Multi-CCD Point Spread Function Modelling

Context. Galaxy imaging surveys observe a vast number of objects that are affected by the instrument’s Point Spread Function (PSF). Weak lensing missions, in particular, aim at measuring the shape of galaxies, and PSF effects represent an important source of systematic errors which must be handled appropriately. This demands a high accuracy in the modelling as well as the estimation of the PSF at galaxy positions.

Aims. Sometimes referred to as non-parametric PSF estimation, the goal of this paper is to estimate a PSF at galaxy positions, starting from a set of noisy star image observations distributed over the focal plane. To accomplish this, we need our model to first of all, precisely capture the PSF field variations over the Field of View (FoV), and then to recover the PSF at the selected positions. Methods. This paper proposes a new method, coined MCCD (Multi-CCD PSF modelling), that creates, simultaneously, a PSF field model over all of the instrument’s focal plane. This allows to capture global as well as local PSF features through the use of two complementary models which enforce different spatial constraints. Most existing non-parametric models build one model per Charge-Coupled Device (CCD), which can lead to difficulties in capturing global ellipticity patterns.

Results. We first test our method on a realistic simulated dataset comparing it with two state-of-the-art PSF modelling methods (PSFEx and RCA). We outperform both of them with our proposed method. Then we contrast our approach with PSFEx on real data from CFIS (Canada-France Imaging Survey) that uses the CFHT (Canada-France-Hawaii Telescope). We show that our PSF model is less noisy and achieves a ~ 22% gain on pixel Root Mean Squared Error (RMSE) with respect to PSFEx.

Conclusions. We present, and share the code of, a new PSF modelling algorithm that models the PSF field on all the focal plane that is mature enough to handle real data.

Reference: Tobias Liaudat, Jérôme Bonnin,  Jean-Luc Starck, Morgan A. Schmitz, Axel Guinot, Martin Kilbinger and Stephen D. J. Gwyn. “Multi-CCD Point Spread Function Modelling, submitted 2020.

arXiv, code.

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



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
Year: 2018
Download: ADS | arXiv



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.