Deconvolution with shapelets

P. Melchior, R. Andrae, M. Maturi, M. Bartelmann

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 n maxh = nmaxg + nmax f, with nmaxf and nmaxg 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 S/N images, which renders our approach suitable for typical, weak-lensing conditions.

Original languageEnglish (US)
Pages (from-to)727-734
Number of pages8
JournalAstronomy and Astrophysics
Issue number2
StatePublished - Jan 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Gravitational lensing
  • Methods: data analysis
  • Techniques: image processing


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