of the first stars and galaxies via direct measurements of the IGM during all the relevant epochs [@hogan_and_rees1979; @scott_and_rees1990; @madau_et_al1997; @tozzi_et_al2000], as well as fundamental cosmological parameters [@mcquinn_et_al2006; @mao_et_al2008; @visbal_et_al2009; @clesse_et_al2012; @liu_et_al2016] and exotic phenomena such as dark matter annihilations [@valdes_et_al2013; @evoli_et_al2014].

Despite its promise, intensity mapping is challenging, and to date the only positive detections have been tentative detections of Ly $\alpha$ at $z \sim 2$ to $3.5$ [@croft_et_al2016] and CO from $z\sim 2.3$ to $3.3$ [@keating_et_al2016], as well as detections of HI at $z\sim 0.8$ via cross-correlation with optical galaxies [@chang_et_al2010; @masui_et_al2013]. To realize the full potential of intensity mapping, it is necessary to overcome a large number of systematics. A prime example would be radiation from foreground astrophysical sources, which are particularly troublesome for HI intensity mapping. Especially at high redshifts, foregrounds add contaminant emission to the measurement that are orders of magnitude brighter than the cosmological signal [@dimatteo_et_al2002; @santos_et_al2005; @wang_et_al2006; @deOliveiraCosta_et_al2008; @sims_et_al2016]. Low frequency measurements (for instance, those targeting the $21\,\textrm{cm}$ EoR signal), are mainly contaminated by broadband foregrounds such as Galactic synchrotron emission or extragalactic point sources (whether they are bright and resolved or are part of a dim and unresolved continuum). These foregrounds are 