This paper addresses the problem of recovering a noise-free High-Resolution (HR) version of a noisy Low- Resolution (LR) textual image. While there has been various works on the resolution enhancement of document images, existing magnification systems assume that the input image is not corrupted by noise. In reality, LR image is often noisy, which limits the efficiency of existing magnification systems. In order tackle such a problem, we propose in this paper a joint denoising and magnification system based on sparse coding which suggests that an input signal could be represented by a linear combinaison of few elements from a suitable dictionary. The proposed system uses online and offline learned dictionaries. In order to take benefit of the non-local self-similarity assumption in textual images, the online learned dictionaries are trained on a clustered dataset of image patches selected from the input image and used for denoising purpose. The offline learned dictionaries are trained on an external LR/HR image patch pair dataset and employed for magnification purpose. These offline and offline learned dictionaries are selected adaptively for each image patch of the input LR noisy image to generate its corresponding HR denoised version. The performance of the proposed system is evaluated visually and quantitatively on different LR noisy textual images and promising results are achieved when compared with other existing systems and conventional approaches dealing with such kind of images.