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Diffuse emission is observed in galaxies in many tracers across theelectromagnetic spectrum, including tracers of star formation, such asH$\alpha$ and ultraviolet (UV), and tracers of gas mass, such as carbonmonoxide (CO) transition lines and the 21-cm line of atomic hydrogen (HI). Itstreatment is key to extracting meaningful information from observations such ascloud-scale star formation rates. Finally, studying diffuse emission can revealinformation about the physical processes taking place in the ISM, such aschemical transitions and the nature of stellar feedback (through the photonescape fraction). We present a physically-motivated method for decomposingastronomical images containing both diffuse emission and compact regions ofinterest, such as HII regions or molecular clouds, into diffuse and compactcomponent images through filtering in Fourier space. We have previouslypresented a statistical method for constraining the evolutionary timeline ofstar formation and mean separation length between compact star forming regionswith galaxy-scale observations. We demonstrate how these measurements arebiased by the presence of diffuse emission in tracer maps and that by using themean separation length as a critical length scale to separate diffuse emissionfrom compact emission, we are able to filter out this diffuse emission, thusremoving its biasing effect. Furthermore, this method provides, without theneed for interferometry or ancillary spectral data, a measurement of thediffuse emission fraction in input tracer maps and decomposed diffuse andcompact emission maps for further analysis.

An uncertainty principle for star formation - IV. On the nature and filtering of diffuse emission