A Self-governing Fourth-order Nonlinear Diffusion Filter for Image Noise Removal
A Self-governing Fourth-order Nonlinear Diffusion Filter for Image Noise Removal
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DOI：
10.2197/ipsjtcva.2.94
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发表时间：
2010
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影响因子：
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通讯作者：
Mohammad Reza Hajiaboli
中科院分区：
文献类型：
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作者：
Mohammad Reza Hajiaboli
四阶非线性扩散去噪滤波器提供了噪声平滑和边缘保持的良好组合，而不会在滤波图像上产生阶梯伪影。然而，找到模型参数的最佳选择（即扩散率函数中的阈值和用于数值求解器的稳定性的时间步长）是一个具有挑战性的问题，并且通常，这些模型参数是依赖于图像内容的。本文提出了一种四阶扩散滤波器，其中扩散率函数是图像梯度模的函数。它示出，这种设置的扩散率函数可以导致一个强大的和快速收敛的过滤器中的模型参数被减少到唯一的阈值中的扩散率函数，可以估计。一个数据无关的时间步长已被解析地发现，以保证所提出的过滤器的数值求解器的收敛性。虽然这个时间步长是小于通常使用的，它示出，所提出的滤波器的数值求解器可以提供一个显着快速的收敛速度相比，由于改进的图像选择性平滑所得到的经典滤波器的扩散函数的建议过滤器。仿真结果表明，所提出的滤波器得到的去噪图像的质量显着高于从现有的滤波器。
Fourth-order nonlinear diffusion denoising filters are providing a good combination of the noise smoothing and the edge preservation without creating the staircase artifacts on the filtered image. However, finding an optimal choice of model parameters (i.e. the threshold value in a diffusivity function and a time step-size for stability of the numerical solver) is a challenging problem and generally, these model parameters are image-content dependent. In this paper, a fourth-order diffusion filter is proposed in which the diffusivity function is a function of modulus of the gradient of the image. It is shown that this setting for the diffusivity function can lead to a robust and fast convergent filter in which the model parameters are reduced to the only threshold value in the diffusivity function that can be estimated. A data-independent time step-size has been analytically found to guarantee the convergence of numerical solver of the proposed filter. Although this time step-size is smaller than the ones typically used, it is shown that the numerical solver of the proposed filter can provide a significantly fast convergence rate compared to the classical filter due to an improvement of the image selective smoothing obtained by the diffusivity function of the proposed filter. Simulation results demonstrate that the quality of denoised images obtained by the proposed filter are noticeably higher than the ones from the existing filters.