Deconvolution with Shapelets

TL;DR

This paper introduces a shapelet-based deconvolution method for galaxy images that achieves unbiased shear measurements and reduces noise, especially effective for complex PSFs and low signal-to-noise data in weak lensing.

Contribution

It presents a novel shapelet-based deconvolution scheme that provides unbiased shear estimates and noise reduction, improving upon previous methods in weak-lensing analysis.

Findings

Achieves unbiased shear estimates with noise reduction.

Effective for complex PSF models and low S/N images.

Provides a maximum-likelihood solution for shapelet coefficient transformation.

Abstract

We seek to find a shapelet-based scheme for deconvolving galaxy images from the PSF which leads to unbiased shear measurements. Based on the analytic formulation of convolution in shapelet space, we construct a procedure to recover the unconvolved shapelet coefficients under the assumption that the PSF is perfectly known. Using specific simulations, we test this approach and compare it to other published approaches. We show that convolution in shapelet space leads to a shapelet model of order $n_{max}^h = n_{max}^g + n_{max}^f$ with $n_{max}^f$ and $n_{max}^g$ being the maximum orders of the intrinsic galaxy and the PSF models, respectively. Deconvolution is hence a transformation which maps a certain number of convolved coefficients onto a generally smaller number of deconvolved coefficients. By inferring the latter number from data, we construct the maximum-likelihood solution for this transformation and obtain unbiased shear estimates with a remarkable amount of noise reduction compared to established approaches. This finding is particularly valid for complicated PSF models and low $S/N$ images, which renders our approach suitable for typical weak-lensing conditions.