Regularized Shock Filters and Complex Diffusion
Abstract
We address the issue of regularizing Osher and Rudin’s shock filter, used for image deblurring, in order to allow processes that are more robust against noise. Previous solutions to the problem suggested adding some sort of diffusion term to the shock equation. We analyze and prove some properties of coupled shock and diffusion processes. Finally we propose an original solution of adding a complex diffusion term to the shock equation. This new term is used to smooth out noise and indicate inflection points simultaneously. The imaginary value, which is an approximated smoothed second derivative scaled by time, is used to control the process. This results in a robust deblurring process that performs well also on noisy signals.
Cite
Text
Gilboa et al. "Regularized Shock Filters and Complex Diffusion." European Conference on Computer Vision, 2002. doi:10.1007/3-540-47969-4_27Markdown
[Gilboa et al. "Regularized Shock Filters and Complex Diffusion." European Conference on Computer Vision, 2002.](https://mlanthology.org/eccv/2002/gilboa2002eccv-regularized/) doi:10.1007/3-540-47969-4_27BibTeX
@inproceedings{gilboa2002eccv-regularized,
title = {{Regularized Shock Filters and Complex Diffusion}},
author = {Gilboa, Guy and Sochen, Nir A. and Zeevi, Yehoshua Y.},
booktitle = {European Conference on Computer Vision},
year = {2002},
pages = {399-413},
doi = {10.1007/3-540-47969-4_27},
url = {https://mlanthology.org/eccv/2002/gilboa2002eccv-regularized/}
}