Image noise removal is one of the most important parts of image processing that can dramatically improve other parts of image processing performance by enhancing the quality of images in databases. Total variation models are second-order partial differential equations for image denoising. These models have some complexities, such as being multidimensional problems, non-linearity, and having large spatial and temporal domains making them challenging problems to be solved numerically. Thus, in this work, we propose the radial basis function generated finite differences (RBF-FD) method in conjunction with a suitable operator splitting technique to overcome these difficulties. This approach has some significant advantages, such as high accuracy, low computational complexity, and the sparsity of the coefficients matrices derived from it. The peak signal-to-noise ratio, structure similarity index measure, and mean-square error metrics are considered to evaluate the proposed approach’s effectiveness and accuracy compared to the other common denoising approaches.

图像噪声去除是图像处理中最重要的部分之一，它可以通过提高数据库中图像的质量来显着提高图像处理的其他部分的性能。全变分模型是用于图像去噪的二阶偏微分方程。这些模型具有一些复杂性，例如多维问题、非线性问题，以及具有较大的空间和时间域，这使得它们具有挑战性的问题，需要用数值解决。因此，在这项工作中，我们提出了径向基函数生成有限差分 (RBF-FD) 方法以及合适的算子分裂技术来克服这些困难。这种方法具有一些显着的优点，例如精度高、计算复杂度低以及由此导出的系数矩阵的稀疏性。