The Weighted Median Filter is a generalization of the median filter, which allows for more flexible control over image processing tasks. The median filter is effective at removing noise and backgrounding images, but it may not always meet specific requirements for feature removal or retention. The Weighted Median Filter (WMF) addresses this by allowing filters to be designed with a wide range of properties, enabling more precise control over image processing. The WMF operates by taking a weighted sum of pixel values in a neighborhood, sorting them, and selecting the median. This approach allows for the removal of high/low streaks while preserving blocks of data, which is crucial for tasks like backgrounding in astronomical images. The filter can be adjusted to handle different scenarios, such as removing lines or preserving corners, by varying the weights assigned to different pixel values. The paper discusses the design and application of a three-dimensional WMF for use in astronomical survey photography. It describes how the filter can be used to remove satellite trails while preserving calibration blocks. The filter is shown to effectively remove lines while preserving blocks, and it is compared to other filters like the Martin filter, which may not meet the same criteria. The paper also explores the enumeration of distinct WMFs within a given class, showing that there are 53 distinct filters of a specific form. These filters are characterized by their weights and how they affect the data. The paper further discusses the performance of these filters on test data, highlighting the importance of maintaining certain properties like the ratio of SIDESQ and DIAGSQ to ensure effective backgrounding. Finally, the paper addresses further considerations, including the use of mixed strategies and the potential for oscillatory values in some filters. It concludes that WMFs provide a flexible and effective method for image processing, allowing for the controlled removal of noise and backgrounding while preserving important image features.The Weighted Median Filter is a generalization of the median filter, which allows for more flexible control over image processing tasks. The median filter is effective at removing noise and backgrounding images, but it may not always meet specific requirements for feature removal or retention. The Weighted Median Filter (WMF) addresses this by allowing filters to be designed with a wide range of properties, enabling more precise control over image processing. The WMF operates by taking a weighted sum of pixel values in a neighborhood, sorting them, and selecting the median. This approach allows for the removal of high/low streaks while preserving blocks of data, which is crucial for tasks like backgrounding in astronomical images. The filter can be adjusted to handle different scenarios, such as removing lines or preserving corners, by varying the weights assigned to different pixel values. The paper discusses the design and application of a three-dimensional WMF for use in astronomical survey photography. It describes how the filter can be used to remove satellite trails while preserving calibration blocks. The filter is shown to effectively remove lines while preserving blocks, and it is compared to other filters like the Martin filter, which may not meet the same criteria. The paper also explores the enumeration of distinct WMFs within a given class, showing that there are 53 distinct filters of a specific form. These filters are characterized by their weights and how they affect the data. The paper further discusses the performance of these filters on test data, highlighting the importance of maintaining certain properties like the ratio of SIDESQ and DIAGSQ to ensure effective backgrounding. Finally, the paper addresses further considerations, including the use of mixed strategies and the potential for oscillatory values in some filters. It concludes that WMFs provide a flexible and effective method for image processing, allowing for the controlled removal of noise and backgrounding while preserving important image features.