120 III.A. Results with a one-dimensional array 120 III.B Application to Green's function estimation and focusing, The Prolate Spheroidal functions .... 117 III 128 V. APPLICATIONS: SUPER-RESOLUTION, TOMOGRAPHY AND MICROCALCIFICATION DIAGNOSIS, p.129 ,
131 APPENDIX A: 131 APPENDIX B: LARGER, 133 APPENDIX C: INVARIANTS FOR 3D OBJECTS WITH 137 Analytical solutions for separable kernels, p.138 ,
Chapter, p.141 ,
143 A. Randomness of the speckle 144 B. First order statistics 147 C. Second order statistics 170 A. Spatial correlation matrix, or Van Cittert Zernike matrix 171 B. Time Reversal Operator for an equivalent virtual object 177 C. Variance and standard deviation of the estimation, 180 D. Interpretation of the first eigenvalue in speckle, 0196. ,
202 B. Maximum Speckle Brightness 204 C. Eigenfunction analysis of backscattering signal, 205 D. Multi-lag cross-correlation, p.205 ,
218 A. Variance of the amplitude of the spatial correlation coefficients, p.218 ,
Focusing in transmit???receive mode through inhomogeneous media: The time reversal matched filter approach, The Journal of the Acoustical Society of America, vol.98, issue.2, pp.1155-1162, 1995. ,
DOI : 10.1121/1.413614
Ultrasonic beam steering through inhomogeneous layers with a time reversal mirror, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.43, issue.1, pp.167-175, 1996. ,
DOI : 10.1109/58.484476
Synthetic elevation beamforming and image acquisition capabilities using an 8 /spl times/ 128 1.75D array, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.50, issue.1, pp.40-57, 2003. ,
DOI : 10.1109/TUFFC.2003.1176524
Time reversal of ultrasonic fields. I. Basic principles, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.39, issue.5, pp.555-566, 1992. ,
DOI : 10.1109/58.156174
Phase-aberration correction using signals from point reflectors and diffuse scatterers: basic principles, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.35, issue.6, pp.758-767, 1988. ,
DOI : 10.1109/58.9333
Relative performance of two-dimensional speckle-tracking techniques: normalized correlation, non-normalized correlation and sum-absolute-difference, 1995 IEEE Ultrasonics Symposium. Proceedings. An International Symposium, pp.1481-1484, 1995. ,
DOI : 10.1109/ULTSYM.1995.495835
Wavefront estimation in the human breast, Proc. SPIE, pp.172-181, 2001. ,
Time-reversal imaging with multiple signal classification considering multiple scattering between the targets, The Journal of the Acoustical Society of America, vol.115, issue.6, pp.3042-3047, 2004. ,
DOI : 10.1121/1.1738451
The effect of abdominal wall morphology on ultrasonic pulse distortion. Part I. Measurements, The Journal of the Acoustical Society of America, vol.104, issue.6, pp.3635-3649, 1998. ,
DOI : 10.1121/1.423946
Phase aberration correction in medical ultrasound using speckle brightness as a quality factor, The Journal of the Acoustical Society of America, vol.85, issue.5, pp.1819-1833, 1989. ,
Correction of ultrasonic wavefront distortion using backpropagation and a reference waveform method for time???shift compensation, The Journal of the Acoustical Society of America, vol.96, issue.2, pp.649-660, 1994. ,
DOI : 10.1121/1.410304
The effect of abdominal wall morphology on ultrasonic pulse distortion. Part II. Simulations, The Journal of the Acoustical Society of America, vol.104, issue.6, pp.3651-3664, 1998. ,
DOI : 10.1121/1.423947
Phase-aberration correction using signals from point reflectors and diffuse scatterers: measurements, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.35, issue.6, pp.768-774, 1988. ,
DOI : 10.1109/58.9334
Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media, Wave Motion, vol.20, issue.2, pp.151-163, 1994. ,
DOI : 10.1016/0165-2125(94)90039-6
Decomposition of the time reversal operator: Detection and selective focusing on two scatterers, The Journal of the Acoustical Society of America, vol.99, issue.4, pp.2067-2076, 1996. ,
DOI : 10.1121/1.415393
Experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix, The Journal of the Acoustical Society of America, vol.114, issue.1, pp.235-243, 2003. ,
DOI : 10.1121/1.1568759
URL : https://hal.archives-ouvertes.fr/hal-00017627
The iterative time reversal mirror: A solution to self???focusing in the pulse echo mode, The Journal of the Acoustical Society of America, vol.90, issue.2, pp.1119-1129, 1991. ,
DOI : 10.1121/1.402301
Improved in vivo abdominal image quality using real-time estimation and correction of wavefront arrival time errors, 2000 IEEE Ultrasonics Symposium. Proceedings. An International Symposium (Cat. No.00CH37121), pp.1645-1653, 2000. ,
DOI : 10.1109/ULTSYM.2000.921639
Autofocusing in medical ultrasound: the scaled covariance matrix algorithm, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.50, issue.7, pp.795-804, 2003. ,
DOI : 10.1109/TUFFC.2003.1214500
Eigenfunction analysis of stochastic backscatter for characterization of acoustic aberration in medical ultrasound imaging, The Journal of the Acoustical Society of America, vol.115, issue.6, pp.3068-3076, 2004. ,
DOI : 10.1121/1.1736274
A comparison of the performance of time-delay estimators in medical ultrasound, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.50, issue.4, pp.392-401, 2003. ,
DOI : 10.1109/TUFFC.2003.1197962
Statistical estimation of ultrasonic propagation path parameters for aberration correction, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.52, issue.5, pp.851-869, 2005. ,
DOI : 10.1109/TUFFC.2005.1503972
Statistical estimation of ultrasonic propagation path parameters for aberration correction, The Journal of the Acoustical Society of America, vol.119, issue.5, p.3376, 2006. ,
DOI : 10.1121/1.4786587
Ultrasonic beam steering through inhomogeneous layers with a time reversal mirror, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.43, issue.1, pp.167-175, 1996. ,
DOI : 10.1109/58.484476
Diffraction Effects in Pulse-Echo Measurement, IEEE Transactions on Sonics and Ultrasonics, vol.31, issue.4, pp.313-329, 1984. ,
DOI : 10.1109/T-SU.1984.31512
Adaptive instant record signals applied to detection with time reversal operator decomposition, The Journal of the Acoustical Society of America, vol.117, issue.6, pp.3757-3765, 2005. ,
DOI : 10.1121/1.1914204
Adaptive instant record signals applied to detection with time reversal operator decomposition, The Journal of the Acoustical Society of America, vol.117, issue.6, pp.3757-3765, 2005. ,
DOI : 10.1121/1.1914204
VIII Evaluation, Design and Extrapolation Methods for Optical Signals, Based on Use of the Prolate Functions, 1971. ,
DOI : 10.1016/S0079-6638(08)70049-0
Multielement synthetic transmit aperture imaging using temporal encoding, IEEE Transactions on Medical Imaging, vol.22, issue.4, pp.552-563, 2003. ,
DOI : 10.1109/TMI.2003.809088
URL : http://orbit.dtu.dk/ws/files/4215830/Gammelmark.pdf
Field: A program for simulating ultrasound systems, Med. Biol. Eng. Comp., col. 10th Nordic-Baltic Conference on Biomedical Imaging, vol.4, issue.1, pp.351-353, 1996. ,
Echographic diffraction filters and the diffraction function for random media through an instantaneous time-frequency approach, The Journal of the Acoustical Society of America, vol.90, issue.2, pp.1074-1084, 1991. ,
Ultrasound research scanner for real-time synthetic aperture data acquisition, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.52, issue.5, pp.881-891, 2005. ,
DOI : 10.1109/TUFFC.2005.1503974
Correction of ultrasonic wavefront distortion using backpropagation and a reference waveform method for time???shift compensation, The Journal of the Acoustical Society of America, vol.96, issue.2, pp.649-660, 1994. ,
DOI : 10.1121/1.410304
Duplex synthetic aperture imaging with tissue motion compensation, 2003. ,
Adaptive focusing in scattering media through sound???speed inhomogeneities: The van Cittert Zernike approach and focusing criterion, The Journal of the Acoustical Society of America, vol.96, issue.6, pp.3721-3732, 1994. ,
DOI : 10.1121/1.410562
Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media, Wave Motion, vol.20, issue.2, pp.151-163, 1994. ,
DOI : 10.1016/0165-2125(94)90039-6
Decomposition of the time reversal operator: Detection and selective focusing on two scatterers, The Journal of the Acoustical Society of America, vol.99, issue.4, pp.2067-2076, 1996. ,
DOI : 10.1121/1.415393
Flaw detection in solid with the D, 1997. ,
Time reversal operator decomposition with focused transmission and robustness to speckle noise: Application to microcalcification detection, The Journal of the Acoustical Society of America, vol.119, issue.6, pp.3848-3859, 2006. ,
DOI : 10.1121/1.2190163
Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I, Bell System Technical Journal, vol.40, issue.1, pp.43-64, 1961. ,
DOI : 10.1002/j.1538-7305.1961.tb03976.x
Stone tracking with time???reversal techniques, The Journal of the Acoustical Society of America, vol.103, issue.5, pp.3071-3071, 1998. ,
DOI : 10.1121/1.422862
Optimum Array Processing -Detection, Estimation, and Modulation Theory, 2002. ,
Statistical Properties of Speckle Pattern. Laser Speckle and Related Phenomena, J. C. Dainty. Berlin, pp.9-75, 1975. ,
Time-reversal imaging with multiple signal classification considering multiple scattering between the targets, The Journal of the Acoustical Society of America, vol.115, issue.6, pp.3042-3047, 2004. ,
DOI : 10.1121/1.1738451
Linear sampling method for acoustic inverse scattering in breast microcalcification detection, The Journal of the Acoustical Society of America, vol.120, issue.5, pp.3025-3025, 2006. ,
DOI : 10.1121/1.4787115
Focusing and imaging using eigenfunctions of the scattering operator, The Journal of the Acoustical Society of America, vol.102, issue.2, pp.715-725, 1997. ,
DOI : 10.1121/1.419898
Experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix, The Journal of the Acoustical Society of America, vol.114, issue.1, pp.235-243, 2003. ,
DOI : 10.1121/1.1568759
URL : https://hal.archives-ouvertes.fr/hal-00017627
Optimum Array Processing -Detection, Estimation, and Modulation Theory, 2002. ,
Image reconstruction using eigenfunctions of a scattering operator, The Journal of the Acoustical Society of America, vol.120, issue.5, pp.3023-3023, 2006. ,
DOI : 10.1121/1.4787109
Imaging with eigenfunctions of the scattering operator, The Journal of the Acoustical Society of America, vol.101, issue.5, pp.3091-3091, 1997. ,
DOI : 10.1121/1.418878
Ultrasonic beam steering through inhomogeneous layers with a time reversal mirror, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.43, issue.1, pp.167-175, 1996. ,
DOI : 10.1109/58.484476
Analyse des effets de la diffraction en echographie medicale, Acta Electronica, vol.26, issue.12, pp.59-80, 1984. ,
Adaptive focusing in scattering media through soundspeed inhomogeneities: The van Cittert Zernike approach and focusing criterion, The Journal of the Acoustical Society of America, vol.96, issue.6, pp.3721-3732, 1994. ,
Imaging with unfocused regions of focused ultrasound beams, The Journal of the Acoustical Society of America, vol.121, issue.3, pp.1491-1498, 2007. ,
A fundamental limit on delay estimation using partially correlated speckle signals, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.42, issue.2, pp.301-308, 1995. ,
DOI : 10.1109/58.365243
Reduction of variance in spectral estimates for correction of ultrasonic aberration, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.53, issue.1, pp.79-89, 2006. ,
DOI : 10.1109/TUFFC.2006.1588393
Multivariate Data Analysis, 1971. ,
Spatial and temporal aberrator stability for real-time adaptive imaging, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.52, issue.9, pp.1504-1517, 2005. ,
DOI : 10.1109/TUFFC.2005.1516023
Off-axis scatterer filters for improved aberration measurements, 2003. ,
Quantitative ultrasonic backscatter measurements in the presence of phase distortion, The Journal of the Acoustical Society of America, vol.72, issue.6, pp.1719-1725, 1982. ,
DOI : 10.1121/1.388665
Synthetic elevation beamforming and image acquisition capabilities using an 8 /spl times/ 128 1.75D array, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.50, issue.1, pp.40-57, 2003. ,
DOI : 10.1109/TUFFC.2003.1176524
Two-dimensional phase aberration correction using an ultrasonic 1, 75D array: case study on breast microcalcifications, 2003. ,
Analyse des effets de la diffraction en echographie medicale, Acta Electronica, vol.26, issue.12, pp.59-80, 1984. ,
Phase-aberration correction using signals from point reflectors and diffuse scatterers: basic principles, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.35, issue.6, pp.758-767, 1988. ,
DOI : 10.1109/58.9333
Wavefront estimation in the human breast, Proc. SPIE, pp.172-181, 2001. ,
Statistical Properties of Speckle Pattern. Laser Speckle and Related Phenomena, J. C. Dainty. Berlin, pp.9-75, 1975. ,
Time-reversal imaging with multiple signal classification considering multiple scattering between the targets, The Journal of the Acoustical Society of America, vol.115, issue.6, pp.3042-3047, 2004. ,
DOI : 10.1121/1.1738451
Field: A program for simulating ultrasound systems, Med. Biol. Eng. Comp., col. 10th Nordic-Baltic Conference on Biomedical Imaging, vol.4, issue.1, pp.351-353, 1996. ,
Spatial coherence analysis applied to aberration correction using a two-dimensional array system, The Journal of the Acoustical Society of America, vol.112, issue.6, pp.2558-2566, 2002. ,
DOI : 10.1121/1.1511756
Adaptive focusing in scattering media through sound???speed inhomogeneities: The van Cittert Zernike approach and focusing criterion, The Journal of the Acoustical Society of America, vol.96, issue.6, pp.3721-3732, 1994. ,
DOI : 10.1121/1.410562
Estimation of ultrasound wave aberration with signals from random scatterers, The Journal of the Acoustical Society of America, vol.115, issue.6, pp.2998-3009, 2004. ,
DOI : 10.1121/1.1738840
Variance analysis of arrival time and amplitude estimates from random speckle signal, The Journal of the Acoustical Society of America, vol.121, issue.1, pp.286-297, 2007. ,
DOI : 10.1121/1.2382748
Iteration of transmit-beam aberration correction in medical ultrasound imaging, The Journal of the Acoustical Society of America, vol.117, issue.1, pp.450-461, 2005. ,
DOI : 10.1121/1.1823213
Phase aberration correction in medical ultrasound using speckle brightness as a quality factor, The Journal of the Acoustical Society of America, vol.85, issue.5, pp.1819-1833, 1989. ,
DOI : 10.1121/1.397889
Phase-aberration correction using signals from point reflectors and diffuse scatterers: measurements, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.35, issue.6, pp.768-774, 1988. ,
DOI : 10.1109/58.9334
Experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix, The Journal of the Acoustical Society of America, vol.114, issue.1, pp.235-243, 2003. ,
DOI : 10.1121/1.1568759
URL : https://hal.archives-ouvertes.fr/hal-00017627
The Spectral Analysis of Time Series., Journal of the Royal Statistical Society. Series A (Statistics in Society), vol.151, issue.3, 1988. ,
DOI : 10.2307/2983035
The Use and Interpretation of Principal Component Analysis in Applied Research, Sankhya A, vol.26, pp.329-358, 1964. ,
Ultrasound scattering model: 2-D cross-correlation and focusing criteria-theory, simulations, and experiments, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.48, issue.4, pp.1023-1030, 2001. ,
DOI : 10.1109/58.935719
Optimum Array Processing -Detection, Estimation, and Modulation Theory, 2002. ,
Eigenfunction analysis of stochastic backscatter for characterization of acoustic aberration in medical ultrasound imaging, The Journal of the Acoustical Society of America, vol.115, issue.6, pp.3068-3076, 2004. ,
DOI : 10.1121/1.1736274
Statistical estimation of ultrasonic propagation path parameters for aberration correction, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.52, issue.5, pp.851-869, 2005. ,
DOI : 10.1109/TUFFC.2005.1503972
Statistical estimation of ultrasonic propagation path parameters for aberration correction, The Journal of the Acoustical Society of America, vol.119, issue.5, p.3376, 2006. ,
DOI : 10.1121/1.4786587
Speckle coherence and implications for adaptive imaging, The Journal of the Acoustical Society of America, vol.101, issue.4, pp.1847-1858, 1997. ,
DOI : 10.1121/1.418235
A fundamental limit on delay estimation using partially correlated speckle signals, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, vol.42, issue.2, pp.301-308, 1995. ,
DOI : 10.1109/58.365243
Spatial coding with curved wavefronts, IEEE Ultrasonics Symposium, 2004, 2004. ,
DOI : 10.1109/ULTSYM.2004.1418017
Super-symmetric decomposition of the fourth-order cumulant tensor. Blind identification of more sources than sensors, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing, pp.3109-3112, 1991. ,
DOI : 10.1109/ICASSP.1991.150113
Resolution enhancement and separation of reverberation from target echo with the time reversal operator decomposition, The Journal of the Acoustical Society of America, vol.113, issue.6, pp.3155-3160, 2003. ,
DOI : 10.1121/1.1571541
Time-reversal imaging with multiple signal classification considering multiple scattering between the targets, The Journal of the Acoustical Society of America, vol.115, issue.6, pp.3042-3047, 2004. ,
DOI : 10.1121/1.1738451
Field: A program for simulating ultrasound systems, Med. Biol. Eng. Comp., col. 10th Nordic-Baltic Conference on Biomedical Imaging, vol.4, issue.1, pp.351-353, 1996. ,
Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media, Wave Motion, vol.20, issue.2, pp.151-163, 1994. ,
DOI : 10.1016/0165-2125(94)90039-6
Decomposition of the time reversal operator: Detection and selective focusing on two scatterers, The Journal of the Acoustical Society of America, vol.99, issue.4, pp.2067-2076, 1996. ,
DOI : 10.1121/1.415393
Decompostion of the time reversal operator applied to detection and focusing in a 12???m???deep channel in Brest Bay, The Journal of the Acoustical Society of America, vol.119, issue.5, pp.3428-3429, 2006. ,
DOI : 10.1121/1.4786881
Experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix, The Journal of the Acoustical Society of America, vol.114, issue.1, pp.235-243, 2003. ,
DOI : 10.1121/1.1568759
URL : https://hal.archives-ouvertes.fr/hal-00017627
The Use and Interpretation of Principal Component Analysis in Applied Research, Sankhya A, vol.26, pp.329-358, 1964. ,