  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.
