  Intensity mapping experiments will soon have surveyed large swathes of the
sky, providing information about the underlying matter distribution of the
early universe. The resulting maps can be used to recover statistical
information, such as the power spectrum, about the measured spectral lines (for
example, HI, [CII], and [OIII]). However precise power spectrum measurements,
such as the 21 cm autocorrelation, continue to be challenged by the presence of
bright foregrounds and non-trivial systematics. By crosscorrelating different
data sets, it may be possible to mitigate the effects of both foreground
uncertainty and uncorrelated instrumental systematics. Beyond their own merit,
crosscorrelations could also be used to recover autocorrelation information.
Such a technique was proposed in Beane et al. (2019) for recovering the 21 cm
power spectrum. Generalizing their result, we develop a statistical framework
for combining multiple crosscorrelation signals in order to infer information
about the corresponding autocorrelations. We do this first within the Least
Squares Estimator (LSE) framework, and show how one can derive their estimator,
along with several alternative estimators. We also investigate the posterior
distribution of recovered autocorrelation and associated model parameters. We
find that for certain noise regimes and cosmological signal modeling
assumptions this procedure is effective at recovering autospectra from a set of
crosscorrelations. Finally, we showcase our framework in the context of several
near-future line intensity mapping experiments.
