Low-Rank Variance Approximation in GMRF Models: Single and Multiscale Approaches

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.

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: Dmitry M. Malioutov, Jason K. Johnson, Myung Jin Choi, Alan S. Willsky
• Keywords: Large-scale Gaussian Markov, Long-range Correlation Case, Low-rank Aliasing Matrix, TSP 2008