Non-negative Matrix Factorization: Robust Extraction of Extended Structures

Abstract

We apply the vectorized non-negative matrix factorization (NMF) method to the post-processing of the direct imaging data of exoplanetary systems such as circumstellar disks. NMF is an iterative approach, which first creates a nonorthogonal and non-negative basis of components using the given reference images and then models a target with the components. The constructed model is then rescaled with a factor to compensate for the contribution from the disks. We compare NMF with existing methods (classical reference differential imaging method, and the Karhunen–Loève image projection algorithm) using synthetic circumstellar disks and demonstrate the superiority of NMF: with no need of prior selection of references, NMF not only can detect fainter circumstellar disks but also better preserves their morphology and does not require forward modeling. As an application to a well-known disk example, we process the archival Hubble Space Telescope STIS coronagraphic observations of HD 181327 with different methods and compare them, and NMF is able to extract some circumstellar materials inside the primary ring for the first time. In an appendix, we mathematically investigate the stability of NMF components during the iteration and the linearity of NMF modeling.