  Image subtraction in astronomy is a tool for transient object discovery and
characterization, particularly useful in wide fields, and is well suited for
moving or photometrically varying objects such as asteroids, extra-solar
planets and supernovae. A convolution technique is used to match point spread
functions (PSFs) between images of the same field taken at different times
prior to pixel-by-pixel subtraction. Particularly suitable for large-scale
images is a spatially-varying kernel, where the convolution is allowed to adapt
to PSF changes as a function of position within the images. The most versatile
basis for fitting the spatially-varying kernel is the Dirac delta function.
However, the convolution kernel based on the delta function does not
discriminate between pixel scale noise variations and the intended stellar
point spread function signals. The situation can frequently lead to reduced
signal to noise ratios for variable objects detectable in the resulting
subtraction. This work presents a cross-correlation method for reducing noise
effects on the delta function derived convolution kernels, thus yielding
significantly improved signal to noise in the resulting subtraction.
