Intensity mapping experiments survey the spectrum of diffuse line radiation rather than detect individual objects at high signal-to-noise ratio. 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 ~102–103 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 themselves. 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.
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