The Tensorial Formulation of the Diagonalized Contrast Source Inversion Method for Nonlinear Inversion in Elastic Tomography

A. Abubakar and T.M. Habashy (USA)


Inverse Scattering, Iterative Technique, Contrast Source, Elastic Wave, Localized Approximation, Conjugate Gradi ent


This study focuses on the inverse scattering of objects em bedded in a homogeneous elastic background. The medium is probed by ultrasonic forces and the scattered fields are observed along a receiver array. The goal is to retrieve the shapes, locations, and constitutive parameters of the ob jects through an inversion procedure. The problem is for mulated using a vector integral equation. As it is known this inverse scattering problem is nonlinear and ill-posed. In a realistic configuration this nonlinear inverse scattering problem involves a large number of unknowns, hence the application of full nonlinear inversion approaches such as Gauss-Newton or nonlinear gradient methods might not be feasible even with present-day computer power. Hence in this study we employed the so-called Diagonalized Con trast Source Inversion (DCSI) method where the nonlinear problem is approximately transformed into a number of lin ear problems. We will show that by using a three-step pro cedure the nonlinear inverse problem can be solved at the cost of solving three constrained linear inverse problems. The robustness and efficiency of this approach is illustrated using a number of synthetic examples.

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