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Estimation of linear operators from scattered impulse responses

Bigot, Jérémie and Escande, Paul and Weiss, Pierre Estimation of linear operators from scattered impulse responses. (2019) Applied and Computational Harmonic Analysis, 47 (3). 730-758. ISSN 1063-5203

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Official URL: https://doi.org/10.1016/j.acha.2017.12.002

Abstract

We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the choice of an appropriate regularization term that takes the smoothness of the operator into account. It is numerically tractable in very large dimensions. We study the stimator’s robustness to noise and analyze its approximation properties with respect to the size and the geometry of the dataset. In addition, we show minimax optimality of the proposed estimator.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Bordeaux INP - BINP (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Université de Bordeaux 1 (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Université de Bordeaux 2 - Victor Segalen (FRANCE)
Other partners > Université de Bordeaux (FRANCE)
Laboratory name:
Funders:
PRES of Toulouse University and Midi-Pyrenees region
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Deposited By: Paul Escande
Deposited On:25 Apr 2017 15:32

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