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Nonparametric estimation of highly oscillatory signals
Skrifað af mou | September 16, 2008
Fyrirlestur Hannesar Helgasonar á vegum IEEE á Íslandi í samstarfi við rafmagns og tölvuverkfræðideild Háskóla Íslands.
Staður: Háskóli Íslands, VRII, stofa 157, 16:30 Mánudaginn 22. September.
Titill: Nonparametric estimation of highly oscillatory signals
Útdráttur/abstract:
We will consider the problem of estimating highly oscillatory signals
from noisy measurements. These signals are often referred to as chirps
in the literature; they are found everywhere in nature, and frequently
arise in scientific and engineering problems. Mathematically, they can
be written in the general form A(t) exp(ilambda varphi(t)), where
lambda is a large constant base frequency, the phase varphi(t) is
time-varying, and the envelope A(t) is slowly varying. Given a
sequence of noisy measurements, we study the problem of estimating
this chirp from the data.
We introduce novel, flexible and practical strategies for addressing
these important nonparametric statistical problems. The main idea is
to calculate correlations of the data with a rich family of local
templates in a first step, the multiscale chirplets, and in a second
step, search for meaningful aggregations or chains of chirplets which
provide a good global fit to the data. From a physical viewpoint,
these chains correspond to realistic signals since they model
arbitrary chirps. From an algorithmic viewpoint, these chains are
identified as paths in a convenient graph. The key point is that this
important underlying graph structure allows to unleash very effective
algorithms such as network flow algorithms for finding those chains
which optimize a near optimal trade-off between goodness of fit and
complexity.
Our estimation procedures provide provably near optimal performance
over a wide range of chirps and numerical experiments show that our
estimation procedures perform exceptionally well over a broad class of
chirps.
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Note that the talk will be in English.
Hannes útskrifaðist með BS gráðu bæði frá rafmagns- og tölvuverkfræðiskor og stærðfræðiskor vorið 2001. Hann varði Phd ritgerð sína frá Applied og Computational Mathematics deild í California Institute of Technology (Caltech), Pasadena, CA í ágúst 2007 og hlaut Phd gráðuna í júní 2008. Hannes fékk W.P.Carey Price in Applied Mathematics fyrir doktorverkefni sitt en þessi viðurkenning er aðeins veitt framúrskarandi doktorsverkefnum í hagnýtri eða hreinni stærðfræði. Leiðbeinandi Hannesar var Prof. Emmanuel Candes. Hannes starfar nú hjá Kaupþingi.
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