Fluorescence images enhancement is important as it can provide more information for medical diagnosis. In this work, we design three simple yet useful filters based on the combinations of mathematical functions, which are proved to be effective in strengthening the images acquired from the fluorescence microscope. Using these filters, detailed objects can be found in the dark sections of the fluorescence images. In addition, these filters can be used to enhance the low-light image, which provide satisfactory visual information and marginal profile for the blurred objects in the image. Moreover, these filters have been used to enhance the image with high degradation by the Gaussian noise, where clear edge profile can be extracted. Finally, we have shown that these filters can be utilized for the image compression. Compression ratio can be obtained to be 0.9688. This study shows the making of the filters with dual functions for the image enhancement and the image compression. Our designed filters are showing the potentials in the field of biomedical imaging and pattern identification.