Image subtraction using a space-varying kernel

Image subtraction is a method by which one image is matched against another by using a convolution kernel, so that they can be differenced to detect a nd measure variable objects. It has been demonstrated that constant optimal -kernel solutions can be derived over small sub-areas of dense stellar fiel ds. Here we generalize the: theory to the case, of space-varying kernels. I n particular, it is shown that the CPU cost required for this new extension of the method is almost the same as for fitting a constant kernel solution . It is also shown that constant flux scaling between the images (constant kernel integral) can be imposed in a simple way. The method is demonstrated with a series of Monte-Carlo images. Differential PSF variations and diffe rential rotation between the images are simulated. It is shown that the new method is able to achieve optimal results even in these difficult cases, t hereby automatically correcting for these common instrumental problems. It is also demonstrated that the method does not suffer due to problems associ ated with undersampling of the images. Finally, the method is applied to im ages taken by the OGLE II collaboration. It is proved that, in comparison t o the constant-kernel method, much larger sub-areas of the images can be us ed for the fit, while still maintaining the same accuracy in the subtracted image. This result is especially important in case of variables located in low density fields, like the Huchra lens. Many other useful applications o f the method are possible for major astrophysical problems; Supernova searc hes anti Cepheids surveys in other galaxies, to mention but two. Many other applications will certainly show-up, since variability searches are a majo r issue in astronomy.