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Mammographic X-ray equipment uses a radiographic grid to remove the scatter radiation and improve image contrast. The grid causes striped lines to appear on the film and may degrade diagnostic information. This study deals with the mechanism of the gridline appearance, the gridline image on the mammographic film, and a method for eliminating the gridlines. In this study, the background noise caused by the radiographic grid is investigated by using a one-dimensional Fourier transform and the characteristics of the gridlines on the X-ray film are clarified. In addition, a new method that reduces the background noise caused by the radiographic grid on mammographic film is proposed by using non-linear image filtering. To eliminate gridlines effectively, the region of the filter is considered and V-filtering and median filtering are performed as methods of image filtering. In an experiment using a breast phantom, a signal-to-noise ratio (SNR) in the microcalcification region is calculated. The SNR of the image processed by median filtering after the V-filtering is increased. The value of the power spectrum at a frequency that represents the periodic noise made by the gridlines is decreased. The validity of image filtering is confirmed. This proposed image-filtering method is found to be useful for eliminating gridlines in the X-ray image.