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.