Constraint matrix factorization for space variant PSFs field restoration
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.
Code (1)
Tasks
Dimensionality ReductionSuper-ResolutionSimilar Papers 제목 키워드 기반
Compact Matrix Factorization With Dependent Subspaces
Traditional matrix factorization methods approximate high dimensional data with a low dimensional subspace. This imposes constraints on the matrix elements which allow for estimation of missing entries. A lower rank prov…
Notes on Low-rank Matrix Factorization
Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the …
ClusteringDimensionality ReductionMatrix CompletionUnsupervised Selective Manifold Regularized Matrix Factorization
Manifold regularization methods for matrix factorization rely on the cluster assumption, whereby the neighborhood structure of data in the input space is preserved in the factorization space. We argue that using the k-ne…
ClusteringA Block Coordinate Descent-based Projected Gradient Algorithm for Orthogonal Non-negative Matrix Factorization
This article utilizes the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalise the orthonormality const…
Self-Supervised Spatially Variant PSF Estimation for Aberration-Aware Depth-from-Defocus
In this paper, we address the task of aberration-aware depth-from-defocus (DfD), which takes account of spatially variant point spread functions (PSFs) of a real camera. To effectively obtain the spatially variant PSFs o…
Depth EstimationSelf-Supervised Learning