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 AzTEC/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, and minimizing information loss. In particular, the GOODS-S survey 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.