Scalable Frames

Details Scalable Frames Scalable Frames

2012-04-09

arxiv.org/abs/1204.1880v3

Mathematics

Numerical Analysis

19 pages

Scientific paper

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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