A Method for Individual Source Brightness Estimation in Single- and
  Multi-band Data
  We present a method of reliably extracting the flux of individual sources
from sky maps in the presence of noise and a source population in which number
counts are a steeply falling function of flux. The method is an extension of a
standard Bayesian procedure in the millimeter/submillimeter literature. As in
the standard method, the prior applied to source flux measurements is derived
from an estimate of the source counts as a function of flux, dN/dS. The key
feature of the new method is that it enables reliable extraction of properties
of individual sources, which previous methods in the literature do not. We
first present the method for extracting individual source fluxes from data in a
single observing band, then we extend the method to multiple bands, including
prior information about the spectral behavior of the source population(s). The
multi-band estimation technique is particularly relevant for classifying
individual sources into populations according to their spectral behavior. We
find that proper treatment of the correlated prior information between
observing bands is key to avoiding significant biases in estimations of
multi-band fluxes and spectral behavior, biases which lead to significant
numbers of misclassified sources. We test the single- and multi-band versions
of the method using simulated observations with observing parameters similar to
that of the South Pole Telescope data used in Vieira, et al. (2010).
