The resolution enhancement of textual images poses a significant challenge mainly in the presence of noise. The inherent difficulties are twofold. First is the reconstruction of an upscaled version of the input low-resolution image without amplifying the effect of noise. Second is the achievement of an improved visual image quality and a better OCR accuracy. Classically, the issue is addressed by the application of a denoising step used as a preprocessing or a post-processing to the magnification process. Starting by a denoising process could be more promising to avoid any magnified artifacts while proceeding otherwise. However, the state of the art underlines the limitations of denoising approaches faced with the low spatial resolution of textual images. Recently, sparse coding has attracted increasing interest due to its effectiveness in different reconstruction tasks. This study proves that the application of an efficient sparse coding-based denoising process followed by the magnification process can achieve good restoration results even if the input image is highly noisy. The main specificities of the proposed sparse coding-based framework are: (1) cascading denoising and magnification of each image patch, (2) the use of sparsity stemmed from the non-local self-similarity given in textual images and (3) the use of dual dictionary learning involving both online and offline dictionaries that are selected adaptively for each local region of the input degraded image to recover its corresponding noise-free high-resolution version. Extensive experiments on synthetic and real low-resolution noisy textual images are carried out to validate visually and quantitatively the effectiveness of the proposed system. Promising results, in terms of image visual quality as well as character recognition rates, are achieved when compared it with the state-of-the-art approaches.