Deconvolution with Shapelets

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.

9 pages, 9 figures, submitted to A&A

References in corpus (6)

• The Shear TEsting Programme 1: Weak lensing analysis of simulated ground-based observations
• The Shear TEsting Programme 2: Factors affecting high precision weak lensing analyses
• Polar Shapelets
• Shears from shapelets
• Weak Lensing by Large-Scale Structure with the FIRST Radio Survey
• Reliable Shapelet Image Analysis

Cited by in corpus (9)

• Weak gravitational lensing with DEIMOS
• Limitations for shapelet-based weak-lensing measurements
• Impact of Atmospheric Chromatic Effects on Weak Lensing Measurements
• Parametrising arbitrary galaxy morphologies: potentials and pitfalls
• Flexion measurement in simulations of Hubble Space Telescope data
• Fundamental Limitations of Pixel Based Image Deconvolution in Radio Astronomy
• Soft clustering analysis of galaxy morphologies: A worked example with SDSS
• Diffuse radio sky models using large scale shapelets
• Three-dimensional shapelets and an automated classification scheme for dark matter haloes