Uncertainty principles and vector quantization

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.

• Type: Journal
• Year: 2010
• Where: TIT
• Authors: Yurii Lyubarskii, Roman Vershynin
• Keywords: Coefficients, Education, Possible Dynamic Range, TIT 2010, Uncertainty Principle