An efficient operator-splitting radial basis function-generated finite difference (RBF-FD) scheme for image noise removal based on nonlinear total variation models

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.