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A Levinson-like fast algorithm for solving block-slanted Toeplitz systems of equations arising in wavelet-based solution of integral equations

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2 Author(s)
Joshi, R.R. ; Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA ; Yagle, A.E.

The Krein integral equation of one-dimensional inverse scattering, which has a symmetric Toeplitz kernel, is transformed using wavelets into a “block-slanted Toeplitz” system of equations. The kernel of the integral equation does not satisfy the Calderon-Zygmund conditions and as a result, application of the wavelet transform to the integral equation does not yield a sparse system matrix. There is therefore a need for a fast algorithm which directly exploits the (symmetric block-slanted-Toeplitz) structure of the system matrix and does not rely on sparsity. The first such O(N2) algorithm is presented

Published in:

Acoustics, Speech, and Signal Processing, 1996. ICASSP-96. Conference Proceedings., 1996 IEEE International Conference on  (Volume:3 )

Date of Conference:

7-10 May 1996