  We present a selection of methods for automatically constructing an optimal
kernel model for difference image analysis which require very few external
parameters to control the kernel design. Each method consists of two
components; namely, a kernel design algorithm to generate a set of candidate
kernel models, and a model selection criterion to select the simplest kernel
model from the candidate models that provides a sufficiently good fit to the
target image. We restricted our attention to the case of solving for a
spatially-invariant convolution kernel composed of delta basis functions, and
we considered 19 different kernel solution methods including six employing
kernel regularisation. We tested these kernel solution methods by performing a
comprehensive set of image simulations and investigating how their performance
in terms of model error, fit quality, and photometric accuracy depends on the
properties of the reference and target images. We find that the irregular
kernel design algorithm employing unregularised delta basis functions, combined
with either the Akaike or Takeuchi information criterion, is the best kernel
solution method in terms of photometric accuracy. Our results are validated by
tests performed on two independent sets of real data. Finally, we provide some
important recommendations for software implementations of difference image
analysis.
