We propose non-negative matrix factorisation with iterative restarts (iNMF) to model a noisy dataset of highly overlapping fluorophores with intermittent intensities. We can recover high-resolution images of individual sources from the optimised model, despite their high mutual overlap in the original data. Each source can have an arbitrary, unknown shape of the PSF and blinking behaviour. This allows us to use quantum dots as bright and stable fluorophores for localisation microscopy. We compare the iNMF results to CSSTORM, 3B and bSOFI. iNMF shows superior performance in the challenging task of super-resolution imaging using quantum dots. We can also retrieve axial localisation of the sources from the shape of the recovered PSF.