Imaging schemes for perfectly conducting cracks

SIAM Journal on Applied Mathematics

Volumn 71, Issue 1, 2011, Pages 68-91

  Ammari, Habib ^a   Garnier, Josselin ^b   Kang, Hyonbae ^c   Park, Won Kwang ^d   Sølna, Knut ^e  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^c Inha University   (South Korea)

^d Kookmin University   (South Korea)

^e UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Asymptotic imaging; Crack detection; Hypothesis testing; Imaging algorithms; Measurement noise; Probability of detection; Random matrices

Indexed keywords

ASYMPTOTIC IMAGING; HYPOTHESIS TESTING; IMAGING ALGORITHMS; MEASUREMENT NOISE; PROBABILITY OF DETECTION; RANDOM MATRICES;

ALGORITHMS; ASYMPTOTIC ANALYSIS; SIGNAL DETECTION; SIGNAL RECEIVERS; SIGNAL TO NOISE RATIO;

CRACK DETECTION;

EID: 79952327149     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/100800130     Document Type: Article

References (22)

1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.
2. N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators on Hilbert Spaces, Vol. 1, Dover, New York, 1993.
3. H. Ammari, H. Kang, and H. Lee, Layer Potential Techniques in Spectral Analysis, Math. Surveys Monogr. 153, American Mathematical Society, Providence, RI, 2009.
4. 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.
5. A. Aubry and A. Derode, Random matrix theory applied to acoustic backscattering and imaging in complex media, Phys. Rev. Lett., 102 (2009), 084301.
6. 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.
7. G. Bal and O. Pinaud, Time reversal based detection in random media, Inverse Problems, 21 (2005), pp. 1593-1620.
8. A. P. Berens, NDE reliability data analysis, in ASM Metals Handbook, Vol. 17, ASM International, Materials Park, OH, 1989, pp. 689-701.
9. L. Borcea, G. Papanicolaou, and C. Tsogka, Adaptive interferometric imaging in clutter and optimal illumination, Inverse Problems, 22 (2006), pp. 1405-1436. (Pubitemid 44102186)
10. M. Brühl, M. Hanke, and M. Pidcock, Crack detection using electrostatic measurements, M2AN Math. Model. Numer. Anal., 35 (2001), pp. 595-605.
11. K. Bryan and M. S. Vogelius, A review of selected works on crack identification, inGeometric Methods in Inverse Problems and PDE Control, IMA Vol. Math. Appl. 137, Springer, New York, 2004, pp. 25-46.
12. M. Capitaine, C. Donati-Martin, and D. Féral, The largest eigenvalue of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations, Ann. Probab., 37 (2009), pp. 1-47.
13. M. Capitaine, C. Donati-Martin, and D. Féral, Central Limit Theorems for Eigenvalues of Deformations of Wigner Matrices, http://arxiv.org/abs/0903.4740.
14. G. Casella and R. L. Berger, Statistical Inference, Duxbury Press, Pacific Grove, CA, 2002.
15. A. C. Davison, Statistical Models, Cambridge University Press, Cambridge, UK, 2003.
16. A. R. Elcrat, V. Isakov, and O. Neculoiu, On finding a surface crack from boundary measurements, Inverse Problems, 11 (1995), pp. 343-351.
17. D. Féral and S. Péché, The largest eigenvalue of rank one deformation of large Wigner matrices, Comm. Math. Phys., 272 (2006), pp. 185-228.
18. J.-P. Fouque, J. Garnier, G. Papanicolaou, and K. Sølna, Wave Propagation and Time Reversal in Randomly Layered Media, Springer, New York, 2007.
19. I. M. Johnstone, On the distribution of the largest eigenvalue in principal component analysis, Ann. Statist., 29 (2001), pp. 295-327.
20. S. M. Kay, Fundamentals of Statistical Signal Processing, Volume II: Detection Theory, Prentice-Hall, Englewood Cliffs, NJ, 1998.
21. M. L. Mehta, Random Matrices, Academic Press, San Diego, CA, 1991.
22. G. A. F. Seber and C. J. Wild, Nonlinear Regression, Wiley, Hoboken, NJ, 2003.