论文标题
多分辨率的β-差异NMF用于盲目光谱
Multi-Resolution Beta-Divergence NMF for Blind Spectral Unmixing
论文作者
论文摘要
许多数据集作为两个对抗性维度之间的解决方案权衡。例如，在音频信号的频谱图的频率和时间分辨率之间，波长的数量与超光/多光谱图像的空间分辨率之间。要使用具有不同分辨率的观测值进行盲目分离，标准方法是使用耦合的非负矩阵因子化（NMF）。以前的大多数作品都集中在最小二乘误差量度上，即$β= 2 $的$β$ divergence。在本文中，我们针对任何$β$ divergence制定了这个多分辨率的NMF问题，并根据乘法更新（MU）提出了算法。我们在数值实验上表明，MU能够在两个应用上的两个维度中获得高分辨率：（1）音频频谱图的盲透未连接：据我们所知，这是在此上下文中首次使用耦合的NMF模型，以及（2）与特定的偏爱和多个MU的融合：我们的融合：MU竞争MU的融合。非高斯噪音。
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.
