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Internal models and recursive estimation for 2-D isotropic random fields

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3 Author(s)
Tewfik, A.H. ; Dept. of Electr. Eng., Minnesota Univ., Minneapolis, MN, USA ; Levy, B.C. ; Willsky, A.S.

Efficient recursive smoothing algorithms are developed for isotropic random fields that can be obtained by passing white noise through rational filters. The estimation problem is shown to be equivalent to a countably infinite set of 1-D separable two-point boundary value smoothing problems. The 1-D smoothing problems are solved using a Markovianization approach followed by a standard 1-D smoothing algorithm. The desired field estimate is then obtained as properly weighted sum of the 1-D smoothed estimates. The 1-D two-point boundary value problems are also shown to have the same asymptotic properties and yield a stable spectral factorization of the power spectrum of the isotropic random fields

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Information Theory, IEEE Transactions on  (Volume:37 ,  Issue: 4 )