Image Subtraction in Fourier Space

TL;DR

The paper introduces the Saccadic Fast Fourier Transform (SFFT) algorithm for image subtraction in astronomy, significantly improving computational efficiency and accommodating spatial variations in wide-field imaging data.

Contribution

The paper presents a novel Fourier-space image subtraction algorithm using delta-function basis, enabling fully parallelized processing and handling spatial variations in astronomical images.

Findings

Achieves about tenfold speed improvement over existing methods.

Effectively models spatial variations in PSF, photometric scaling, and sky background.

Validated with real astronomical data from various telescopes.

Abstract

Image subtraction is essential for transient detection in time-domain astronomy. The point spread function (PSF), photometric scaling, and sky background generally vary with time and across the field-of-view for imaging data taken with ground-based optical telescopes. Image subtraction algorithms need to match these variations for the detection of flux variability. An algorithm that can be fully parallelized is highly desirable for future time-domain surveys. Here we show the Saccadic Fast Fourier Transform (SFFT) algorithm for image differencing. SFFT uses $\delta$-function basis for kernel decomposition, and the image subtraction is performed in Fourier Space. This brings about a remarkable improvement of computational performance of about an order of magnitude compared to other published image subtraction codes. SFFT can accommodate the spatial variations in wide-field imaging data, including PSF, photometric scaling, and sky background. However, the flexibility of the $\delta$-function basis may also make it more prone to overfitting. The algorithm has been tested extensively in real astronomical data taken by a variety of telescopes. Moreover, the SFFT code allows for the spatial variations of the PSF and sky background to be fitted by spline functions.