Geometric optimization on spaces of finite frames

Nate Strawn

doi:10.1117/12.894981

27 September 2011 Geometric optimization on spaces of finite frames

Nate Strawn

Proceedings Volume 8138, Wavelets and Sparsity XIV; 81380R (2011) https://doi.org/10.1117/12.894981
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

A finite (μ; S)-frame variety consists of the real or complex matrices F = [f₁...f_N] with frame operator FF* = S, and satisfying IIf_iII = μ_i for all i = 1,...,N. Here, S is a fixed Hermitian positive definite matrix and μ = [μ₁,..., μ_N] is a fixed list of lengths. These spaces generalize the well-known spaces of finite unit norm tight frames. We explore the local geometry of these spaces and develop geometric optimization algorithms based on the resulting insights.

Citation Download Citation

Nate Strawn "Geometric optimization on spaces of finite frames", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81380R (27 September 2011); https://doi.org/10.1117/12.894981

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