This paper presents a new method to remove edge noise from graphical document images using geometrical regularities of the graphics contours that exist in the images. Denoising is understood as a recovery problem and is accomplished by employing a sparse representation framework in the form of a basis pursuit denoising algorithm. Directional information of the graphics contours is encoded by atoms in an overcomplete dictionary which is designed to match the input data. The optimal precision parameter used in this framework is shown to have a linear relationship with the level of the noise that exists in the image. Experimental results show the superiority of the proposed method over existing ones in terms of image recovery and contour raggedness.