In non-homogeneous media with unknown wave speed, it could be difficult to recover wave sources or scatters from measurements of the wave field at distant receivers. The Kirchhoff migration may fail, as well as the full inversion from a least squares approach. This is mainly due to the large dephasing occurred by the wave speed variations that especially affect the high frequency data..
            In the regime of smoothly varying random media, it is known that the cross-correlations between measurements at nearby receivers remain much more stable than linear measurements. The interferometric inversion aims at recovering the source directly from some of the cross-correlations called the interferometric data. This is a challenging, non-convex, quadratic problem..
            In this talk, we will discuss the conditions for the interferometric inversion to be well-posed, and provide new recovery estimates from interferometric data. We will also see that under the same conditions, and despite the non-convexity of the problem, a Wirtinger flow descend applied on the interferometric misfit functional “locally” converges to the solution. Finally, we will see, in numerical examples, that this approach outperforms by far classical methods to recover sparse scatters in slowly varying random environment..

https://indico.math.cnrs.fr/event/15249/