We present an implementation of a blind source separation algorithm to remove foregrounds off millimeter surveys made by single-channel instruments. In order to make possible such a decomposition over single-wavelength data, we generate levels of artificial redundancy, then perform a blind decomposition, calibrate the resulting maps, and lastly measure physical information. We simulate the reduction pipeline using mock data: atmospheric fluctuations, extended astrophysical foregrounds, and point-like sources, but we apply the same methodology to the Aztronomical Thermal Emission Camera/ASTE survey of the Great Observatories Origins Deep Survey-South (GOODS-S). In both applications, our technique robustly decomposes redundant maps into their underlying components, reducing flux bias, improving signal-to-noise ratio, and minimizing information loss. In particular, GOODS-S is decomposed into four independent physical components: one of them is the already-known map of point sources, two are atmospheric and systematic foregrounds, and the fourth component is an extended emission that can be interpreted as the confusion background of faint sources.