The Wilson–Burg method of spectral factorization with application to helical filtering |
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| Authors: | Sergey Fomel Paul Sava James Rickett Jon F Claerbout |
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| Institution: | Bureau of Economic Geology, The University of Texas at Austin, University Station, Box X, Austin, TX 78713-8972;, Stanford Exploration Project, Department of Geophysics, Stanford University, Stanford, CA 94305;, and ChevronTexaco Exploration and Production Technology Company, 6001 Bollinger Canyon Road, San Ramon, CA 94583-2324, USA |
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| Abstract: | Spectral factorization is a computational procedure for constructing minimum-phase (stable inverse) filters required for recursive inverse filtering. We present a novel method of spectral factorization. The method iteratively constructs an approximation of the minimum-phase filter with the given autocorrelation by repeated forward and inverse filtering and rearranging of the terms. This procedure is especially efficient in the multidimensional case, where the inverse recursive filtering is enabled by the helix transform. To exemplify a practical application of the proposed method, we consider the problem of smooth two-dimensional data regularization. Splines in tension are smooth interpolation surfaces whose behaviour in unconstrained regions is controlled by the tension parameter. We show that such surfaces can be efficiently constructed with recursive filter preconditioning and we introduce a family of corresponding two-dimensional minimum-phase filters. The filters are created by spectral factorization on a helix. |
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