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Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields

Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields,10.1109/TIT.2011.2104612,IEEE Transactions on Information Theory,Di

Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields
We present \emph{telescoping} recursive representations for both continuous and discrete indexed noncausal Gauss-Markov random fields. Our recursions start at the boundary (a hypersurface in $\R^d$, $d \ge 1$) and telescope inwards. For example, for images, the telescoping representation reduce recursions from $d = 2$ to $d = 1$, i.e., to recursions on a single dimension. Under appropriate conditions, the recursions for the random field are linear stochastic differential/difference equations driven by white noise, for which we derive recursive estimation algorithms, that extend standard algorithms, like the Kalman-Bucy filter and the Rauch-Tung-Striebel smoother, to noncausal Markov random fields.
Journal: IEEE Transactions on Information Theory - TIT , vol. 57, no. 3, pp. 1645-1663, 2011
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Citation Context (1)

• ...Recently, we derived a recursive representation for Gauss-Markov random fields where the recursions initiate at the boundary and telescope inwards [6]...
• ...Recursive representations and recursive estimators for Gaussian reciprocal processes have been derived in [6], [12], [13]...
• ...we can directly use the results of [6] to derive the recursive representation...
• ...Proof: The proof follows similar steps as the proof of Theorem 9 in [6]...

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