We develop an efficient inversion method for thin high contrast scatterers when the contrast is on the order of the reciprocal of the thickness of the scatterer. We extend prior theory for the Helmholtz equation to arbitrary bounded domains and multiple scatterers in two and three dimensions to obtain a fast forward solver with complexity of one dimension lower. The lower-dimensional approximation is then paired with optimization to form the basis for parameter inversion. We show numerical results for the forward and inverse problems in two dimensions and describe extensions to Maxwell.
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