  21 cm tomography is expected to be difficult in part because of serious
foreground contamination. Previous studies have found that line-of-sight
approaches are capable of cleaning foregrounds to an acceptable level on large
spatial scales, but not on small spatial scales. In this paper, we introduce a
Fourier-space formalism for describing the line-of-sight methods, and use it to
introduce an improved new method for 21 cm foreground cleaning. Heuristically,
this method involves fitting foregrounds in Fourier space using weighted
polynomial fits, with each pixel weighted according to its information content.
We show that the new method reproduces the old one on large angular scales, and
gives marked improvements on small scales at essentially no extra computational
cost.
