Orthogonal decompositions of 2-D nonhomogeneous discrete random fields |
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Authors: | Joseph M. Francos Boaz Porat A. Zvi Meiri |
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Affiliation: | (1) Electrical and Computer Engineering Department, Ben-Gurion University, 84105 Beer-Sheva, Israel;(2) Electrical Engineering Department, Technion-Israel Institute of Technology, 32000 Haifa, Israel;(3) Elscint, P.O. Box 550, 31004 Haifa, Israel |
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Abstract: | Imposing atotal-order on a two-dimensional (2-D) discrete random field induces an orthogonal decomposition of the random field into two components: Apurely-indeterministic field and adeterministic one. The purely-indeterministic component is shown to have a 2-D white-innovations driven moving-average representation. The 2-D deterministic random field can be perfectly predicted from the field's past with respect to the imposed total-order definition. The deterministic field is further orthogonally decomposed into anevanescent field, and aremote past field. The evanescent field is generated by the columnto-column innovations of the deterministic field with respect to the imposed nonsymmetrical-half-plane total-ordering definition. The presented decomposition can be obtained with respect to any nonsymmetrical-half-plane total-ordering definition, for which the nonsymmetrical-half-plane boundary line has rational slope. |
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Keywords: | Two-dimensional (2-D) nonhomogeneous random fields Total-order Wold decomposition Purely-indeterministic random fields Deterministic random fields Evanescent random fields |
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