Laurent Seppecher, Associate Professor at École Centrale de Lyon, presents "New perspectives on interferometric inversion, well-posedness and convexity issues" at the MIT Earth Resources Laboratory as part of the Friday Informal Seminar Hour.
"Inversion of sources and scatterers from interferometric measurements of a wave field is of great interest as these data present interesting stability properties with respect to phase uncertainties. This occurs, for instance, in the case of a smoothly varying wave-speed inside the medium. Unfortunately, the interferometric inversion problem turns out to be much more complex than the linear inversion. It is non-convex and possibly ill-posed. We will see that it is still possible to derive interesting stability estimates and prove a convexity property in a suitable admissible set of possible sources. Combining the associated interferometric cost functional with an L-1 penalty, we propose an efficient algorithm to recover sparse sources from highly corrupted data. This technique could have powerful applications to radar/sonar inverse problems, as well as geoseismic or medical imaging modalities."