Combination of anisotropic diffusion and non-subsampled shearlet transform for image denoising

In this work, a non-subsampled shearlet transform (NSST) based anisotropic diffusion method is proposed. In the proposed method, the NSST transform is firstly applied to the noisy image to provide several scale and directional components. Then, the NSST coefficients are classified into textured regions and noise-related ones by using Sparse Un-mixing by the variable Splitting and Augmented Lagrangian (SUnSAL) classifier. Subsequently, an energy function is formed by the noise-related coefficients to be minimized by diffusion equations. The noisy free image is approximated from the denoised coefficients obtained by the anisotropic diffusion method and textured coefficients which are remained unchanged. Visual and quantitative assessments demonstrate that the proposed method outperforms the state-of-art denoising methods in terms of noise removal and detail preservation.