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- Title
Tight Frame Completions with Prescribed Norms.
- Authors
Massey, P. G.; Ruiz, M. A.
- Abstract
Let H be a finite dimensional (real or complex) Hilbert space and let {ai}i=1∞ be a non-increasing sequence of positive numbers. Given a finite sequence of vectors F = {fi}i=1p in H we find necessary and sufficient conditions for the existence of r ∈ N ∪ {∞} and a Bessel sequence G = {gi}i=1r in H such that F ∪ G is a tight frame for H and ∥gi∥2 = ai for every i. Moreover, in this case we compute the minimum r ∈ N ∪ {∞} with this property. We also describe algorithms that perform completions of a given set of vectors to tight frames.
- Subjects
FRAMES (Vector analysis); HILBERT space; VECTOR analysis; ALGORITHMS; SIGNAL processing; IMAGE processing
- Publication
Sampling Theory in Signal & Image Processing, 2008, Vol 7, Issue 1, p1
- ISSN
1530-6429
- Publication type
Article
- DOI
10.1007/bf03549482