26 September 2013 Preconditioning of frames
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Abstract
The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight frame. In this paper we define m−scalability, a refinement of scalability based on the number of non-zero weights used in the rescaling process. We enlighten a close connection between this notion and elements from convex geometry. Another focus lies in the topology of scalable frames. In particular, we prove that the set of scalable frames with “usual” redundancy is nowhere dense in the set of frames.
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Gitta Kutyniok, Gitta Kutyniok, Kasso Okoudjou, Kasso Okoudjou, Friedrich Philipp, Friedrich Philipp, } "Preconditioning of frames", Proc. SPIE 8858, Wavelets and Sparsity XV, 88580G (26 September 2013); doi: 10.1117/12.2022667; https://doi.org/10.1117/12.2022667
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