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.
2010 by the Information Processing Society of Japan