In this paper, we propose an algorithm for denoising document images using sparse representations. Following a training set, this algorithm is able to learn the main document characteristics and also, the kind of noise included into the documents. In this perspective, we propose to model the noise energy based on the normalized cross-correlation between pairs of noisy and non-noisy documents. Experimental results on several datasets demonstrate the robustness of our method compared with the state-of-the-art.