A Simultaneous Stacking and Deblending Algorithm for Astronomical Images
  Stacking analysis is a means of detecting faint sources using a priori
position information to estimate an aggregate signal from individually
undetected objects. Confusion severely limits the effectiveness of stacking in
deep surveys with limited angular resolution, particularly at far infrared to
submillimeter wavelengths, and causes a bias in stacking results. Deblending
corrects measured fluxes for confusion from adjacent sources; however, we find
that standard deblending methods only reduce the bias by roughly a factor of
two while tripling the variance. We present an improved algorithm for
simultaneous stacking and deblending that greatly reduces bias in the flux
estimate with nearly minimum variance. When confusion from neighboring sources
is the dominant error, our method improves upon RMS error by at least a factor
of three and as much as an order of magnitude compared to other algorithms.
This improvement will be useful for Herschel and other telescopes working in a
source confused, low signal to noise regime.
