  Herschel and Planck are surveying the sky at unprecedented angular scales and
sensitivities over large areas. But both experiments are limited by source
confusion in the submillimeter. The high confusion noise in particular
restricts the study of the clustering properties of the sources that dominate
the cosmic infrared background. At these wavelengths, it is more appropriate to
consider the statistics of the unresolved component. In particular, high
clustering will contribute in excess of Poisson noise in the power spectra of
CIB anisotropies. These power spectra contain contributions from sources at all
redshift. We show how the stacking technique can be used to separate the
different redshift contributions to the power spectra. We use simulations of
CIB representative of realistic Spitzer, Herschel, Planck, and SCUBA-2
observations. We stack the 24um sources in longer wavelengths maps to measure
mean colors per redshift and flux bins. The information retrieved on the mean
spectral energy distribution obtained with the stacking technique is then used
to clean the maps, in particular to remove the contribution of low-redshift
undetected sources to the anisotropies. Using the stacking, we measure the mean
flux of populations 4 to 6 times fainter than the total noise at 350um at
redshifts z=1 and z=2, respectively, and as faint as 6 to 10 times fainter than
the total noise at 850um at the same redshifts. In the deep Spitzer fields, the
detected 24um sources up to z~2 contribute significantly to the submillimeter
anisotropies. We show that the method provides excellent (using COSMOS 24um
data) to good (using SWIRE 24um data) removal of the z<2 (COSMOS) and z<1
(SWIRE) anisotropies. Using this cleaning method, we then hope to have a set of
large maps dominated by high redshift galaxies for galaxy evolution study
(e.g., clustering, luminosity density).
