Astronomical Image Subtraction by Cross-Convolution
  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. 
Fang Yuan, Carl W. Akerlof