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

Abstract

Lens modelling 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.