  The Herschel very wide-field surveys have charted hundreds of square degrees
in multiple far-IR (FIR) bands. While the Sloan Digital Sky Survey (SDSS) is
currently the best resource for optical counterpart identifications over such
wide areas, it does not detect a large number of Herschel FIR sources and
leaves their nature undetermined. As a test case, we studied seven
"SDSS-invisible", very bright 250um sources (S_{250} > 55 mJy) in the Cosmic
Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) fields where
we have a rich multi-wavelength data set. We took a new approach to decompose
the FIR sources, using the near-IR or the optical images directly for position
priors. This is an improvement over the previous decomposition efforts where
the priors are from mid-IR data that still suffer from the source blending
problem in the first place. We found that in most cases the single Herschel
sources are made of multiple components that are not necessarily at the same
redshifts. Our decomposition succeeded in identifying and extracting their
major contributors. We show that these are all ULIRGs at z ~ 1--2 whose high
L_IR is mainly due to dust-obscured star formation. Most of them would not be
selected as sub-mm galaxies. They all have complicated morphologies indicative
of merger or violent instability, and their stellar populations are
heterogeneous in terms of stellar masses, ages and formation histories. Their
current ULIRG phases are of various degrees of importance in their stellar mass
assembly. Our practice provides a promising starting point to develop an
automatic routine to reliably study bright Herschel sources.
