Date: Wednesday, February 06, 2013
Location: 4096 East Hall (4:10 PM to 5:00 PM)
Title: Consistent reconstruction and some geometry of random polytopes
Abstract: Consistent reconstruction is a linear programming approach for estimation problems involving bounded noise (for example, the problem of reconstructing a signal from a set of quantized linear measurements). We prove new mean squared error bounds for consistent reconstruction in the setting of random frames and under the uniform quantization noise model. In particular, we prove that the mean squared error for consistent reconstruction is of the optimal order C/N^2 where N is the number of measurements, and we prove bounds on the associated dimension dependent constant C. For comparison, in the 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 main results involve an analysis of random polytopes and of associated coverage processes on the sphere. This is joint work with Tyler Whitehouse.
Speaker: Alexander Powell
Institution: Vanderbilt University
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