Constraint matrix factorization for space variant PSFs field restoration

TL;DR

This paper introduces RCA, a robust matrix factorization method that leverages spatial correlation and sparsity to accurately restore noise-free, high-resolution PSFs across a telescope's field of view, outperforming existing techniques.

Contribution

The paper presents RCA, a novel noise-robust matrix factorization approach that exploits spatial correlation and sparsity for improved PSF restoration and subspace identification.

Findings

RCA outperforms existing PSF restoration methods on simulated Euclid telescope data.

Coupled sparsity constraints significantly improve PSF shape restoration.

Method effectively handles aliasing and noise in PSF measurements.

Abstract

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.