24 August 2017 Finding the closest probabilistic Parseval frame in the 2-Wasserstein metric
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Abstract
It is known in the standard l2 distance that the closest Parseval frame to a given frame {Φi}mi=1d is {S-1/2(Φi)}mi=1 where S is the frame operator of the original frame. We show this is also the case for probabilistic frames in the 2-Wasserstein distance. In the process we develop some regularity properties for the map taking a probabilistic frame to its closest Parseval frame.
Conference Presentation
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Desai Cheng, Kasso A. Okoudjou, "Finding the closest probabilistic Parseval frame in the 2-Wasserstein metric", Proc. SPIE 10394, Wavelets and Sparsity XVII, 103940N (24 August 2017); doi: 10.1117/12.2271002; https://doi.org/10.1117/12.2271002
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