On the Improvement of Volterra Equation Based Filtering for Image Denoising

This paper presents a simple but effective approach for the removal of additive white Gaussian noise from digital images. In our approach, a generalization of a linear heat equation, obtained by replacing time derivative to a fractional time derivative of order between 1 and 2 has been used and a pixel by pixel technique applied. The choice of order of fractional time derivative has been made for each pixel by using structure tensor of image, which allows us to control the diffusion process without introducing nonlinearities in equation as in classical approaches. The proposed model is well posed and numerical scheme adopted is stable. Several experiments showing improvement of our approach visually and in terms of SNR, PSNR are also provided.