Applied Math And Analysis Seminar
Monday, February 6, 2012, 4:30pm, 119 Physics
Tyler Whitehouse (Vanderbilt University)
Consistent signal reconstruction and the geometry of some random polytopes
Abstract:- 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. [video]
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