In digital radiography imaging, the anti-scatter grid is usually employed to reduce scattered radiation and to enhance contrast. The shadow of this grid cause irregular stripes artifacts in the x-ray image. To remove these artifacts, most image processing methods adopt a band stop filter which leaves ringing artifact or degrades the clinical contain. In this paper, we propose a new anti-scatter grid suppression method based on spectral estimation and on a physical image formation model of the grid, of the clinical content and of the noise. Patch processing preserve the stationarity assumption and assume high accuracy of the model. The new method was applied on synthetic grid and on clinical images where it suppressed grid-lines artifacts while maintaining the image details and avoiding ringing artifacts. It produced better results compared to the conventional filtering approaches, especially when the metallic materials present in or on the patients.