Euclid: Non-parametric point spread function field recovery through interpolation on a Graph Laplacian

 

Authors: M.A. Schmitz, J.-L. Starck, F. Ngole Mboula, N. Auricchio, J. Brinchmann, R.I. Vito Capobianco, R. Clédassou, L. Conversi, L. Corcione, N. Fourmanoit, M. Frailis, B. Garilli, F. Hormuth, D. Hu, H. Israel, S. Kermiche, T. D. Kitching, B. Kubik, M. Kunz, S. Ligori, P.B. Lilje, I. Lloro, O. Mansutti, O. Marggraf, R.J. Massey, F. Pasian, V. Pettorino, F. Raison, J.D. Rhodes, M. Roncarelli, R.P. Saglia, P. Schneider, S. Serrano, A.N. Taylor, R. Toledo-Moreo, L. Valenziano, C. Vuerli, J. Zoubian
Journal: submitted to A&A
Year: 2019
Download:  arXiv

 


Abstract

Context. Future weak lensing surveys, such as the Euclid mission, will attempt to measure the shapes of billions of galaxies in order to derive cosmological information. These surveys will attain very low levels of statistical error and systematic errors must be extremely well controlled. In particular, the point spread function (PSF) must be estimated using stars in the field, and recovered with high accuracy.
Aims. This paper's contributions are twofold. First, we take steps toward a non-parametric method to address the issue of recovering the PSF field, namely that of finding the correct PSF at the position of any galaxy in the field, applicable to Euclid. Our approach relies solely on the data, as opposed to parametric methods that make use of our knowledge of the instrument. Second, we study the impact of imperfect PSF models on the shape measurement of galaxies themselves, and whether common assumptions about this impact hold true in a Euclid scenario.
Methods. We use the recently proposed Resolved Components Analysis approach to deal with the undersampling of observed star images. We then estimate the PSF at the positions of galaxies by interpolation on a set of graphs that contain information relative to its spatial variations. We compare our approach to PSFEx, then quantify the impact of PSF recovery errors on galaxy shape measurements through image simulations.
Results. Our approach yields an improvement over PSFEx in terms of PSF model and on observed galaxy shape errors, though it is at present not sufficient to reach the required Euclid accuracy. We also find that different shape measurement approaches can react differently to the same PSF modelling errors.

Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

 

Authors: M.A. Schmitz, M. Heitz, N. Bonneel, F.-M. Ngolè, D. Coeurjolly, M. Cuturi, G. Peyré & J.-L. Starck
Journal: SIAM SIIMS
Year: 2018
Download: ADS | arXiv

 


Abstract

This article introduces a new non-linear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so called displacement interpolations (a.k.a. Wasserstein barycenters) between dictionary atoms; such atoms are themselves synthetic histograms in the probability simplex. Our method simultaneously estimates such atoms, and, for each datapoint, the vector of weights that can optimally reconstruct it as an optimal transport barycenter of such atoms. Our method is computationally tractable thanks to the addition of an entropic regularization to the usual optimal transportation problem, leading to an approximation scheme that is efficient, parallel and simple to differentiate. Both atoms and weights are learned using a gradient-based descent method. Gradients are obtained by automatic differentiation of the generalized Sinkhorn iterations that yield barycenters with entropic smoothing. Because of its formulation relying on Wasserstein barycenters instead of the usual matrix product between dictionary and codes, our method allows for non-linear relationships between atoms and the reconstruction of input data. We illustrate its application in several different image processing settings.

PSF field learning based on Optimal Transport Distances

 

Authors: F. Ngolè Mboula, J-L. Starck
Journal: arXiv
Year: 2017
Download: ADS | arXiv

 


Abstract

Context: in astronomy, observing large fractions of the sky within a reasonable amount of time implies using large field-of-view (fov) optical instruments that typically have a spatially varying Point Spread Function (PSF). Depending on the scientific goals, galaxies images need to be corrected for the PSF whereas no direct measurement of the PSF is available. Aims: given a set of PSFs observed at random locations, we want to estimate the PSFs at galaxies locations for shapes measurements correction. Contributions: we propose an interpolation framework based on Sliced Optimal Transport. A non-linear dimension reduction is first performed based on local pairwise approximated Wasserstein distances. A low dimensional representation of the unknown PSFs is then estimated, which in turn is used to derive representations of those PSFs in the Wasserstein metric. Finally, the interpolated PSFs are calculated as approximated Wasserstein barycenters. Results: the proposed method was tested on simulated monochromatic PSFs of the Euclid space mission telescope (to be launched in 2020). It achieves a remarkable accuracy in terms of pixels values and shape compared to standard methods such as Inverse Distance Weighting or Radial Basis Function based interpolation methods.