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Proceedings Paper

Frame completions for optimally robust reconstruction
Author(s): Matthew Fickus; Dustin G. Mixon; Miriam J. Poteet
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Paper Abstract

In information fusion, one is often confronted with the following problem: given a preexisting set of measurements about an unknown quantity, what new measurements should one collect in order to accomplish a given fusion task with optimal accuracy and efficiency. We illustrate just how difficult this problem can become by considering one of its more simple forms: when the unknown quantity is a vector in a Hilbert space, the task itself is vector reconstruction, and the measurements are linear functionals, that is, inner products of the unknown vector with given measurement vectors. Such reconstruction problems are the subject of frame theory. Here, we can measure the quality of a given frame by the average reconstruction error induced by noisy measurements; the mean square error is known to be the trace of the inverse of the frame operator. We discuss preliminary results which help indicate how to add new vectors to a given frame in order to reduce this mean square error as much as possible.

Paper Details

Date Published: 13 September 2011
PDF: 8 pages
Proc. SPIE 8138, Wavelets and Sparsity XIV, 81380Q (13 September 2011); doi: 10.1117/12.891813
Show Author Affiliations
Matthew Fickus, Air Force Institute of Technology (United States)
Dustin G. Mixon, Princeton Univ. (United States)
Miriam J. Poteet, Air Force Institute of Technology (United States)

Published in SPIE Proceedings Vol. 8138:
Wavelets and Sparsity XIV
Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal, Editor(s)

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