  Though debated, the existence of claimed large-scale anomalies in the CMB is
not totally dismissed. In parallel to the debate over their statistical
significance, recent work focussed on masks and secondary anisotropies as
potential sources of these anomalies. In this work we investigate
simultaneously the impact of the method used to account for masked regions and
the impact of the ISW effect, which is the large-scale secondary anisotropy
most likely to affect the CMB anomalies. In this sense, our work is an update
of both Francis & Peacock 2010 and Kim et al. 2012. Our aim is to identify
trends in CMB data with different mask treatments. We reconstruct the ISW
signal due to 2MASS and NVSS galaxies. We account for missing data using the
sparse inpainting technique of Abrial et al. 2008 and sparse inpainting of the
CMB, LSS and ISW and find that it constitutes a bias-free reconstruction method
suitable to study large-scale statistical isotropy and the ISW effect. We focus
on three large-scale CMB anomalies: the low quadrupole, the quad/oct alignment,
and the octopole planarity. After sparse inpainting, the low quadrupole becomes
more anomalous, whilst the quad/oct alignment becomes less anomalous. The
significance of the low quadrupole is unchanged after subtraction of the ISW
effect, while the trend is that the quad/oct alignment has reduced
significance, yet other hypotheses remain possible as well (e.g. exotic
physics). Our results also suggest that both of these anomalies may be due to
the quadrupole alone. The octopole planarity significance is also reduced after
inpainting and after ISW subtraction, however, we do not find that it was very
anomalous to start with. In the spirit of reproducible research, we make all
codes and resulting products which constitute main results of this paper public
here: http://www.cosmostat.org/anomaliesCMB.html.
