The lattice algorithm of linear prediction applied to the inverse scattering problem given transmission data

A layer-recursive algorithm is derived for reconstructing an equal-travel-time layered acoustic medium from its transmission response to an impulsive plane wave incident from below. The medium is bounded below by an infinite half-space from which it is probed, and it is bounded above by a free surface at which its transmission response is measured. This problem arises in the nondestructive evaluation of layered composite materials, in which the transmission response is measured. The algorithm is related to the lattice algorithm for computing the QR factorization of a matrix. The algorithm is related to the Levinson, fast Cholesky, and lattice algorithms, all of which are known fast algorithms for signal processing.<
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