Interferometric inversion: a robust approach to linear inverse problems

Abstract

In this abstract, we present a new approach to linear wavebased inverse problems (e.g. inverse source, inverse Born scattering). Instead of looking directly at the data, we propose to match cross-correlations and other quadratic data combinations that generalize cross-correlations. This approach is expected to be robust to a wide variety of modeling uncertainties. In deriving a method to perform inversion using data pairs, a non-convex optimization problem is first advanced. It is then convexified by lifting the problem to a higher dimension space. The lifted problem is studied and sufficient conditions for invertibility are obtained. The lifted formulation is however too computationally intensive to be used for imaging, so a less-expansive non-convex approximation is considered. We illustrate the remarkable robustness of interferometric inversion numerically.