Regularization using truncated singular value decomposition for estimating the Fourier spectrum of a noised space distribution over an extended support

Abstract : This paper is devoted to a theoretical and numerical study of different ways of calculating the Fourier transform of a noisy signal where the boundary conditions at the lateral boundaries of the measurement interval are not precisely known. This happens in different characterization problems where infrared camera is used for temperature measurements. In order to overcome this difficulty, the interval where the Fourier transform (its support) is supposed to be larger than the measurement domain is defined. Thus, this virtual interval larger than the measurement interval is used. We show that regularization by truncated singular value decomposition is able to yield good estimates to this very ill-posed inverse problem.
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Article dans une revue
Computer Assisted Methods in Engineering and Science, Polish Academy of Sciences, 2014, pp.211-222
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https://hal.univ-lorraine.fr/hal-01425596
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Soumis le : mardi 3 janvier 2017 - 16:23:11
Dernière modification le : dimanche 9 septembre 2018 - 09:54:02

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  • HAL Id : hal-01425596, version 1

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Waseem Al Hadad, Maillet Denis, Stéphane André, Rémy Benjamin. Regularization using truncated singular value decomposition for estimating the Fourier spectrum of a noised space distribution over an extended support. Computer Assisted Methods in Engineering and Science, Polish Academy of Sciences, 2014, pp.211-222. 〈hal-01425596〉

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