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19 May 2011 Practical optimal processing in hyperdimensional spaces via domain-reducing mappings
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Modern multi- and hyper-dimensional processing problems, such as those encountered in many applications involving image processing, adaptive beamforming, hyperspectral IR detection, medical imaging, STAP, Volterra calibration, etc., are numerically very demanding due to the vast amounts of data involved. Further compounding the situation is the fact that many such applications require estimating a set of parameters of interest that may be so large that the data available, despite its massiveness, may not be enough to properly calculate the pertinent statistics. The approach presented here addresses such problems by projecting the available data - both, modeled and measured - into a reduced-dimensionality domain where the estimation process is then performed. This strategy is extremely useful when the parameter set is not the final objective per se, but rather just a means to an end (e.g., a classification decision, detecting a signal of interest, etc.). In particular, we will concentrate on the case of finding the optimal projector for a given problem of interest where a priori information may be available. This means that the reduced-dimensionality domain must be selected as one incorporating and preserving that knowledge. We explore the use of Krylov Subspaces to achieve this end, as they inherently allow the inclusion of such data. In order to maintain a visage of practicality, we have chosen to present our developments from the perspective of the adaptive processing (filtering) problem, as this enables our presentation to be applicable to the endless expanse of optimization problems that can be addressed via a Least Squares formulation. Regularization issues, as well as extensions to non-linear filters (Taylor/Volterra/polynomial), will also be presented so as to provide additional ideas regarding the usefulness and malleability of our methods.
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Manuel Fernández, Tom Aridgides, and Firooz Sadjadi "Practical optimal processing in hyperdimensional spaces via domain-reducing mappings", Proc. SPIE 8049, Automatic Target Recognition XXI, 80490R (19 May 2011);

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