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On the stability of some imaging functionals
1. | Department of Applied Physics and Applied Mathematics, Columbia University, New York NY, 10027 |
2. | Department of Mathematics, Colorado State University, Fort Collins CO 80523, United States |
3. | Department of Mathematics, Stanford University, Stanford, CA 94305 |
References:
[1] |
H. Ammari, E. Bretin, J. Garnier and V. Jugnon, Coherent interferometry algorithms for photoacoustic imaging, SIAM J. Numer. Anal., 50 (2012), 2259-2280.
doi: 10.1137/100814275. |
[2] |
H. Ammari, J. Garnier, V. Jugnon and H. Kang, Stability and resolution analysis for a topological derivative based imaging functional, SIAM Journal of Control and Optimization, 50 (2012), 48-76.
doi: 10.1137/100812501. |
[3] |
A. Baggeroer, W. Kuperman and P. Mikhalevsky, An overview of matched-field methods in ocean acoustics, IEEE Journal of Ocean Engineering, 18 (1993), 401-424.
doi: 10.1109/48.262292. |
[4] |
G. Bal, On the self-averaging of wave energy in random media, SIAM Mult. Mod. Simul., 2 (2004), 398-420.
doi: 10.1137/S1540345903426298. |
[5] |
G. Bal, I. Langmore and O. Pinaud, Single scattering estimates for the scintillation function of waves in random media, J. Math. Phys., 51 (2010), 022903, 18pp.
doi: 10.1063/1.3276437. |
[6] |
G. Bal and O. Pinaud, Dynamics of wave scintillation in random media, CPDE, 35 (2010), 1176-1235.
doi: 10.1080/03605301003801557. |
[7] |
G. Bal and O. Pinaud, Imaging using transport models for wave-wave correlations, M3AS, 21 (2011), 1071-1093.
doi: 10.1142/S0218202511005258. |
[8] |
G. Bal and O. Pinaud, Analysis of the double scattering scintillation of waves in random media, CPDE, 38 (2013), 945-984.
doi: 10.1080/03605302.2013.777451. |
[9] |
G. Bal and K. Ren, Transport-based imaging in random media, SIAM Applied Math., 68 (2008), 1738-1762.
doi: 10.1137/070690122. |
[10] |
G. Bal, Homogenization in random media and effective medium theory for high frequency waves, Discrete Contin. Dyn. Syst. Ser. B, 8 (2007), 473-492 (electronic).
doi: 10.3934/dcdsb.2007.8.473. |
[11] |
N. Bleistein, J. K. Cohen and J. W. Stockwell Jr., Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion, vol. 13 of Interdisciplinary Applied Mathematics, Springer-Verlag, New York, 2001, Geophysics and Planetary Sciences.
doi: 10.1007/978-1-4613-0001-4. |
[12] |
L. Borcea, J. Garnier, G. Papanicolaou and C. Tsogka, Enhanced statistical stability in coherent interferometric imaging, Inverse Problems, 27 (2011), 085004, 33 pp.
doi: 10.1088/0266-5611/27/8/085004. |
[13] |
L. Borcea, L. Issa and C. Tsogka, Source localization in random acoustic waveguides, Multiscale Model. Simul., 8 (2010), 1981-2022.
doi: 10.1137/100782711. |
[14] |
L. Borcea, G. Papanicolaou and C. Tsogka, Interferometric array imaging in clutter, Inverse Problems, 21 (2005), 1419-1460.
doi: 10.1088/0266-5611/21/4/015. |
[15] |
L. Borcea, G. Papanicolaou and C. Tsogka, Adaptive interferometric imaging in clutter and optimal illumination, Inverse Problems, 22 (2006), 1405-1436.
doi: 10.1088/0266-5611/22/4/016. |
[16] |
J. F. claerbout, Fundamentals of Geophysical Data Processing: With Applications to Petroleum Prospecting, Blackwell scientific, Palo Alto, 1985. |
[17] |
S. Dolan, C. Bean and R. B., The broad-band fractal nature of heterogeneity in the upper crust from petrophysical logs, Geophys. J. Int., 132 (1998), 489-507.
doi: 10.1046/j.1365-246X.1998.00410.x. |
[18] |
M. Fink and C. Prada, Acoustic time-reversal mirrors, Imaging of Complex Media with Acoustic and Seismic Waves, 84 (2002), 17-43.
doi: 10.1007/3-540-44680-X_2. |
[19] |
J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Sølna, Wave Propagation and Time Reversal in Randomly Layered Media, vol. 56 of Stochastic Modelling and Applied Probability, Springer, New York, 2007.
doi: 10.1007/978-0-387-49808-9_4. |
[20] |
J. Garnier and K. Sølna, Background velocity estimation with cross correlations of incoherent waves in the parabolic scaling, Inverse Problems, 25 (2009), 045005, 34 pp.
doi: 10.1088/0266-5611/25/4/045005. |
[21] |
J. Garnier and G. Papanicolaou, Pulse propagation and time reversal in random waveguides, SIAM J. Appl. Math., 67 (2007), 1718-1739 (electronic).
doi: 10.1137/060659235. |
[22] |
I. M. Gelfand and G. E. Shilov, Generalized Functions, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1964 [1977], Properties and operations, Translated from the Russian by Eugene Saletan. |
[23] |
P. Gérard, P. A. Markowich, N. J. Mauser and F. Poupaud, Homogenization limits and Wigner transforms, Comm. Pure Appl. Math., 50 (1997), 323-379.
doi: 10.1002/(SICI)1097-0312(199704)50:4<323::AID-CPA4>3.0.CO;2-C. |
[24] |
F. C. Karal Jr. and J. B. Keller, Elastic, electromagnetic, and other waves in a random medium, J. Mathematical Phys., 5 (1964), 537-547.
doi: 10.1063/1.1704145. |
[25] |
P.-L. Lions and T. Paul, Sur les mesures de Wigner, Rev. Mat. Iberoamericana, 9 (1993), 553-618.
doi: 10.4171/RMI/143. |
[26] |
M. Reed and B. Simon, Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-Adjointness, 2nd edition, Academic Press, Inc., New York, 1980. |
[27] |
L. Ryzhik, G. Papanicolaou and J. B. Keller, Transport equations for elastic and other waves in random media, Wave Motion, 24 (1996), 327-370.
doi: 10.1016/S0165-2125(96)00021-2. |
[28] |
P. J. Shull, Nondestructive Evaluation. Theory, Techniques and Applications, Marcel Dekker, New York, 2002. |
[29] |
C. Sidi and F. Dalaudier, Turbulence in the stratified atmosphere: Recent theoretical devel- opments and experimental results, Adv. in Space Res., 10 (1990), 25-36. |
show all references
References:
[1] |
H. Ammari, E. Bretin, J. Garnier and V. Jugnon, Coherent interferometry algorithms for photoacoustic imaging, SIAM J. Numer. Anal., 50 (2012), 2259-2280.
doi: 10.1137/100814275. |
[2] |
H. Ammari, J. Garnier, V. Jugnon and H. Kang, Stability and resolution analysis for a topological derivative based imaging functional, SIAM Journal of Control and Optimization, 50 (2012), 48-76.
doi: 10.1137/100812501. |
[3] |
A. Baggeroer, W. Kuperman and P. Mikhalevsky, An overview of matched-field methods in ocean acoustics, IEEE Journal of Ocean Engineering, 18 (1993), 401-424.
doi: 10.1109/48.262292. |
[4] |
G. Bal, On the self-averaging of wave energy in random media, SIAM Mult. Mod. Simul., 2 (2004), 398-420.
doi: 10.1137/S1540345903426298. |
[5] |
G. Bal, I. Langmore and O. Pinaud, Single scattering estimates for the scintillation function of waves in random media, J. Math. Phys., 51 (2010), 022903, 18pp.
doi: 10.1063/1.3276437. |
[6] |
G. Bal and O. Pinaud, Dynamics of wave scintillation in random media, CPDE, 35 (2010), 1176-1235.
doi: 10.1080/03605301003801557. |
[7] |
G. Bal and O. Pinaud, Imaging using transport models for wave-wave correlations, M3AS, 21 (2011), 1071-1093.
doi: 10.1142/S0218202511005258. |
[8] |
G. Bal and O. Pinaud, Analysis of the double scattering scintillation of waves in random media, CPDE, 38 (2013), 945-984.
doi: 10.1080/03605302.2013.777451. |
[9] |
G. Bal and K. Ren, Transport-based imaging in random media, SIAM Applied Math., 68 (2008), 1738-1762.
doi: 10.1137/070690122. |
[10] |
G. Bal, Homogenization in random media and effective medium theory for high frequency waves, Discrete Contin. Dyn. Syst. Ser. B, 8 (2007), 473-492 (electronic).
doi: 10.3934/dcdsb.2007.8.473. |
[11] |
N. Bleistein, J. K. Cohen and J. W. Stockwell Jr., Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion, vol. 13 of Interdisciplinary Applied Mathematics, Springer-Verlag, New York, 2001, Geophysics and Planetary Sciences.
doi: 10.1007/978-1-4613-0001-4. |
[12] |
L. Borcea, J. Garnier, G. Papanicolaou and C. Tsogka, Enhanced statistical stability in coherent interferometric imaging, Inverse Problems, 27 (2011), 085004, 33 pp.
doi: 10.1088/0266-5611/27/8/085004. |
[13] |
L. Borcea, L. Issa and C. Tsogka, Source localization in random acoustic waveguides, Multiscale Model. Simul., 8 (2010), 1981-2022.
doi: 10.1137/100782711. |
[14] |
L. Borcea, G. Papanicolaou and C. Tsogka, Interferometric array imaging in clutter, Inverse Problems, 21 (2005), 1419-1460.
doi: 10.1088/0266-5611/21/4/015. |
[15] |
L. Borcea, G. Papanicolaou and C. Tsogka, Adaptive interferometric imaging in clutter and optimal illumination, Inverse Problems, 22 (2006), 1405-1436.
doi: 10.1088/0266-5611/22/4/016. |
[16] |
J. F. claerbout, Fundamentals of Geophysical Data Processing: With Applications to Petroleum Prospecting, Blackwell scientific, Palo Alto, 1985. |
[17] |
S. Dolan, C. Bean and R. B., The broad-band fractal nature of heterogeneity in the upper crust from petrophysical logs, Geophys. J. Int., 132 (1998), 489-507.
doi: 10.1046/j.1365-246X.1998.00410.x. |
[18] |
M. Fink and C. Prada, Acoustic time-reversal mirrors, Imaging of Complex Media with Acoustic and Seismic Waves, 84 (2002), 17-43.
doi: 10.1007/3-540-44680-X_2. |
[19] |
J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Sølna, Wave Propagation and Time Reversal in Randomly Layered Media, vol. 56 of Stochastic Modelling and Applied Probability, Springer, New York, 2007.
doi: 10.1007/978-0-387-49808-9_4. |
[20] |
J. Garnier and K. Sølna, Background velocity estimation with cross correlations of incoherent waves in the parabolic scaling, Inverse Problems, 25 (2009), 045005, 34 pp.
doi: 10.1088/0266-5611/25/4/045005. |
[21] |
J. Garnier and G. Papanicolaou, Pulse propagation and time reversal in random waveguides, SIAM J. Appl. Math., 67 (2007), 1718-1739 (electronic).
doi: 10.1137/060659235. |
[22] |
I. M. Gelfand and G. E. Shilov, Generalized Functions, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1964 [1977], Properties and operations, Translated from the Russian by Eugene Saletan. |
[23] |
P. Gérard, P. A. Markowich, N. J. Mauser and F. Poupaud, Homogenization limits and Wigner transforms, Comm. Pure Appl. Math., 50 (1997), 323-379.
doi: 10.1002/(SICI)1097-0312(199704)50:4<323::AID-CPA4>3.0.CO;2-C. |
[24] |
F. C. Karal Jr. and J. B. Keller, Elastic, electromagnetic, and other waves in a random medium, J. Mathematical Phys., 5 (1964), 537-547.
doi: 10.1063/1.1704145. |
[25] |
P.-L. Lions and T. Paul, Sur les mesures de Wigner, Rev. Mat. Iberoamericana, 9 (1993), 553-618.
doi: 10.4171/RMI/143. |
[26] |
M. Reed and B. Simon, Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-Adjointness, 2nd edition, Academic Press, Inc., New York, 1980. |
[27] |
L. Ryzhik, G. Papanicolaou and J. B. Keller, Transport equations for elastic and other waves in random media, Wave Motion, 24 (1996), 327-370.
doi: 10.1016/S0165-2125(96)00021-2. |
[28] |
P. J. Shull, Nondestructive Evaluation. Theory, Techniques and Applications, Marcel Dekker, New York, 2002. |
[29] |
C. Sidi and F. Dalaudier, Turbulence in the stratified atmosphere: Recent theoretical devel- opments and experimental results, Adv. in Space Res., 10 (1990), 25-36. |
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