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 2 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 3 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.
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