A Spatially Adaptive Edge-Preserving Denoising Method Based on Fractional-Order Variational PDEs

Image denoising is a basic problem in image processing. An important task of image denoising is to preserve the significant geometric features such as edges and textures while filtering out noise. So far, this is still a problem to be further studied. In this paper, we firstly introduce an edge detection function based on the Gaussian filtering operator and then analyze the filtering characteristic of the fractional derivative operator. On the basis, we establish the spatially adaptive fractional edge-preserving denoising model in the variational framework, discuss the existence and uniqueness of our proposed model solution and derive the nonlinear fractional Euler-Lagrange equation for solving our proposed model. This forms a fractional order extension of the first and second order variational approaches. Finally, we apply the proposed method to the synthetic images and real seismic data denoising to verify the effectiveness of our method and compare the experimental results of our method with the related state-of-the-art methods. Experimental results illustrate that our proposed method can not only improve the signal to noise ratio (SNR) but also adaptively preserve the structural information of an image compared with other contrastive methods. Our proposed method can also be applied to remote sensing imaging, medical imaging and so on.