  Intensity mapping experiments survey the spectrum of diffuse line radiation
rather than detect individual objects at high signal-to-noise. Spectral maps of
unresolved atomic and molecular line radiation contain three-dimensional
information about the density and environments of emitting gas, and efficiently
probe cosmological volumes out to high redshift. Intensity mapping survey
volumes also contain all other sources of radiation at the frequencies of
interest. Continuum foregrounds are typically ~10^2-10^3 times brighter than
the cosmological signal. The instrumental response to bright foregrounds will
produce new spectral degrees of freedom that are not known in advance, nor
necessarily spectrally smooth. The intrinsic spectra of foregrounds may also
not be well-known in advance. We describe a general class of quadratic
estimators to analyze data from single-dish intensity mapping experiments, and
determine contaminated spectral modes from the data itself. The key attribute
of foregrounds is not that they are spectrally smooth, but instead that they
have fewer bright spectral degrees of freedom than the cosmological signal.
Spurious correlations between the signal and foregrounds produce additional
bias. Compensation for signal attenuation must estimate and correct this bias.
A successful intensity mapping experiment will control instrumental systematics
that spread variance into new modes, and it must observe a large enough volume
that contaminant modes can be determined independently from the signal on
scales of interest.
