Diffuse emission is observed in galaxies in many tracers across the electromagnetic spectrum, including tracers of star formation, such as H$alpha$ and ultraviolet (UV), and tracers of gas mass, such as carbon monoxide (CO) transition lines and the 21-cm line of atomic hydrogen (HI). Its treatment is key to extracting meaningful information from observations such as cloud-scale star formation rates. Finally, studying diffuse emission can reveal information about the physical processes taking place in the ISM, such as chemical transitions and the nature of stellar feedback (through the photon escape fraction). We present a physically-motivated method for decomposing astronomical images containing both diffuse emission and compact regions of interest, such as HII regions or molecular clouds, into diffuse and compact component images through filtering in Fourier space. We have previously presented a statistical method for constraining the evolutionary timeline of star formation and mean separation length between compact star forming regions with galaxy-scale observations. We demonstrate how these measurements are biased by the presence of diffuse emission in tracer maps and that by using the mean separation length as a critical length scale to separate diffuse emission from compact emission, we are able to filter out this diffuse emission, thus removing its biasing effect. Furthermore, this method provides, without the need for interferometry or ancillary spectral data, a measurement of the diffuse emission fraction in input tracer maps and decomposed diffuse and compact emission maps for further analysis.
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