Using anti-scatter grids with high-resolution imaging detectors could result in grid-line artifacts, with increasing severity as detector resolution improves. Grid-line mask subtraction can result in residual artifacts that are due to residual scatter penetrating the grid and not subtracted. By subtracting this residual scatter, the grid artifacts can be minimized. In the previous works, an initial residual-scatter estimate was derived by placing lead markers on a test object; however, any change in the object geometry requires a new scatter estimate. Such a method is impractical to implement during a clinical procedure. In this work, we present a new method to derive the initial scatter estimate to eliminate grid-line artifacts during a procedure. A standard stationary Smit-Roentgen x-ray grid (line density - 70 lines/cm, grid ratio - 13:1) was used with a high-resolution CMOS detector (Dexela Model 1207, pixel size - 75 μm) to image an anthropomorphic head phantom. The initial scatter estimate was derived from the image itself and the grid artifacts were eliminated using recursive correction estimation; this result was compared to that with the estimate derived from placing lead markers on the phantom. In both cases, the contrast-to-noise ratio (CNR) was improved compared to the original image with grid artifacts. Percentage differences in CNR’s for three regions between the images corrected with the two estimates were less than 5%. With the new method no a priori scatter distribution profiles are needed, eliminating the need to have libraries of pre-calculated scatter profiles and making the implementation more clinically practical.