Uncertainty principles, frames and vector quantizationRoman Vershynin University of Michigan JFAA - Editor UNITED STATES given at strobl07 (21.06.07 11:00) id: 630 length: 50min status: invited type: talk www: http://www.math.ucdavis.edu/~vershynin/ LINK-Preprint: http://www.math.ucdavis.edu/~vershynin/papers/quantization.pdf LINK-Presentation: ABSTRACT: The uncertainty principle in harmonic analysis has been interpreted and enriched in a way to yield algorithms for signal reconstruction (sparse recovery). We will see a new application of the uncertainty principles -- robust vector quantization. For frames in N dimensions that satisfy the Uncertainty Principle, one can quickly convert every frame representation into a more regular Kashin's representation, whose coefficients all have the same magnitude. Information tends to spread evenly among these coefficients. These representations have great error reduction power. In particular, scalar quantization of Kashin's representations yields robust vector quantizers. Joint work with Yuri Lyubarskii. |