Multi-Resolution Beta-Divergence NMF for Blind Spectral Unmixing [article]

Valentin Leplat, Nicolas Gillis, Cédric Févotte
2021 arXiv   pre-print
Many datasets are obtained as a resolution trade-off between two adversarial dimensions; for example between the frequency and the temporal resolutions for the spectrogram of an audio signal, and between the number of wavelengths and the spatial resolution for a hyper/multi-spectral image. To perform blind source separation using observations with different resolutions, a standard approach is to use coupled nonnegative matrix factorizations (NMF). Most previous works have focused on the least
more » ... uares error measure, which is the β-divergence for β = 2. In this paper, we formulate this multi-resolution NMF problem for any β-divergence, and propose an algorithm based on multiplicative updates (MU). We show on numerical experiments that the MU are able to obtain high resolutions in both dimensions on two applications: (1) blind unmixing of audio spectrograms: to the best of our knowledge, this is the first time a coupled NMF model is used in this context, and (2) the fusion of hyperspectral and multispectral images: we show that the MU compete favorable with state-of-the-art algorithms in particular in the presence of non-Gaussian noise.
arXiv:2007.03893v3 fatcat:whbh53miajfa3l6hxk7mk3theq