Quadrupole and octopole values (μK²) for the different reconstructed ISW maps. The ISW maps are reconstructed from sparsely inpainted CMB and LSS maps using Eq. (7), where the auto- and cross-correlations are measured directly from the data. Small variations in the phases of different renditions of CMB maps can lead to negligible differences in the auto-correlation (see Fig. 2) and to larger differences in a cross-correlation with a second map. This in turn can result in larger variations in the amplitude of the ISW signal, explaining why the reconstructed ISW maps vary slightly more between CMB maps than the observed temperature power does.