We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell 12 (1990) 629-639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell 14 (1998) 826-835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.
Keywords: image restoration, edge detection, Perona-Malik equation, time-delay regularization
@article{M2AN_2005__39_2_231_0,
author = {Belahmidi, Abdelmounim and Chambolle, Antonin},
title = {Time-delay regularization of anisotropic diffusion and image processing},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {231--251},
year = {2005},
publisher = {EDP Sciences},
volume = {39},
number = {2},
doi = {10.1051/m2an:2005010},
mrnumber = {2143948},
zbl = {1101.68102},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2005010/}
}
TY - JOUR AU - Belahmidi, Abdelmounim AU - Chambolle, Antonin TI - Time-delay regularization of anisotropic diffusion and image processing JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2005 SP - 231 EP - 251 VL - 39 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2005010/ DO - 10.1051/m2an:2005010 LA - en ID - M2AN_2005__39_2_231_0 ER -
%0 Journal Article %A Belahmidi, Abdelmounim %A Chambolle, Antonin %T Time-delay regularization of anisotropic diffusion and image processing %J ESAIM: Modélisation mathématique et analyse numérique %D 2005 %P 231-251 %V 39 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2005010/ %R 10.1051/m2an:2005010 %G en %F M2AN_2005__39_2_231_0
Belahmidi, Abdelmounim; Chambolle, Antonin. Time-delay regularization of anisotropic diffusion and image processing. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 2, pp. 231-251. doi: 10.1051/m2an:2005010
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