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Telescoping Recursive Representations and Estimation of Gauss–Markov Random Fields

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2 Author(s)
Vats, D. ; Dept. of Electr. & Comput. Eng., Carnegie Mellon Univ., Pittsburgh, PA, USA ; Moura, J.M.F.

We present telescoping recursive representations for both continuous and discrete indexed noncausal Gauss-Markov random fields. Our recursions start at the boundary (a hypersurface in ) and telescope inwards. For example, for images, the telescoping representation reduce recursions from to , 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.

Published in:

Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 3 )