By applying band-rejection filters (BRFs) in the frequency domain, we can efficiently reduce the grid artifacts, which are caused by using the antiscatter grid in obtaining x-ray digital images. However, if the frequency component of the grid artifact is relatively close to that of the object, then simply applying a BRF may seriously distort the object and cause the ringing artifacts. Since the ringing artifacts are quite dependent on the shape of the object to be recovered in the spatial domain, the spatial property of the x-ray image should be considered in applying BRFs. In this paper, we propose an adaptive filtering scheme, which can cooperate such different properties in the spatial domain. In the spatial domain, we compare several approaches, such as the mangnitude, edge, and frequency-modulation (FM) model-based algorithms, to detect the ringing artifact or the grid artifact component. In order to perform a robust detection whether the ringing artifact is strong or not, we employ the FM model for the extracted signal, which corresponds to a specific grid artifact. A detection of the position for the ringing artifact is then conducted based on the slope detection algorithm, which is commonly used as an FM discriminator in the communication area. However, the detected position of the ringing artifact is not accurate. Hence, in order to obtain an accurate detection result, we combine the edge-based approach with the FM model approach. Numerical result for real x-ray images shows that applying BRFs in the frequency domain in conjunction with the spatial property of the ringing artifact can successfully remove the grid artifact, distorting the object less.