The periodic structure of the underlying support of paintings on canvas can become quite prominent and disturbing in high resolution digital recordings. In this paper, we construct a new model and method for the digital removal of canvas which is considered as a noise component superimposed on the painting artwork. The high resolution of the images prohibits the efficient application of existing adaptive denoising filters. Hence, a two-step approach is proposed. First a (smoothing) Wiener filter is applied to the complete image. The second step consists of a spatially adaptive extension with low-complexity to obtain a generic digital canvas removal filter.