Low-Rank Variance Approximation in GMRF Models: Single and Multiscale Approaches
Malioutov, D.M.
Johnson, J.K.
Myung Jin Choi
Willsky, A.S.
Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA;
This paper appears in: Signal Processing, IEEE Transactions on
Publication Date: Oct. 2008
Volume: 56,
Issue: 10, Part 1
On page(s): 4621-4634
ISSN: 1053-587X
Digital Object Identifier: 10.1109/TSP.2008.927482
First Published: 2008-06-20
Current Version Published: 2008-09-16
Abstract We present a versatile framework for tractable computation of approximate variances in large-scale Gaussian Markov random field estimation problems. In addition to its efficiency and simplicity, it also provides accuracy guarantees. Our approach relies on the construction of a certain low-rank aliasing matrix with respect to the Markov graph of the model. We first construct this matrix for single-scale models with short-range correlations and then introduce spliced wavelets and propose a construction for the long-range correlation case, and also for multiscale models. We describe the accuracy guarantees that the approach provides and apply the method to a large interpolation problem from oceanography with sparse, irregular, and noisy measurements, and to a gravity inversion problem.
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