Multi-Resolution Beta-Divergence NMF for Blind Spectral Unmixing
This work addresses blind spectral unmixing for applications like audio processing and remote sensing, offering an incremental improvement by generalizing error measures in existing NMF frameworks.
The paper tackles blind source separation for multi-resolution data by extending coupled nonnegative matrix factorization (NMF) to any β-divergence, proposing a multiplicative updates algorithm. It demonstrates high-resolution results in audio spectrogram unmixing and hyperspectral-multispectral image fusion, competing favorably with state-of-the-art methods, especially under non-Gaussian noise.
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 squares 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.