A technique of removing large-scale variations in astronomical observations

In many astrophysical systems, smoothly-varying large-scale variations coexist with small-scale fluctuations. For example, a large-scale velocity or density gradient can exist in molecular clouds that exhibit small-scale turbulence. In redshifted 21cm observations, we also have two types of signals - the Galactic foreground emissions that change smoothly and the redshifted 21cm signals that change fast in frequency space. Sometimes the large-scale variations make it difficult to extract information on small-scale fluctuations. We propose a simple technique to remove smoothly varying large-scale variations. Our technique relies on multi-point structure functions and can obtain the magnitudes of small-scale fluctuations. It can also help us to filter out large-scale variations and retrieve small-scale maps. We discuss applications of our technique to astrophysical observations.