In this paper we present a new discrete implementation of ridgelet transforms based on Reveillès discrete 2D lines. Ridgelet transforms are particular invertible wavelet transforms. Our approach uses the arithmetical thickness parameter of Reveillès lines to adapt the Ridgelet transform to specific applications. We illustrate this with a color denoising algorithm. The broader aimof this paper is to show how results of discrete analytical geometry can be sucessfully used in color image analysis.