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Uncertainty Principles and Vector Quantization

Yurii Lyubarskii·Roman Vershynin
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Abstract

Given a frame in C^n which satisfies a form of the uncertainty principle (as introduced by Candes and Tao), it is shown how to quickly convert the frame representation of every vector into a more robust Kashin's representation whose coefficients all have the smallest possible dynamic range O(1/\sqrt{n}). The information tends to spread evenly among these coefficients. As a consequence, Kashin's representations have a great power for reduction of errors in their coefficients, including coefficient losses and distortions.

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Yurii Lyubarskii, Roman Vershynin. 2010-04-06. Uncertainty Principles and Vector Quantization. https://doi.org/10.1109/tit.2010.2048458

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