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An Anisotropic Convection-Diffusion Model Using Tailored Finite Point Method for Image Denoising and Compression

Part of: Communication, information Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  17 May 2016

Yu-Tuan Lin ,
Yin-Tzer Shih  and
Chih-Ching Tsai
Yu-Tuan Lin*
Affiliation:
Department of Applied Mathematics, National Chung Hsing University, Taichung 40227, Taiwan Institute of Mathematics, Academia Sinica, Taiwan
Yin-Tzer Shih*
Affiliation:
Department of Applied Mathematics, National Chung Hsing University, Taichung 40227, Taiwan
Chih-Ching Tsai*
Affiliation:
Department of Applied Mathematics, National Chung Hsing University, Taichung 40227, Taiwan
*
*Corresponding author. Email addresses:ytlin@math.sinica.edu.tw (Y.-T. Lin), yintzer_shih@nchu.edu.tw (Y.-T. Shih), jet.tsai98004@gmail.com (C.-C. Tsai)
*Corresponding author. Email addresses:ytlin@math.sinica.edu.tw (Y.-T. Lin), yintzer_shih@nchu.edu.tw (Y.-T. Shih), jet.tsai98004@gmail.com (C.-C. Tsai)
*Corresponding author. Email addresses:ytlin@math.sinica.edu.tw (Y.-T. Lin), yintzer_shih@nchu.edu.tw (Y.-T. Shih), jet.tsai98004@gmail.com (C.-C. Tsai)
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Abstract

In this paper we consider an anisotropic convection-diffusion (ACD) filter for image denoising and compression simultaneously. The ACD filter is discretized by a tailored finite point method (TFPM), which can tailor some particular properties of the image in an irregular grid structure. A quadtree structure is implemented for the storage in multi-levels for the compression. We compare the performance of the proposed scheme with several well-known filters. The numerical results show that the proposed method is effective for removing a mixture of white Gaussian and salt-and-pepper noises.

Keywords

Perona-Malik filterimage denoisingconvection-diffusiontailored finite point methodsingular perturbation problemadaptive grid

MSC classification

Secondary: 65M50: Mesh generation and refinement 65M75: Probabilistic methods, particle methods, etc. 68U10: Image processing 94A08: Image processing (compression, reconstruction, etc.)
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1357 - 1374
Copyright
Copyright © Global-Science Press 2016 

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