Fast linear inversion for highly overdetermined inverse scattering problems

Abstract

In this paper we present a fast numerical method for solving large-scale inverse scattering problems. The computational efficiency of the proposed method stems from the utilization of the special structure of the linear forward scattering operator, and does not require or assume any symmetries of the measurement geometry. The described approach is especially useful for inverse problems involving large data sets. As an illustration, we have performed direct numerical inversions for the problem of diffuse optical tomography in measurement geometries with up to ∼108 independent data points and ∼ unknowns.