Nonlinear Inverse Problems in Optical Tomography

John Schotland
University of Pennsylvania
Bioengineering

I will discuss a formally exact analytic
solution to the nonlinear inverse scattering problem which arises in
diffusion tomography. This solution has the form of a functional series
expansion for the absorption and scattering coefficients of the medium,
expressed as powers of the scattering data. The first
term in the expansion corresponds to the pseudoinverse solution to the
linearized inverse problem. The higher order terms may be interpreted
as nonlinear corrections. It can be shown that summing the inverse series
to all orders is equivalent to the Newton-Kantorovich method.


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