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. 
Gitta Kutyniok, Kasso A. Okoudjou, Friedrich Philipp, Elizabeth K.   Tuley
math.NA cs.IT cs.NA math.FA math.IT