一种基于耦合扩散的图像去噪模型的分析与仿真
Analysis and Simulation of a Coupled Diffusion based Image Denoising Model
摘要：
提出了一种新的基于耦合偏微分方程（CPDE）的图像去噪模型，该模型将时空正则化与非线性扩散相结合。该模型采用加性高斯噪声拟合，在保持边缘和精细结构的同时实现了有效的图像平滑。为此，我们提出了一个新的功能最小化框架，以消除图像噪声，这导致在解决三个偏微分方程（PDE）的系统。我们提出的模型是不同于现有的CPDE模型，因为它包括两个额外的发展方程处理边缘强度函数和数据保真度项。这两个发展方程控制平滑过程，并迫使得到的去噪解接近初始解。据我们所知，所提出的模型是唯一的工作，它破译了这两个条款使用单独的偏微分方程的综合效果。此外，我们建立了该系统的弱解的存在性和唯一性使用的时间离散方法与$H^1$初始数据。最后，采用广义加权平均有限差分格式对该耦合系统进行了有效求解，实验结果表明了该CPDE模型的有效性。
英文摘要：
In this study, a new coupled Partial Differential Equation (CPDE) based image denoising model incorporating space-time regularization into non-linear diffusion is proposed. This proposed model is fitted with additive Gaussian noise which performs efficient image smoothing along with the preservation of edges and fine structures. For this purpose, we propose a new functional minimization framework to remove the image noise, which results in solving a system of three partial differential equations (PDEs). Our proposed model is dissimilar from the existing CPDE models as it includes two additional evolution equations to handle edge strength function and data fidelity term. These two evolution equations control the smoothing process and force the resultant denoised solution to be close to the initial solution. To the best of our knowledge, the proposed model is the only work, which deciphers the combined effect of both the terms using separate PDEs. Furthermore, we establish the existence and uniqueness of a weak solution of the proposed system using the time discretization method with $H^1$ initial data. Finally, we used a generalized weighted average finite difference scheme to efficiently solve the coupled system and experiment results show the effectiveness of the proposed CPDE model.
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