Source extraction and photometry for the far-infrared and sub-millimeter continuum in the presence of complex backgrounds

(Abridged) We present a new method for detecting and measuring compact sources in conditions of intense, and highly variable, fore/background. While all most commonly used packages carry out the source detection over the signal image, our proposed method builds from the measured image a "curvature" image by double-differentiation in four different directions. In this way point-like as well as resolved, yet relatively compact, objects are easily revealed while the slower varying fore/background is greatly diminished. Candidate sources are then identified by looking for pixels where the curvature exceeds, in absolute terms, a given threshold; the methodology easily allows us to pinpoint breakpoints in the source brightness profile and then derive reliable guesses for the sources extent. Identified peaks are fit with 2D elliptical Gaussians plus an underlying planar inclined plateau, with mild constraints on size and orientation. Mutually contaminating sources are fit with multiple Gaussians simultaneously using flexible constraints. We ran our method on simulated large-scale fields with 1000 sources of different peak flux overlaid on a realistic realization of diffuse background. We find detection rates in excess of 90% for sources with peak fluxes above the 3-sigma signal noise limit; for about 80% of the sources the recovered peak fluxes are within 30% of their input values.