Weighted and well-balanced anisotropic diffusion scheme for image denoising and restoration

Anisotropic diffusion is a key concept in digital image denoising and restoration. To improve the anisotropic diffusion based schemes and to avoid the well-known drawbacks such as edge blurring and 'staircasing' artifacts, in this paper, we consider a class of weighted anisotropic diffusion partial differential equations (PDEs). By considering an adaptive parameter within the usual divergence process, we retain the powerful denoising capability of anisotropic diffusion PDE without any oscillating artifacts. A well-balanced flow version of the proposed scheme is considered which adds an adaptive fidelity term to the usual diffusion term. The scheme is general, in the sense that, different diffusion coefficient functions can be utilized according to the need and imaging modality. To illustrate the advantage of the proposed methodology, we provide some examples, which are applied in restoring noisy synthetic and real digital images. A comparison study with other anisotropic diffusion based schemes highlight the superiority of the proposed scheme.