A statistical approach to target detection and localization in the presence of noise

Waves in Random and Complex Media

Volumn 22, Issue 1, 2012, Pages 40-65

  Ammari, Habib ^a   Garnier, Josselin ^b   Slna, Knut ^c  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARRAY IMAGING; ARRAY RESPONSE; DETECTION AND LOCALIZATION; FALSE ALARM RATE; LOCALIZATION ERRORS; MEASUREMENT NOISE; NOISY ENVIRONMENT; POINT REFLECTOR; RESPONSE MATRICES; SINGULAR VALUES; STANDARD DEVIATION; STATISTICAL APPROACH;

SENSOR ARRAYS;

REFLECTION;

EID: 79961232362     PISSN: 17455030     EISSN: 17455049     Source Type: Journal    
DOI: 10.1080/17455030.2010.532518     Document Type: Article

References (26)

1. A. Aubry and A. Derode, Random matrix theory applied to acoustic backscattering and imaging in complex media, Phys. Rev. Lett. 102 (2009), 084301.
2. A. Aubry and A. Derode, Singular value distribution of the propagation matrix in random scattering media, Waves Random Complex Media 20 (2010), pp. 333-363.
3. M.L. Mehta, Random Matrices, Academic Press, San Diego, 1991.
4. R. Adler and J. Taylor, Random Fields and Geometry, Springer, New York, 2007.
5. G. Casella and R.L. Berger, Statistical Inference, Duxbury Press, Pacific Grove, 2002.
6. N. Bleistein, J. Cohen, and J.S. Stockwell Jr, Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion, Springer, New York, 2001.
7. L. Borcea, G. Papanicolaou, C. Tsogka, and J. Berryman, Imaging and time reversal in random media, Inverse Problems 18 (2002), pp. 1247-1279. (Pubitemid 35208366)
8. A.J. Devaney, Time reversal imaging of obscured targets from multistatic data, IEEE Trans. Antennas Propagat. 523 (2005), pp. 1600-1610. (Pubitemid 40715023)
9. H. Lev-Ari and A.J. Devaney, The time-reversal technique reinterpreted: subspace based signal processing for multi-static target location, in Proceedings of the 1st IEEE Sensor Array and Multichannel Signal Processing Workshop, IEEE, Cambridge, MA, 2000, pp. 509-513.
10. C. Prada, S. Manneville, D. Spolianski, and M. Fink, Decomposition of the time reversal operator: detection and selective focusing on two scatterers, J. Acoust. Soc. Am. 99 (1996), pp. 2067-2076.
11. A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic Press, New York, 1978.
12. J.-P. Fouque, J. Garnier, G. Papanicolaou, and K. Sølna, Wave Propagation and Time Reversal in Randomly Layered Media, Springer, New York, 2007.
13. E. Akkermans and G. Montambaux, Coherent Multiple Scattering in Disordered Media, in Waves and Imaging Through Complex Media, P. Sebbah, ed., Kluwer, Dordrecht, 2001, pp. 29-52 (condmat/0104013).
14. D. Féral and S. Péché , The largest eigenvalue of rank one deformation of large Wigner matrices, Commun. Math. Phys. 272 (2007), pp. 185-228.
15. M. Capitaine, C. Donati-Martin, and D. Fé ral, The largest eigenvalue of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations, Ann. Probab. 37 (2009), pp. 1-47.
16. A. Gut, Probability: A Graduate Course, Springer-Verlag, New-York, 2005.
17. R.A. DeVore and G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993.
18. J. Bayk, R. Buckingham, and J. DiFranco, Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function, Commun. Math. Phys. 280 (2008), pp. 463-397.
19. A. Aubry and A. Derode, Detection and imaging in a random medium: A matrix method to overcome multiple scattering and aberration, J. Appl. Phys. 106 (2009), 044903.
20. M. Born and E. Wolf, Principles of Optics, Academic Press, New York, 1970.
21. L. Borcea, G. Papanicolaou, and F.G. Vasquez, Edge illumination and imaging of extended reflectors, SIAM J. Imaging Sci. 1 (2008), pp. 75-114.
22. W. Bryc, A. Dembo, and T. Jiang, Spectral measure of large random Hankel, Markov and Toeplitz matrices, Ann. Probab. 34 (2006), pp. 1-38. (Pubitemid 43409918)
23. H. Ammari and H. Kang, Reconstruction of Small Inhomogeneities from Boundary Measurements, Lecture Notes in Mathematics, Vol. 1846, Springer-Verlag, Berlin, 2004.
24. H. Ammari, H. Kang, H. Lee, and W.K. Park, Asymptotic imaging of perfectly conducting cracks, SIAM J. Sci. Comput. 32 (2010), pp. 894-922.
25. M. Capitaine, C. Donati-Martin, and D. Fé ral, Central limit theorems for eigenvalues of deformations of Wigner matrices, preprint (2009), submitted for publication. Available at http://arxiv.org/abs/0903.4740v1.
26. K.J. Worsley, Local maxima and the expected Euler characteristic of excursion sets of 2, F, and t fields, Adv. Appl. Probab. 26 (1994), pp. 13-42.