Optimal illumination and wave form design for imaging in random media.

The problem of optimal illumination for selective array imaging of small and not well separated scatterers in clutter is considered. The imaging algorithms introduced are based on the coherent interferometric (CINT) imaging functional, which can be viewed as a smoothed version of travel-time migration. The smoothing gives statistical stability to the image but it also causes blurring. The trade-off between statistical stability and blurring is optimized with an adaptive version of CINT. The algorithm for optimal illumination and for selective array imaging uses CINT. It is a constrained optimization problem that is based on the quality of the image obtained with adaptive CINT. The resulting optimal illuminations and selectivity improve the resolution of the images significantly, as can be seen in the numerical simulations presented in the paper.

[1]  Mathias Fink,et al.  The iterative time reversal process: Analysis of the convergence , 1995 .

[2]  Patrick Joly,et al.  An Analysis of New Mixed Finite Elements for the Approximation of Wave Propagation Problems , 2000, SIAM J. Numer. Anal..

[3]  Liliana Borcea,et al.  Adaptive interferometric imaging in clutter and optimal illumination , 2006 .

[4]  Liliana Borcea,et al.  Asymptotics for the Space-Time Wigner Transform with Applications to Imaging , 2007 .

[5]  Josselin Garnier,et al.  Wave Propagation and Time Reversal in Randomly Layered Media , 2007 .

[6]  Mathias Fink,et al.  Revisiting iterative time reversal processing: application to detection of multiple targets. , 2004, The Journal of the Acoustical Society of America.

[7]  M Fink,et al.  Imaging in the presence of grain noise using the decomposition of the time reversal operator. , 2003, The Journal of the Acoustical Society of America.

[8]  G. Papanicolaou,et al.  Interferometric array imaging in clutter , 2005 .

[9]  Derode,et al.  Limits of time-reversal focusing through multiple scattering: long-range correlation , 2000, The Journal of the Acoustical Society of America.

[10]  G. Papanicolaou,et al.  Optimal waveform design for array imaging , 2007 .

[11]  Jack K. Cohen,et al.  Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion , 2001 .

[12]  George Papanicolaou,et al.  Self-Averaging from Lateral Diversity in the Itô-Schrödinger Equation , 2007, Multiscale Model. Simul..

[13]  Jon F. Claerbout,et al.  DOWNWARD CONTINUATION OF MOVEOUT‐CORRECTED SEISMOGRAMS , 1972 .

[14]  George Christakos,et al.  Random Field Models in Earth Sciences , 1992 .

[15]  Liliana Borcea,et al.  Coherent interferometric imaging in clutter , 2006 .

[16]  Mathias Fink,et al.  Eigenmodes of the time reversal operator: a solution to selective focusing in multiple-target media , 1994 .

[17]  Liliana Borcea,et al.  Statistically stable ultrasonic imaging in random media. , 2002, The Journal of the Acoustical Society of America.

[18]  René Marklein,et al.  Recent Applications and Advances of Numerical Modeling and Wavefield Inversion in Nondestructive Testing , 2005 .

[19]  David Isaacson,et al.  Optimal Acoustic Measurements , 2001, SIAM J. Appl. Math..

[20]  M. V. Rossum,et al.  Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion , 1998, cond-mat/9804141.

[21]  G. Papanicolaou,et al.  Imaging and time reversal in random media , 2001 .

[22]  George Papanicolaou,et al.  Transport equations for elastic and other waves in random media , 1996 .

[23]  Wavefield Inversion in Nondestructive Testing , 2004 .

[24]  Hongkai Zhao,et al.  Super-resolution in time-reversal acoustics. , 2002, The Journal of the Acoustical Society of America.