Difference image analysis: Automatic kernel design using information criteria

TL;DR

This paper introduces automated methods for designing optimal convolution kernels in difference image analysis, focusing on minimal external parameters and selecting models based on information criteria, validated through simulations and real data.

Contribution

It proposes a new automatic kernel design algorithm combined with information criteria for optimal kernel selection in difference image analysis.

Findings

Unregularised delta basis functions with AIC or TIC yield the best photometric accuracy.

The proposed methods outperform other kernel solution techniques in simulations.

Validated results on real datasets confirm the effectiveness of the approach.

Abstract

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.