Scalable Frames
Numerical Analysis
2012-04-17 v3 Information Theory
Numerical Analysis
Functional Analysis
math.IT
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.
Keywords
Cite
@article{arxiv.1204.1880,
title = {Scalable Frames},
author = {Gitta Kutyniok and Kasso A. Okoudjou and Friedrich Philipp and Elizabeth K. Tuley},
journal= {arXiv preprint arXiv:1204.1880},
year = {2012}
}
Comments
19 pages