We present a method for adaptively smoothing an astronornical image. The method surpasses the previous algorithms in that the present method takes the spatial variations in the exposure into account. The method adjusts the smoothing scale such that, at every position in the image, the resulting smoothed image has a signal-to-noise ratio above a prescribed critical value. We applied our new method to data from FIMS (Far-ultraviolet Waging Spectrograph; also known as SPEAR), the main payload of the first Korean scientific satellite "STSAT-l." The negative signal problem often encountered in photon-counting experiments after subtracting the background rate from an estimate of the signal plus background rate, which is also commonly found in FIMS data, is avoided by adopting the correct estimate of the source signal rate based on Bayesian probability theory.