On the use of shapelets in modelling resolved, gravitationally lensed images

TL;DR

This paper introduces a shapelets-based method for gravitational lens modeling that simplifies source reconstruction by reducing parameters and producing less noisy posterior distributions within a Bayesian framework.

Contribution

The paper integrates shapelets into Bayesian lens modeling, enabling analytical source reconstruction and regularization, and significantly reduces the number of source parameters needed.

Findings

Reduces source parameters from thousands to hundreds.

Produces less noisy posterior probability distributions.

Analytical computation of flux and regularization enhances efficiency.

Abstract

Lens modeling of resolved image data has advanced rapidly over the past two decades. More recently pixel-based approaches, wherein the source is reconstructed on an irregular or adaptive grid, have become popular. Generally, the source reconstruction takes place in a Bayesian framework and is guided by a set of sensible priors. We discuss the integration of a shapelets-based method into a Bayesian framework and quantify the required regularization. In such approaches, the source is reconstructed analytically, using a subset of a complete and orthonormal set of basis functions, known as shapelets. To calculate the flux in an image plane pixel, the pixel is split into two or more triangles (depending on the local magnification), and each shapelet basis function is integrated over the source plane. Source regularization (enforcement of priors on the source) can also be performed analytically. This approach greatly reduces the number of source parameters from the thousands to hundreds and results in a posterior probability distribution that is much less noisy than pixel-based approaches.