Combining ILC and moment expansion techniques for extracting average-sky
  signals and CMB anisotropies
  The method of weighted addition of multi-frequency maps, more commonly
referred to as {\it Internal Linear Combination} (ILC), has been extensively
employed in the measurement of cosmic microwave background (CMB) anisotropies
and its secondaries along with similar application in 21cm data analysis. Here
we argue and demonstrate that ILC methods can also be applied to data from
absolutely-calibrated CMB experiments to extract average-sky signals in
addition to the conventional CMB anisotropies. The performance of the simple
ILC method is, however, limited, but can be significantly improved by adding
constraints informed by physics and existing empirical information. In recent
work, a moment description has been introduced as a technique of carrying out
high precision modeling of foregrounds in the presence of inevitable averaging
effects. We combine these two approaches to construct a heavily constrained
form of the ILC, dubbed \milc, which can be used to recover tiny monopolar
spectral distortion signals in the presence of realistic foregrounds and
instrumental noise. This is a first demonstration for measurements of the
monopolar and anisotropic spectral distortion signals using ILC and extended
moment methods. We also show that CMB anisotropy measurements can be improved,
reducing foreground biases and signal uncertainties when using the \milc. While
here we focus on CMB spectral distortions, the scope extends to the 21cm
monopole signal and $B$-mode analysis. We briefly discuss augmentations that
need further study to reach the full potential of the method.
