A New Algorithm For Difference Image Analysis

TL;DR

This paper introduces a novel difference image analysis method that models the convolution kernel as a pixel array, simplifying the process and improving flexibility over traditional basis function approaches.

Contribution

The paper presents a pixel-based kernel modeling approach for difference image analysis, eliminating the need for basis functions and allowing correction for image misalignments.

Findings

Eliminates the need for basis function selection.

Handles image misalignments without resampling.

Supports spatially varying kernels through regional solutions.

Abstract

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.