Deconvolution with shapelets

Zentrum für Astronomie, ITA, Universität Heidelberg, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany e-mail: pmelchior@ita.uni-heidelberg.de

Received: 27 June 2008
Accepted: 12 September 2008

Abstract

Aims. We seek a shapelet-based scheme for deconvolving galaxy images from the PSF that leads to unbiased shear measurements.

Methods. Based on the analytic formulation of convolution in shapelet space, we constructed 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.

Results. We show that convolution in shapelet space leads to a shapelet model of order , with and being the maximum orders of the intrinsic galaxy and the PSF models, respectively. Deconvolution is hence a transformation that 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 images, which renders our approach suitable for typical weak-lensing conditions.