  In recent years, there has been a proliferation of wide-field sky surveys to
search for a variety of transient objects. Using relatively short focal
lengths, the optics of these systems produce undersampled stellar images often
marred by a variety of aberrations. As participants in such activities, we have
developed a new algorithm for image subtraction that no longer requires high
quality reference images for comparison. The computational efficiency is
comparable with similar procedures currently in use. The general technique is
cross-convolution: two convolution kernels are generated to make a test image
and a reference image separately transform to match as closely as possible. In
analogy to the optimization technique for generating smoothing splines, the
inclusion of an RMS width penalty term constrains the diffusion of stellar
images. In addition, by evaluating the convolution kernels on uniformly spaced
subimages across the total area, these routines can accomodate point spread
functions that vary considerably across the focal plane.
