Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields

Details Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields

2009-07-30

arxiv.org/abs/0907.5397v4

IEEE Transactions on Information Theory, vol. 57, no. 3, pp 1645-1663, March 2011

Computer Science

Information Theory

To appear in the Transactions on Information Theory

Scientific paper

10.1109/TIT.2011.2104612

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.

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