Matrix factorization for the multi-static data and its application to shape recovery of a planar inclusion
Doosung Choi
Inverse Problems and Mathematical Imaging Group
We present a new factorization method for recovering a conductivity inclusion in two dimensions from multi-static measurements. A conductivity inclusion induces a perturbation in the background potential, and the perturbation admits a multipole expansion whose coefficients are the so-called generalized polarization tensors (GPTs). We derive a factorization formula for the matrix composed of the GPTs in terms of the material parameters and the coefficients of the exterior conformal mapping associated with the inclusion. Using this formula, we induce accurate representations for the coefficients of the conformal mapping in terms of the GPTs. Our approach provides a non-iterative method for recovering the shape of a Lipschitz inclusion with arbitrary finite conductivity.