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SUMMARY:Estimation of linear operators from scattered impulse responses -
Pierre Weiss (Université de Toulouse)
DTSTART:20170908T101000Z
DTEND:20170908T110000Z
UID:TALK78471@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Co-authors: Paul Escande (Université\; de Toulous
e)\, Jé\;ré\;mie Bigot (Université\; de Toulouse)
In this talk\, I will propose a variational method to rec
onstruct operators with smooth kernels from scattered and noisy impulse re
sponses. The proposed approach relies on the formalism of smoothing in rep
roducing kernel Hilbert spaces and on the choice of an appropriate regular
ization term that takes the smoothness of the operator into account. It is
numerically tractable in very large dimensions and yields a representatio
n that can be used for achieving fast matrix-vector products. We study the
estimator'\;s robustness to noise and analyze its approximation proper
ties with respect to the size and the geometry of the dataset. It turns ou
t to be minimax optimal.
We finally show applications of the prop
osed algorithms to reconstruction of spatially varying blur operators in m
icroscopy imaging.
Related Links
LOCATION:Seminar Room 1\, Newton Institute
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