Fully fractional anisotropic diffusion for image denoising
Fully fractional anisotropic diffusion for image denoising
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DOI：
10.1016/j.mcm.2011.03.017
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发表时间：
2011-07
期刊：
影响因子：
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通讯作者：
Marko Janev;S. Pilipovic;T. Atanacković;Radovan Obradovic;N. Ralević
中科院分区：
文献类型：
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作者：
Marko Janev;S. Pilipovic;T. Atanacković;Radovan Obradovic;N. Ralević
本文提出了一种新的用于噪声去除的全分数阶各向异性扩散方程，它包含空间和时间分数阶导数。它是Cuesta提出的方法的推广，Cuesta通过使用时间分数阶导数在热和波动方程之间插值，以及Bai和Feng提出的方法，通过使用空间分数阶导数在二阶和四阶各向异性扩散方程之间插值。该方程具有这两种方法的优点。为了构造数值格式，将偏微分方程（PDE）转化为空间离散的分数阶常微分方程（FODE）模型，然后采用分数阶线性多步法（FLMM）结合离散傅立叶变换（DFT）。我们证明了所提出的FODE的解析解具有一定的规律性，足以应用收敛和稳定的分数数值程序。实验结果证实，我们的模型管理，以保持边缘，特别是高度振荡的地区，比基线抛物线扩散模型更有效。
This paper introduces a novel Fully Fractional Anisotropic Diffusion Equation for noise removal which contains spatial as well as time fractional derivatives. It is a generalization of a method proposed by Cuesta which interpolates between the heat and the wave equation by the use of time fractional derivatives, and the method proposed by Bai and Feng, which interpolates between the second and the fourth order anisotropic diffusion equation by the use of spatial fractional derivatives. This equation has the benefits of both of these methods. For the construction of a numerical scheme, the proposed partial differential equation (PDE) has been treated as a spatially discretized Fractional Ordinary Differential Equation (FODE) model, and then the Fractional Linear Multistep Method (FLMM) combined with the discrete Fourier transform (DFT) is used. We prove that the analytical solution to the proposed FODE has certain regularity properties which are sufficient to apply a convergent and stable fractional numerical procedure. Experimental results confirm that our model manages to preserve edges, especially highly oscillatory regions, more efficiently than the baseline parabolic diffusion models.