In the field of ophthalmology, retinal images are essential for the diagnosis of many diseases. These images are acquired with a device called the retinal camera. However, often small dust particles in the sensor produce image artifacts that can be confused with small lesions, such as micro-aneurysms. The digital removal of artifacts can be understood as an inpainting process in which a set of pixels are replaced with a value obtained from the surrounding area. In this paper, we propose a methodology based on the sparse representations and dictionary learning for the removal of artifacts in retinal images. We test our method on real retinal images coming from the clinical setting with actual dust artifacts. We compare our restoration results with a diffusion-based inpainting technique. Encouraging experimental results show that our method can successfully remove the artifacts, while assuring the continuity of the retinal structures, like blood vessels.