A nested recursive approach to MAP estimation based on Gauss-Markov random fields

Many large multidimensional space-time signal processing and data inversion applications (e.g. deconvolution) require some form of regularization to extract meaningful information. A popular approach to regularizing such problems in a statistical context is via a Gauss-Markov random field (GMRF) prior model in a maximum a posteriori (MAP) estimation framework. While providing good reconstructions, the high dimensionality of these problems can lead to prohibitive computational constraints which limit their practical applicability, particularly in real or near-real time applications. It has been shown that GMRF models possess a particular recursive structure. Conversely, complementary work in suboptimal filtering has been based on reduced order GMRF modeling. In, this work, we combine these two results to present a suboptimal filter design which repeatedly takes advantage of this recursive GMRF structure to subdivide a large problem into a series of smaller, more tractable problems. In this way we present a method for approximate, model-based, recursive solution to such high dimensional problems based on their inherent recursive structure