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Electrical and Computer Engineering
Dean of Engineering
Faculty Host: Rich Baraniuk

Speaker: L. Daniel Abreu

ECE Seminar Series: MSE bounds for Thomson's estimator and off-grid compressive sensing

Tuesday, May 9, 2017
4:00 PM  to 5:00 PM

1049  Duncan Hall
Rice University
6100 Main St
Houston, Texas, USA

We obtain estimates for the Mean Squared Error (MSE) for the multitaper spectral estimator and certain compressive acquisition methods for multi-band signals. We confirm a fact discovered by Thomson [Spectrum estimation and harmonic analysis, Proc. IEEE, 1982]: assuming bandwidth W and N time domain observations, the average of the square of the first K=2NW Slepian functions approaches, as K grows, an ideal band-pass kernel for the interval [-W,W]. We provide an analytic proof of this fact and measure the corresponding rate of convergence in the L1 norm. This validates a heuristic approximation used to control the MSE of the multitaper estimator. The estimates have also consequences for the method of compressive acquisition of multi-band signals introduced by Davenport and Wakin, giving MSE approximation bounds for the dictionary formed by modulation of the critical number of prolates. We will also discuss extensions of the methods to other settings, in particular for the analysis of acoustic signals, which are in general non-stationary. This is a joint work with José Luis Romero.

Biography of L. Daniel Abreu:
Luis Daniel Abreu is at the Austrian Academy of Sciences in Vienna, in the Acoustics Research Institute. He works on time-frequency analysis, wavelets and Random Point Process, with a view to applications in Acoustics and Statistical Mechanics. Much of his recent research has focused in the relation between Determinantal Point Processes, the analysis of multi-taper methods for spectral estimation and off-grid compressed sensing.

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