Non-negative matrix factorization approach to sky subtraction for optical spectroscopy

Numerous sky background subtraction techniques have been developed since the first implementations of computer-based reduction of spectra. Kurtz & Mink (2000) described a singular value decomposition-based method which allowed them to subtract night sky background from multi-fiber spectroscopic observations without any additional sky observations. We hereby take this approach one step further with usage of non-negative matrix factorization instead of principal component analysis and generalize it to 2D spectra. This allows us to generate approximately 10 times as many valid eigenspectra because of non-negativity. We apply our method to short-slit spectra of low-mass galaxies originating from intermediate-resolution Echelle spectrographs (ESI at Keck, MagE at Magellan, X-Shooter at the VLT) when sources fill the entire slit. We demonstrate its efficiency even when no offset sky observations were collected.