/j.crma.2014.09.009
%G en
%F CRMATH_2014__352_11_917_0
Wahab, Abdul; Rasheed, Amer; Nawaz, Rab; Anjum, Saman. Localization of extended current source with finite frequencies. Comptes Rendus. Mathématique, Tome 352 (2014) no. 11, pp. 917-921. doi : 10.1016/j.crma.2014.09.009. http://www.numdam.org/articles/10.1016/j.crma.2014.09.009/

[1] Ammari, H. Introduction to Mathematics of Emerging Biomedical Imaging, Mathématiques et Applications, vol. 62, Springer-Verlag, Berlin, 2008

[2] Ammari, H.; Bretin, E.; Garnier, J.; Wahab, A. Time reversal in attenuating acoustic media, Mathematical and Statistical Methods for Imaging, Contemporary Mathematics, vol. 548, American Mathematical Society, Providence, USA, 2011, pp. 151-163

[3] Ammari, H.; Bretin, E.; Garnier, J.; Wahab, A. Noise source localization in an attenuating medium, SIAM J. Appl. Math., Volume 72 (2012), pp. 317-336

[4] Ammari, H.; Bretin, E.; Jugnon, V.; Wahab, A. Photoacoustic imaging for attenuating acoustic media, Mathematical Modeling in Biomedical Imaging II, Lecture Notes in Mathematics, vol. 2035, Springer-Verlag, Berlin, 2012, pp. 57-84

[5] Ammari, H.; Bretin, E.; Garnier, J.; Wahab, A. Time reversal algorithms in viscoelastic media, Eur. J. Appl. Math., Volume 24 (2013), pp. 565-600

[6] Ammari, H.; Garnier, J.; Jing, W.; Kang, H.; Lim, M.; Sølna, K.; Wang, H. Mathematical and Statistical Methods for Multistatic Imaging, Lecture Notes in Mathematics, vol. 2098, Springer, 2014

[7] Beck, A.; Teboulle, M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci., Volume 2 (2009), pp. 183-202

[8] Carminati, R.; Pierrat, R.; de Rosny, J.; Fink, M. Theory of the time reversal cavity for electromagnetic fields, Opt. Lett., Volume 32 (2007), pp. 3107-3109

[9] Chen, J.; Chen, Z.; Huang, G. Reverse time migration for extended obstacles: electromagnetic waves, Inverse Probl., Volume 29 (2013) (Paper ID. 085006)

[10] Fink, M. Time reversed acoustics, Phys. Today, Volume 50 (1997) no. 3, pp. 34-40

[11] Fouque, J.P.; Garnier, J.; Papanicolaou, G.; Sølna, K. Wave Propagation and Time Reversal in Randomly Layered Media, Springer, 2007

[12] Gdoura, S.; Wahab, A.; Lesselier, D. Electromagnetic time reversal and scattering by a small dielectric inclusion, J. Phys. Conf. Ser., Volume 386 (2012) (Paper ID. 012010)

[13] Valdivia, N.P. Electromagnetic source identification using multiple frequency information, Inverse Probl., Volume 28 (2012) (Paper ID. 115002)

[14] Wahab, A.; Rasheed, A.; Hayat, T.; Nawaz, R. Electromagnetic time reversal algorithms and localization in lossy dielectric media, Commun. Theor. Phys. (2014) (forthcoming)

Cité par Sources :