Convergence and Stability of the Inverse Scattering Series for Diffuse Waves

We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence, stability and approximation error of the serie

On the Convergence of the Born Series in Optical Tomography with Diffuse Light

We provide a simple sufficient condition for convergence of Born series in the forward problem of optical diffusion tomography. The condition does not depend on the shape or spatial extent of the inhomogeneity but only on its amplitude.Comment: 23 pages, 7 figures, submitted to Inverse Problem

Multi-Dimensional Seismic Imaging Using the Inverse Scattering Series

The inverse scattering series (ISS) is a comprehensive multidimensional theory for processing and inverting seismic reflection data, that may be task-separated such that meaningful sub-problems of the seismic inverse problem may be accomplished individually, each without an accurate velocity model. We describe a task-separated subseries of the ISS geared towards accurate location in depth of reflectors, in particular the mechanisms of the series that act in multiple dimensions. We show that some 2D ISS imaging terms have analogs in previously developed 1D ISS imaging theory (e.g., Weglein et al., 2002; Shaw, 2005) and others do not; the former are used to create a 2D depth-only imaging prototype algorithm which is tested on synthetic salt-model data, and the latter are used to discuss ongoing research into reflector location activity within the series that acts only in the case of lateral variation and the presence of, e.g., diffraction energy in the data. Numerical tests are encouraging and show clear added value