Josselin Garnier - Ecole Polytechnique
Uncertainy quantification methods can be used to study wave-based imaging techniques in complex media. By modeling the unknown, complex medium as a realization of a random medium, wave propagation in complex media can be studied by multi-scale and stochastic analysis. We first consider the direct problem and show that, in a physically relevant regime of separation of scales, wave propagation is governed by a Schrodinger-type equation driven by a Brownian field. Moment calculations then show that coherent (mean) waves are exponentially damped and transformed into incoherent (zero-mean) wave fluctuations. Uncertainty quantification can therefore assess under which conditions coherent imaging methods can be efficient. Moreover stochastic analysis also reveals that information about the object can be encoded in the correlations of the zero-mean incoherent wave fluctuations. This paves the way for the introduction of original, incoherent, correlation-based imaging techniques.