Constraint matrix factorization for space variant PSFs field restoration
This addresses the challenge of accurate PSF restoration for astronomical imaging, particularly for telescopes like Euclid, but is incremental as it builds on matrix factorization with sparsity constraints.
The paper tackles the problem of estimating noise-free, well-resolved Point Spread Functions (PSFs) from aliased and noisy star images in large-scale spatial surveys, where PSFs vary across the field of view. The result shows that the proposed RCA method outperforms existing restoration and dimension reduction methods, with significant improvements in PSF shapes and subspace identification in the presence of aliasing.
Context: in large-scale spatial surveys, the Point Spread Function (PSF) varies across the instrument field of view (FOV). Local measurements of the PSFs are given by the isolated stars images. Yet, these estimates may not be directly usable for post-processings because of the observational noise and potentially the aliasing. Aims: given a set of aliased and noisy stars images from a telescope, we want to estimate well-resolved and noise-free PSFs at the observed stars positions, in particular, exploiting the spatial correlation of the PSFs across the FOV. Contributions: we introduce RCA (Resolved Components Analysis) which is a noise-robust dimension reduction and super-resolution method based on matrix factorization. We propose an original way of using the PSFs spatial correlation in the restoration process through sparsity. The introduced formalism can be applied to correlated data sets with respect to any euclidean parametric space. Results: we tested our method on simulated monochromatic PSFs of Euclid telescope (launch planned for 2020). The proposed method outperforms existing PSFs restoration and dimension reduction methods. We show that a coupled sparsity constraint on individual PSFs and their spatial distribution yields a significant improvement on both the restored PSFs shapes and the PSFs subspace identification, in presence of aliasing. Perspectives: RCA can be naturally extended to account for the wavelength dependency of the PSFs.