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We report contributions to cosmic infrared background (CIB) intensitiesoriginating from known galaxies and their faint companions at submillimeterwavelengths. Using the publicly-available UltraVISTA catalog, and maps at 250,350, and 500 {\mu}m from the \emph{Herschel} Multi-tiered Extragalactic Survey(HerMES), we perform a novel measurement that exploits the fact thatuncatalogued sources may bias stacked flux densities --- particularly if theresolution of the image is poor --- and intentionally smooth the images beforestacking and summing intensities. By smoothing the maps we are capturing thecontribution of faint (undetected in K_S ~ 23.4) sources that are physicallyassociated, or correlated, with the detected sources. We find that thecumulative CIB increases with increased smoothing, reaching 9.82 +- 0.78, 5.77+- 0.43, and 2.32 +- 0.19$\, \rm nW m^{-2} sr^{-1}$ at 250, 350, and 500 {\mu}mat 300 arcsec FWHM. This corresponds to a fraction of the fiducial CIB of 0.94+- 0.23, 1.07 +- 0.31, and 0.97 +- 0.26 at 250, 350, and 500 {\mu}m, where theuncertainties are dominated by those of the absolute CIB. We then propose, witha simple model combining parametric descriptions for stacked flux densities andstellar mass functions, that emission from galaxies with log(M/Msun) > 8.5 canaccount for the most of the measured total intensities, and argue againstcontributions from extended, diffuse emission. Finally, we discuss prospectsfor future survey instruments to improve the estimates of the absolute CIBlevels, and observe any potentially remaining emission at z > 4.

HerMES: Current Cosmic Infrared Background Estimates Can be Explained by Known Galaxies and their Faint Companions at z < 4