Finding the closest probabilistic Parseval frame in the 2-Wasserstein metric

Desai Cheng; Kasso A. Okoudjou

doi:10.1117/12.2271002

24 August 2017 Finding the closest probabilistic Parseval frame in the 2-Wasserstein metric

Desai Cheng, Kasso A. Okoudjou

Proceedings Volume 10394, Wavelets and Sparsity XVII; 103940N (2017) https://doi.org/10.1117/12.2271002
Event: SPIE Optical Engineering + Applications, 2017, San Diego, California, United States

Abstract

It is known in the standard l² distance that the closest Parseval frame to a given frame {Φ_i}^m_i=1 ⊂ ℜ ^d is {S^-1/2(Φ_i)}^m_i=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.

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Citation Download Citation

Desai Cheng and 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); https://doi.org/10.1117/12.2271002

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