The paper introduces the Weighted Median Filter (WMF), a generalization of the median filter that allows for more flexible and controlled filtering. The median filter, while effective for removing high and low data values, has limitations in preserving certain features of the image, such as blocks of high or low values. The WMF is designed to address these limitations by allowing the user to specify different weights for the values in the neighborhood of a pixel, enabling the filter to remove unwanted noise while preserving desired features. The author discusses the design of the WMF, including the constraints on the filter coefficients and the conditions under which the filter should remove or retain specific features. The paper also introduces the concept of a minimal WMF, which is a filter with the smallest sum of weights that still meets the specified requirements. The number of distinct WMFs that can be derived from a given set of parameters is analyzed, and a method for enumerating these distinct filters is presented. The paper includes a detailed example of applying a WMF to remove satellite trails from an astronomical image while preserving calibration blocks. The effectiveness of different WMFs is evaluated through various tests, including the preservation of the relative variation in side and diagonal neighbor values (R value) and the convergence of the filter over multiple iterations. Finally, the paper discusses the use of mixed strategies, where multiple WMFs are applied in sequence to achieve better results, and addresses issues such as oscillatory behavior and computational efficiency. The conclusions highlight the flexibility and controlled nature of WMFs, making them suitable for a wide range of image processing tasks.The paper introduces the Weighted Median Filter (WMF), a generalization of the median filter that allows for more flexible and controlled filtering. The median filter, while effective for removing high and low data values, has limitations in preserving certain features of the image, such as blocks of high or low values. The WMF is designed to address these limitations by allowing the user to specify different weights for the values in the neighborhood of a pixel, enabling the filter to remove unwanted noise while preserving desired features. The author discusses the design of the WMF, including the constraints on the filter coefficients and the conditions under which the filter should remove or retain specific features. The paper also introduces the concept of a minimal WMF, which is a filter with the smallest sum of weights that still meets the specified requirements. The number of distinct WMFs that can be derived from a given set of parameters is analyzed, and a method for enumerating these distinct filters is presented. The paper includes a detailed example of applying a WMF to remove satellite trails from an astronomical image while preserving calibration blocks. The effectiveness of different WMFs is evaluated through various tests, including the preservation of the relative variation in side and diagonal neighbor values (R value) and the convergence of the filter over multiple iterations. Finally, the paper discusses the use of mixed strategies, where multiple WMFs are applied in sequence to achieve better results, and addresses issues such as oscillatory behavior and computational efficiency. The conclusions highlight the flexibility and controlled nature of WMFs, making them suitable for a wide range of image processing tasks.