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arXiv · 1204.1880

Scalable Frames

Gitta Kutyniok·Kasso A. Okoudjou·Friedrich Philipp·Elizabeth K. Tuley
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Abstract

Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process which can also be regarded as perfect preconditioning of a frame by a diagonal operator. A frame is called scalable, if such a diagonal operator exists. We derive various characterizations of scalable frames, thereby including the infinite-dimensional situation. Finally, we provide a geometric interpretation of scalability in terms of conical surfaces.

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Gitta Kutyniok, Kasso A. Okoudjou, Friedrich Philipp, Elizabeth K. Tuley. 2012-04-15. Scalable Frames. https://arxiv.org/abs/1204.1880

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