Uncertainty Principles and Vector Quantization

Details Uncertainty Principles and Vector Quantization Uncertainty Principles and Vector Quantization

2006-11-12

arxiv.org/abs/math/0611343v2

Mathematics

Numerical Analysis

Final version, to appear in IEEE Trans. Information Theory. Introduction updated, minor inaccuracies corrected.

Scientific paper

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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