Multiresolution model development for overlapping trees via canonical correlation analysis

TitleMultiresolution model development for overlapping trees via canonical correlation analysis
Publication TypeConference Paper
Year of Publication1995
AuthorsFieguth, P., W. W. Irving, and A. S. Willsky
Conference NameInternational Conference on Image Processing
Keywordscanonical correlation analysis, correlation methods, covariance analysis, error analysis, error covariance information, estimation algorithm, estimation theory, fast statistically optimal algorithm, Gaussian processes, Gaussian random processes, image domain, image pixel, image representation, image resolution, multiresolution model, multiscale representations, multiscale stochastic models, optimal estimation results, overlapping trees, random processes, scale recursive dynamics, statistics, tree nodes, trees (mathematics)

A class of multiscale stochastic models has been introduced in which Gaussian random processes are described by scale-recursive dynamics that are indexed by the nodes of a tree. One of the primary reasons the framework is useful is that it leads to an extremely fast, statistically optimal algorithm for least-squares estimation in the context of 2-D images. We refine this approach to estimation by eliminating the visually distracting blockiness that has been observed in the previous work. We eliminate the blockiness by discarding the standard assumption that distinct nodes at a given level of our tree correspond to disjoint portions of the image domain; as a consequence of this simple idea, a given image pixel may now correspond to several tree nodes. We develop tools for systematically building overlapping-tree multiscale representations of prespecified statistics, and we develop a corresponding estimation algorithm for this processes. In this way, we achieve nearly optimal estimation results, we generate corresponding error covariance information, and we eliminate blockiness without sacrificing the resolution of fine-scale detail