Summary: We present a convection-diffusion equation for processing image denoising, edge preservation and compression. We compare it with a popular nonlinear diffusion model which has been widely implemented in image denoising for Gaussian white noise. Here we show that this convection-diffusion model effectively removes noise, especially for the mixture of Gaussian and salt-and-pepper noises. We propose the modified streamline diffusion method [

*Y. Shih, H. C. Elman*, Comput. Methods Appl. Mech. Eng. 174, No. 1–2, 137–151 (1999;

Zbl 0957.76035)] for the discretization of this convection-diffusion model to prevent internal layers because of the discontinuities while using the coarsening algorithm for the image compression. Numerical experiments have shown that our convection-diffusion model for removing both Gaussian and salt-and-pepper noises, efficiently and reliably preserves edges quite satisfactorily.