Yugoslav Journal of Operations Research (Jan 2022)

Correction of thermographic images based on the minimization method of Tikhonov functional

  • Baaj Obaida,
  • Chernikova Natalia Yu.,
  • Laneev Eugeniy B.

DOI
https://doi.org/10.2298/YJOR211015026B
Journal volume & issue
Vol. 32, no. 3
pp. 407 – 424

Abstract

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The paper considers the method of correction of thermographic images (thermograms) obtained by recording in the infrared range of radiation from the surface of the object under study using a thermal imager. A thermogram with a certain degree of reliability transmits an image of the heat-generating structure inside the body. In this paper, the mathematical correction of images on a thermogram is performed based on an analytical continuation of the stationary temperature distribution as a harmonic function from the surface of the object under study towards the heat sources. The continuation is carried out by solving an ill-posed mixed problem for the Laplace equation in a cylindrical region of rectangular cross-section. To construct a stable solution to the problem, the principle of the minimum of the Tikhonov smoothing functional we used.

Keywords