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

Waseem Al Hadad; Denis Maillet; Stéphane André; Benjamin Rémy

doi:10.24423/cames.39

Waseem Al Hadad LEMTA, University of Lorraine and CNRS, Nancy
Denis Maillet LEMTA, University of Lorraine and CNRS, Nancy
Stéphane André LEMTA, University of Lorraine and CNRS, Nancy
Benjamin Rémy LEMTA, University of Lorraine and CNRS, Nancy

DOI: http://dx.doi.org/10.24423/cames.39

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.

Keywords

integral transforms, thermal quadrupoles, heat transfer in mini-channel, inverse heat conduction and convection,

References

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