27 September 2011 Geometric optimization on spaces of finite frames
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Abstract
A finite (μ; S)-frame variety consists of the real or complex matrices F = [f1...fN] with frame operator FF* = S, and satisfying IIfiII = μi for all i = 1,...,N. Here, S is a fixed Hermitian positive definite matrix and μ = [μ1,..., μN] 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.
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Nate Strawn, "Geometric optimization on spaces of finite frames", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81380R (27 September 2011); doi: 10.1117/12.894981; https://doi.org/10.1117/12.894981
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