Imaging in Random Media - Week 2
Paris VII (Jussieu)
Introduction to active array imaging, passive array imaging, time reversal experiments and cross correlation imaging techniques. Comparisons in homogeneous media and in random media. Some useful identites: reciprocity, Green's identities, Helmholtz-Kirchhoff identity. Basic resolution theory not covered during week 1. Least-square imaging, weighted subspace imaging (including MUSIC).
Wave propagation in random media: The one-dimensional case. One-dimensional random processes, a little bit of theory and simulation techniques. Limit theorems for differential equations with random coefficients: homogenization and diffusion approximation. Applications to imaging and time-reversal in random media. Resolution and statistical stability analysis.
Wave propagation in random media: The paraxial regime. Multi-dimensional random processes, a little bit of theory and simulation techniques. The white-noise paraxial regime. Theoretical (statistical) aspects and simulation. Importance of the Wigner distribution. Applications to imaging and time-reversal in random media.
Introduction to Random Matrix Theory. Structure of the response matrix in the presence of electronic noise, in the presence of cluttered noise due to a random medium in the single-scattering approximation, in the presence of cluttered noise due to a random medium in the multiple-scattering regime. Statistical hypothesis testing. Detection test and localization of a point target. Optimal (weighted subspace) migration techniques for a point target and for an extended target.
Passive sensor imaging using ambient noise. The ideal case when the noise sources are uniformly distributed. The problem when the noise sources are spatially localized. Use of geometric optics approximation (in coordination with Demanet's course). Role of scattering due to a random medium: trade-off between enhanced resolution due to directional diversity enhancement and signal-to-noise ratio reduction.