Applied Math Colloquium with Dr. Josselin Garnier, Ecole Polytechnique

Speaker: Dr. Josselin Garnier, Ecole Polytechnique

Title: "From Wave Statistics to Imaging in Random Media"

Abstract: Wave propagation through randomly heterogeneous media arises in optics, acoustics, and seismic imaging. Random scattering can strongly distort the coherent wave field, making conventional imaging methods unreliable, but the statistical properties of the scattered field can still contain useful information.
In this talk, I will discuss mathematical models for wave propagation in random media and their implications for imaging. In the paraxial regime, multiscale analysis leads to an Itô-Schrödinger equation that makes it possible to characterize the moments and statistical stability of the wave field. A central question is whether the field develops Gaussian statistics after long propagation, a property that holds in some regimes but fails in others. 
I will illustrate how these statistical properties affect imaging through examples involving speckle correlations and ghost imaging. I will also discuss random waveguides, where strong non-Gaussian fluctuations highlight both the limitations of correlation-based imaging and the potential value of information contained in higher-order statistics. 

Bio: Josselin Garnier has been a professor of applied mathematics in France since 2001. He held positions in Toulouse, at Université Paris Diderot and École Normale Supérieure in Paris, before joining École Polytechnique in 2016. His research spans several areas of applied mathematics and probability, with particular interests in wave propagation and imaging in random and complex media, uncertainty quantification, and the design and analysis of stochastic algorithms.