Preconditioning of frames

Gitta Kutyniok; Kasso Okoudjou; Friedrich Philipp

doi:10.1117/12.2022667

26 September 2013 Preconditioning of frames

Gitta Kutyniok, Kasso Okoudjou, Friedrich Philipp

Proceedings Volume 8858, Wavelets and Sparsity XV; 88580G (2013) https://doi.org/10.1117/12.2022667
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

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.

Citation Download Citation

Gitta Kutyniok, Kasso Okoudjou, and Friedrich Philipp "Preconditioning of frames", Proc. SPIE 8858, Wavelets and Sparsity XV, 88580G (26 September 2013); https://doi.org/10.1117/12.2022667

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