We derive lower and upper bounds for the distance between a frame and the set of equal-norm Parseval frames. The lower bound results from variational inequalities. The upper bound is obtained with a technique that uses a family of ordinary differential equations for Parseval frames which can be shown to converge to an equal-norm Parseval frame, if the number of vectors in a frame and the dimension of the Hilbert space they span are relatively prime, and if the initial frame consists of vectors having sufficiently nearly equal norms.

Date Published: 3 September 2009
PDF: 8 pages
Proc. SPIE 7446, Wavelets XIII, 744616 (3 September 2009); doi: 10.1117/12.825705

Published in SPIE Proceedings Vol. 7446:
Wavelets XIII
Vivek K. Goyal; Manos Papadakis; Dimitri Van De Ville, Editor(s)