Tuesday, August 06, 2013

SAHD: Going off the Grid - Benjamin Recht

From the SAHD workshop:

This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, in nite dictionary. We show how to compute the estimator via semide nite programming and provide guarantees on its mean-square error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semide nite programming approach outperforms two classical spectral estimation techniques
but also:
Thank you to the organizers of SAHDDavid BradyRobert Calderbank,Lawrence CarinIngrid Daubechies,David DunsonMauro MaggioniSayan MukherjeeGuillermo Sapiro and Rebecca Willett for making these videos available.

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