Result of an unrestricted denoising of the spectrum in Fig. 3a with an FDR threshold corresponding to an allowed rate of false detections of α = 4.55%. The [O III] doublet, H_α and H_β are all cleanly identified. There are small features corresponding to [O II] and [S II], and a spurious feature at just over 8000 Å. The FDR denoising of Fig. 3b fails to detect any features for this particular spectrum, noise-realisation and choice of FDR threshold, and thus returns a null spectrum (not shown).