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Proceedings Paper

Constructing fusion frames with desired parameters
Author(s): Robert Calderbank; Peter G. Casazza; Andreas Heinecke; Gitta Kutyniok; Ali Pezeshki
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Paper Abstract

A fusion frame is a frame-like collection of subspaces in a Hilbert space. It generalizes the concept of a frame system for signal representation. In this paper, we study the existence and construction of fusion frames. We first introduce two general methods, namely the spatial complement and the Naimark complement, for constructing a new fusion frame from a given fusion frame. We then establish existence conditions for fusion frames with desired properties. In particular, we address the following question: Given M, N, m ∈ N and {λj}Mj =1, does there exist a fusion frame in RM with N subspaces of dimension m for which {λj}Mj =1 are the eigenvalues of the associated fusion frame operator? We address this problem by providing an algorithm which computes such a fusion frame for almost any collection of parameters M, N, m ∈ N and {λj}Mj =1. Moreover, we show how this procedure can be applied, if subspaces are to be added to a given fusion frame to force it to become tight.

Paper Details

Date Published: 4 September 2009
PDF: 10 pages
Proc. SPIE 7446, Wavelets XIII, 744612 (4 September 2009); doi: 10.1117/12.825782
Show Author Affiliations
Robert Calderbank, Princeton Univ. (United States)
Peter G. Casazza, Univ. of Missouri, Columbia (United States)
Andreas Heinecke, Univ. of Missouri, Columbia (United States)
Gitta Kutyniok, Univ. of Osnabrück (Germany)
Ali Pezeshki, Colorado State Univ. (United States)


Published in SPIE Proceedings Vol. 7446:
Wavelets XIII
Vivek K. Goyal; Manos Papadakis; Dimitri Van De Ville, Editor(s)

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