  In the context of difference image analysis (DIA), we present a new method
for determining the convolution kernel matching a pair of images of the same
field. Unlike the standard DIA technique which involves modelling the kernel as
a linear combination of basis functions, we consider the kernel as a discrete
pixel array and solve for the kernel pixel values directly using linear
least-squares. The removal of basis functions from the kernel model is
advantageous for a number of compelling reasons. Firstly, it removes the need
for the user to specify such functions, which makes for a much simpler user
application and avoids the risk of an inappropriate choice. Secondly, basis
functions are constructed around the origin of the kernel coordinate system,
which requires that the two images are perfectly aligned for an optimal result.
The pixel kernel model is sufficiently flexible to correct for image
misalignments, and in the case of a simple translation between images, image
resampling becomes unnecessary. Our new algorithm can be extended to spatially
varying kernels by solving for individual pixel kernels in a grid of image
sub-regions and interpolating the solutions to obtain the kernel at any one
pixel.
