When scanning a page with printing on both sides, the printing on the back-side often shows through in the scan of the front-side because the page is not completely opaque. This phenomenon of show-through is analyzed and an image processing method for removal of this commonly encountered degradation is developed. A simplified mathematical model is obtained from first physical principles. The model is linearized using suitable transformations and simplifying approximations. Based on the linearized model, an adaptive linear-filtering scheme is developed for the electronic removal of show-through using scans of both sides of the document. Experimental results demonstrating the effectiveness of the method developed are presented.