Abstract
ABSTRACT We present a GPU-accelerated numerical approach for fast kernel and differential background solutions. The model image proposed in the Bramich Difference Image Analysis (DIA) algorithm is analogous to a very simple convolutional neural network (CNN), with a single convolutional filter (i.e. the kernel) and an added scalar bias (i.e. the differential background). Here, we do not solve for the discrete pixel array in the classical, analytical linear least-squares sense. Instead, by making use of PyTorch tensors (GPU compatible multidimensional matrices) and associated deep learning tools, we solve for the kernel via an inherently massively parallel optimization. By casting the DIA problem as a GPU-accelerated optimization that utilizes automatic differentiation tools, our algorithm is both flexible to the choice of scalar objective function, and can perform DIA on astronomical data sets at least an order of magnitude faster than its classical analogue. More generally, we demonstrate that tools developed for machine learning can be used to address generic data analysis and modelling problems.
Highlights
Difference Image Analysis (DIA) describes several astronomical image processing algorithms with the shared goal of delivering precise photometric measurements of variable astronomical sources
A decade later, the linear least-squares solution was advanced by Bramich (2008) who modelled the kernel as a highly flexible discrete pixel array, which is analogous to the AL98 algorithm, but with a choice of delta basis functions for the kernel model
In the computer science literature, this is exactly analogous to an extremely simple convolution neural network (CNN), with a single input and output related by a single convolutional filter, with some additional scalar bias added to the output
Summary
Difference Image Analysis (DIA) describes several astronomical image processing algorithms with the shared goal of delivering precise photometric measurements of variable astronomical sources. For a (square) pair of images each of size n, and a (square) kernel of size m the construction of the normal matrix for the B08 approach – which implements the same model for the kernel as our algorithm – scales as O (n2m4) (i.e. the run-time increases with the square of the input image size and with the kernel size to the power of four). In the era of wide FoV sky surveys such as the upcoming Legacy Survey of Space and Time (LSST) (Ivezić et al 2019), or the ongoing Zwicky Transient Facility (ZTF) (Bellm et al 2018) etc., which aim to deliver prompt alerts of transient astronomical phenomena detected through image subtraction, many current popular approaches make real-time event discovery impractical This has driven some recent advances in the DIA literature, most notably the ZOGY algorithm (Zackay et al 2016), and even a machine-learning approach (Sedaghat & Mahabal 2018).
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