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Paper detail

Scalable Frames

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.

preprint2012arXivOpen access
Gitta KutyniokKasso A. OkoudjouFriedrich PhilippElizabeth K. Tuley
math.ITInformation Theorymath.FAmath.NANumerical Analysis
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Gitta KutyniokKasso A. OkoudjouFriedrich PhilippElizabeth K. Tuley

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