Research Overview:

My research interests lie in the domain of multidimensional signal processing and large-scale estimation problems in which the key challenge is a computational one. My research is focused on continuing the development of the theory and understanding of scale recursive estimation algorithms for multiresolution stochastic processes. Such algorithms use a statistically meaningful divide-and-conquer strategy to break large estimation problems into smaller pieces, leading to vast improvements in efficiency.

These multiscale estimation algorithms are capable of extremely fast assimilation (a more sophisticated form of averaging) of data, but suffer from a few drawbacks: it is difficult to determine the appropriate multiscale model for a given application of interest, the model assumes a time-invariant model underlying the measurements, and the estimates produced by the model often possess certain multiscale artifacts. The goal of my research has been to address these limitations in the context of a specific data assimilation problem involving a time-varying system: the shape of the surface of the world's oceans. This approach has allowed us to make a contribution to a problem in oceanography while simultaneously giving us access to an extensive data set on which to test our algorithms.

Current Graduate Students

Former Graduate Students

(The background image shows a hierarchical quadtree which has played a fundamental role in my statistical modeling research.)

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