A new parametric method for edge noise removal in graphical document images is presented using geometrical regularities of the graphics contours that exists in the images. Denoising is understood as a recovery problem and is done by employing a sparse representation framework with a basis pursuit denoising algorithm for denoising and curvelet frames for encoding directional information of the graphics contours. The optimal precision parameter used in this framework is shown to have linear relationship with the level of the noise. Experimental results show the superiority of the proposed method over existing ones in terms of image recovery and contour raggedness.