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

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,
Published
Jan 25, 2017
How to Cite
HADAD, Waseem Al et al. 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, [S.l.], v. 21, n. 3/4, p. 211-222, jan. 2017. ISSN 2299-3649. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/39>. Date accessed: 18 jan. 2020.
Section
Articles