Multi-Resolution Beta-Divergence NMF for Blind Spectral Unmixing
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.
Code (0)
등록된 구현이 없습니다.
Tasks
blind source separationHyperspectral UnmixingSimilar Papers 제목 키워드 기반
Nonnegative Tucker Decomposition with Beta-divergence for Music Structure Analysis of Audio Signals
Nonnegative Tucker decomposition (NTD), a tensor decomposition model, has received increased interest in the recent years because of its ability to blindly extract meaningful patterns, in particular in Music Information …
Information RetrievalMusic Information RetrievalRetrievaltensor algebra+1Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMF
Considering a mixed signal composed of various audio sources and recorded with a single microphone, we consider on this paper the blind audio source separation problem which consists in isolating and extracting each of t…
Audio Source SeparationDeep Blind Hyperspectral Image Fusion
Hyperspectral image fusion (HIF) reconstructs high spatial resolution hyperspectral images from low spatial resolution hyperspectral images and high spatial resolution multispectral images. Previous works usually assume …
Super-ResolutionDeep Nonnegative Matrix Factorization with Beta Divergences
Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all existing deep NMF models and algorithms have …
Joint Majorization-Minimization for Nonnegative Matrix Factorization with the $β$-divergence
This article proposes new multiplicative updates for nonnegative matrix factorization (NMF) with the $\beta$-divergence objective function. Our new updates are derived from a joint majorization-minimization (MM) scheme, …
CPU