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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Francos, J.M., Porat, B. & Meiri, A.Z. Orthogonal decompositions of 2-D nonhomogeneous discrete random fields. Math. Control Signal Systems 8, 375–389 (1995). https://doi.org/10.1007/BF01209691
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DOI: https://doi.org/10.1007/BF01209691