  The measurement of the anisotropies in the cosmic infrared background (CIB)
is a powerful mean of studying the evolution of galaxies and large-scale
structures. These anisotropies have been measured by a number of experiments,
from the far-infrared to the millimeter. One of the main impediments to an
accurate measurement on large scales is the contamination of the foreground
signal by Galactic dust emission. Our goal is to show that we can remove the
Galactic cirrus contamination using HI data, and thus accurately measure the
clustering of starburst galaxies in the CIB. We use observations of the ELAIS
N1 field at far-infrared (100 and 160{\mu}m) and radio (21 cm) wavelengths. We
compute the correlation between dust emission, traced by far-infrared
observations, and HI gas traced by 21cm observations, and derive dust
emissivities that enable us to subtract the cirrus emission from the
far-infrared maps. We then derive the power spectrum of the CIB anisotropies,
as well as its mean level at 100{\mu}m and 160{\mu}m. We also combine the HI
data and Spitzer total power mode absolute measurements to determine the CIB
mean level at 160{\mu}m. We find B160=0.77\pm0.04\pm0.12MJy/sr,where the first
error is statistical and the second systematic. Combining this measurement with
the B100/B160 color of the correlated anisotropies, we also derive the CIB mean
at 100 {\mu}m, B100=0.24\pm0.08\pm0.04 MJy/sr. This measurement is in line with
values obtained with recent models of infrared galaxy evolution and
Herschel/PACS data, but is much smaller than the previous DIRBE measurements.
The use of high-angular resolution Hi data is mandatory to accurately
differentiate the cirrus from the CIB emission. The 100 {\mu}m IRAS map (and
thus the map developed by Schlegel and collaborators) in such extragalactic
fields is highly contaminated by the CIB anisotropies and hence cannot be used
as a Galactic cirrus tracer.
