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Volume 9, Issue 1
Compound PDE-Based Additive Denoising Solution Combining an Improved Anisotropic Diffusion Model to a 2D Gaussian Filter Kernel

Tudor Barbu & C. Moroşanu

DOI: 10.4208/eajam.270318.260518

East Asian J. Appl. Math., 9 (2019), pp. 1-12.

Published online: 2019-01

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  • Abstract

A second-order nonlinear anisotropic diffusion-based model for Gaussian additive noise removal is proposed. The method is based on a properly constructed edge-stopping function and provides an efficient detail-preserving denoising. It removes additive noise, overcomes blurring effect, reduces the image staircasing and does not generate multiplicative noise, thus preserving boundaries and all the essential image features very well. The corresponding PDE model is solved by a robust finite-difference based iterative scheme consistent with the diffusion model. The method converges very fast to the model solution, the existence and regularity of which is rigorously proved.

  • Keywords

Image restoration, nonlinear anisotropic, diffusion, qualitative properties of solutions, boundary value problems for nonlinear parabolic PDE, Leray-Schauder principle.

  • AMS Subject Headings

35Bxx, 94A08, 35K55, 35K60, 35Qxx, 65Nxx

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-1, author = {Tudor Barbu and C. Moroşanu}, title = {Compound PDE-Based Additive Denoising Solution Combining an Improved Anisotropic Diffusion Model to a 2D Gaussian Filter Kernel}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {1}, pages = {1--12}, abstract = {

A second-order nonlinear anisotropic diffusion-based model for Gaussian additive noise removal is proposed. The method is based on a properly constructed edge-stopping function and provides an efficient detail-preserving denoising. It removes additive noise, overcomes blurring effect, reduces the image staircasing and does not generate multiplicative noise, thus preserving boundaries and all the essential image features very well. The corresponding PDE model is solved by a robust finite-difference based iterative scheme consistent with the diffusion model. The method converges very fast to the model solution, the existence and regularity of which is rigorously proved.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.270318.260518}, url = {http://global-sci.org/intro/article_detail/eajam/12931.html} }
TY - JOUR T1 - Compound PDE-Based Additive Denoising Solution Combining an Improved Anisotropic Diffusion Model to a 2D Gaussian Filter Kernel AU - Tudor Barbu & C. Moroşanu JO - East Asian Journal on Applied Mathematics VL - 1 SP - 1 EP - 12 PY - 2019 DA - 2019/01 SN - 9 DO - http://doi.org/10.4208/eajam.270318.260518 UR - https://global-sci.org/intro/article_detail/eajam/12931.html KW - Image restoration, nonlinear anisotropic, diffusion, qualitative properties of solutions, boundary value problems for nonlinear parabolic PDE, Leray-Schauder principle. AB -

A second-order nonlinear anisotropic diffusion-based model for Gaussian additive noise removal is proposed. The method is based on a properly constructed edge-stopping function and provides an efficient detail-preserving denoising. It removes additive noise, overcomes blurring effect, reduces the image staircasing and does not generate multiplicative noise, thus preserving boundaries and all the essential image features very well. The corresponding PDE model is solved by a robust finite-difference based iterative scheme consistent with the diffusion model. The method converges very fast to the model solution, the existence and regularity of which is rigorously proved.

Tudor Barbu and C. Moroşanu. (2019). Compound PDE-Based Additive Denoising Solution Combining an Improved Anisotropic Diffusion Model to a 2D Gaussian Filter Kernel. East Asian Journal on Applied Mathematics. 9 (1). 1-12. doi:10.4208/eajam.270318.260518
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