Multi-Resolution Beta-Divergence NMF for Blind Spectral Unmixing

TL;DR

This paper introduces a multi-resolution beta-divergence NMF framework for blind spectral unmixing, extending previous models to arbitrary beta-divergence measures and demonstrating its effectiveness in audio and hyperspectral image applications.

Contribution

It formulates a novel multi-resolution NMF model for any beta-divergence and develops a multiplicative update algorithm, enabling high-resolution spectral unmixing in diverse datasets.

Findings

MU algorithms achieve high resolution in both dimensions.

First application of coupled NMF in audio spectrogram unmixing.

Favorable performance in hyperspectral and multispectral image fusion, especially with non-Gaussian noise.

Abstract

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 $\beta$-divergence for $\beta = 2$. In this paper, we formulate this multi-resolution NMF problem for any $\beta$-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.