Geodesic
Correction of Thermographic Images Based on the MIinimization Method of Tikhonov Functional
Yugoslav journal of operations research, Tome 32 (2022) no. 3, p. 407 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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.We performed the mathematical correction of images on a thermogram, 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 is used.
Classification : 35R25, 35R30
Keywords: termogram, ill-posed problem, inverse problem, Cauchy problem for the Laplace equation, integral equation of the first kind, Tikhonov regularization method 
@article{YJOR_2022_32_3_a6,
     author = {Obaida Baaj and Natalia Yu. Chernikova and Eugeniy B. Laneev},
     title = {Correction of {Thermographic} {Images} {Based} on the {MIinimization} {Method} of {Tikhonov} {Functional}},
     journal = {Yugoslav journal of operations research},
     pages = {407 },
     publisher = {mathdoc},
     volume = {32},
     number = {3},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2022_32_3_a6/}
}
TY  - JOUR
AU  - Obaida Baaj
AU  - Natalia Yu. Chernikova
AU  - Eugeniy B. Laneev
TI  - Correction of Thermographic Images Based on the MIinimization Method of Tikhonov Functional
JO  - Yugoslav journal of operations research
PY  - 2022
SP  - 407 
VL  - 32
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/YJOR_2022_32_3_a6/
LA  - en
ID  - YJOR_2022_32_3_a6
ER  - 
%0 Journal Article
%A Obaida Baaj
%A Natalia Yu. Chernikova
%A Eugeniy B. Laneev
%T Correction of Thermographic Images Based on the MIinimization Method of Tikhonov Functional
%J Yugoslav journal of operations research
%D 2022
%P 407 
%V 32
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/YJOR_2022_32_3_a6/
%G en
%F YJOR_2022_32_3_a6
Obaida Baaj; Natalia Yu. Chernikova; Eugeniy B. Laneev. Correction of Thermographic Images Based on the MIinimization Method of Tikhonov Functional. Yugoslav journal of operations research, Tome 32 (2022) no. 3, p. 407 . http://geodesic.mathdoc.fr/item/YJOR_2022_32_3_a6/