Frame Scaling by Graphs

Abstract

In this paper, we investigate the scalability of a given frame in ${\mathbb{R}}^n$ by using graphs. For each frame $\ddot{I}•$ in ${\mathbb{R}}^n$, we associate a simple undirected graph $G(\ddot{I}•)$ and use it to verify the scalability of $\ddot{I}•$. We provide some necessary conditions to test the scalability of a given frame. Finally, we study the scalability of some special classes of frames by using graphs.

13 pages