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Uncertainty Principles and Vector Quantization

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2 Author(s)
Lyubarskii, Y. ; Dept. of Math. Sci., Norwegian Univ. of Sci. & Technol., Trondheim, Norway ; Vershynin, R.

Given a frame in Cn 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/ √(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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Information Theory, IEEE Transactions on  (Volume:56 ,  Issue: 7 )