When are frames close to equal-norm Parseval frames?

Bernhard G. Bodmann; Peter G. Casazza

doi:10.1117/12.825705

3 September 2009 When are frames close to equal-norm Parseval frames?

Proceedings Volume 7446, Wavelets XIII; 744616 (2009) https://doi.org/10.1117/12.825705
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

Abstract

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.

Citation Download Citation

Bernhard G. Bodmann and Peter G. Casazza "When are frames close to equal-norm Parseval frames?", Proc. SPIE 7446, Wavelets XIII, 744616 (3 September 2009); https://doi.org/10.1117/12.825705

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