Replacing standard galaxy profiles with mixtures of Gaussians

TL;DR

This paper introduces a method to approximate galaxy profiles with mixtures of Gaussians, significantly speeding up image fitting processes while maintaining high accuracy, by leveraging the mathematical properties of MoGs for efficient convolution and transformation.

Contribution

The authors demonstrate that galaxy profiles can be accurately approximated with mixtures of Gaussians, enabling faster and more precise image fitting in astronomical data analysis.

Findings

MoG approximations speed up galaxy profile fitting by an order of magnitude.

MoGs allow exact convolution and transformation, improving accuracy and efficiency.

The provided MoG models are compatible with existing image-fitting codes.

Abstract

Exponential, de Vaucouleurs, and S\'ersic profiles are simple and successful models for fitting two-dimensional images of galaxies. One numerical issue encountered in this kind of fitting is the pixel rendering and convolution (or correlation) of the models with the telescope point-spread function (PSF); these operations are slow, and easy to get slightly wrong at small radii. Here we exploit the realization that these models can be approximated to arbitrary accuracy with a mixture (linear superposition) of two-dimensional Gaussians (MoGs). MoGs are fast to render and fast to affine-transform. Most importantly, if you have a MoG model for the pixel-convolved PSF, the PSF-convolved, affine-transformed galaxy models are themselves MoGs and therefore very fast to compute, integrate, and render precisely. We present worked examples that can be directly used in image fitting; we are using them ourselves. The MoG profiles we provide can be swapped in to replace the standard models in any image-fitting code; they sped up model fitting in our projects by an order of magnitude; they ought to make any code faster at essentially no cost in precision.