# Tyler Whitehouse : Consistent signal reconstruction and the geometry of some random polytopes

Consistent reconstruction is a linear programming technique for reconstructing a signal $x\in\RR^d$ from a set of noisy or quantized linear measurements. In the setting of random frames combined with noisy measurements, we prove new mean squared error (MSE) bounds for consistent reconstruction. In particular, we prove that the MSE for consistent reconstruction is of the optimal order $1/N^2$ where $N$ is the number of measurements, and we prove bounds on the associated dimension dependent constant. For comparison, in the important case of unit-norm tight frames with linear reconstruction (instead of consistent reconstruction) the mean squared error only satisfies a weaker bound of order $1/N$. Our results require a mathematical analysis of random polytopes generated by affine hyperplanes and of associated coverage processes on the sphere. This is joint work with Alex Powell.

**Category**: Applied Math and Analysis**Duration**: 01:34:44**Date**: February 6, 2012 at 4:25 PM**Views**: 107-
**Tags:**seminar, Applied Math And Analysis Seminar

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