Application of multiscale estimation to large scale multidimensional imaging and remote sensing problems

A recently developed multiresolution estimation framework offers the possibility of highly efficient statistical analysis, interpolation, and smoothing of extremely large data sets in a multiscale fashion. This framework enjoys a number of advantages not shared by other statistically-based methods, particularly in terms of the ability to evaluate estimates and error variances in a computationally efficient manner, however there remain several barriers which constrain the widespread use of this framework: • The multiscale framework has been characterized as well-suited for large-scale estimation problems such as in remote sensing, however no such scientific endeavors have been undertaken which might motivate the use of the framework among scientists. • Past research efforts have developed a rich class of multiscale models; however given the selection of a particular multiscale model structure or class, the identification of unknown parameters within the model remains unclear. • The estimates produced by the estimator typically possess artifacts introduced by the multiscale structure; these artifacts are distracting to the human eye, limiting the use of the framework in certain image processing applications. This thesis directly addresses each of the above limitations: • Two problems of current scientific interest are addressed: the estimation of the ocean surface height from satellite data, and the estimation of the earth's gravitational equipotential. Both lines of research produce results of potential interest to the scientific community. • We demonstrate a technique for estimating multiscale parameters in simple models by developing an estimator for the fractal dimension of fractional Brownian motion processes. Furthermore, for a 1/f-like class of multiscale models a Cramer-Rao bound can be determined for the maximum-likelihood estimation of model parameters. Significant improvements in estimate smoothness are achieved using a novel overlapping multiscale framework capable of reducing artifacts below the level of delectability with a modest computational burden. The performance of the overlapping framework is demonstrated in the context of the surface reconstruction problem of computer vision. Thesis Supervisor: Alan S. Willsky Title: Professor of Electrical Engineering