Scalable frames

Kutyniok, Gitta ; Okoudjou, Kasso A.; Philipp, Friedrich und Tuley, Elizabeth K. (2013): Scalable frames. In: Linear Algebra and its Applications, Vol. 438, No. 5: pp. 2225-2238

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 00243795
• Language: English