In this paper we propose a novel approach to the problem of noise reduction in color images. The new technique of multichannel image enhancement is capable of reducing impulse and Gaussian noise and it outperforms the standard methods of noise reduction in color images. In the paper a new smoothing operator, based on a random walk model and a fuzzy similarity measure between the image pixels connected by a digital geodesic path contained in the filter window is introduced. The efficiency of the proposed method was tested on the standard color images using the widely used objective image quality measures.