Telescoping Recursive Representations and Estimation of Gauss-Markov Random Fields

Abstract

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 ${\mathbb{R}}^d$, $d\ge 1$) 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.

To appear in the Transactions on Information Theory

References in corpus (1)

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