Uncertainty principles and vector quantization

Authors:
Yurii Lyubarskii;Roman Vershynin
Affiliations:
Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway;Department of Mathematics, University of Michigan, Ann Arbor, MI
Venue:
IEEE Transactions on Information Theory
Year:
2010

Citing 13
Cited 0

Uncertainty principles and signal recovery

SIAM Journal on Applied Mathematics
Ten lectures on wavelets

Ten lectures on wavelets
Stable distributions, pseudorandom generators, embeddings and data stream computation

FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions

Foundations of Computational Mathematics
One sketch for all: fast algorithms for compressed sensing

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantized overcomplete expansions in IRN: analysis, synthesis, and algorithms

IEEE Transactions on Information Theory
Quantization

IEEE Transactions on Information Theory
Resilience properties of redundant expansions under additive noise and quantization

IEEE Transactions on Information Theory
Decoding by linear programming

IEEE Transactions on Information Theory
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information

IEEE Transactions on Information Theory
A/D conversion with imperfect quantizers

IEEE Transactions on Information Theory
Robust and Practical Analog-to-Digital Conversion With Exponential Precision

IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?

IEEE Transactions on Information Theory

Quantified Score

Hi-index	754.84

Visualization

Abstract

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.