Tensor Factorization with Application to Convolutive Blind Source Separation of Speech

2010 ◽  
pp. 186-206
Author(s):  
Saeid Sanei ◽  
Bahador Makkiabadi
Keyword(s):  
Frequency Domain ◽  
Blind Source Separation ◽  
Source Separation ◽  
Real Data ◽  
Tensor Factorization ◽  
Major Application ◽  
Parallel Factor ◽  
New Formulation ◽  
Permutation Problems ◽  
Signal Sources

Tensor factorization (TF) is introduced as a powerful tool for solving multi-way problems. As an effective and major application of this technique, separation of sound particularly speech signal sources from their corresponding convolutive mixtures is described and the results are demonstrated. The method is flexible and can easily incorporate all possible parameters or factors into the separation formulation. As a consequence of that fewer assumptions (such as uncorrelatedness and independency) will be required. The new formulation allows further degree of freedom to the original parallel factor analysis (PARAFAC) problem in which the scaling and permutation problems of the frequency domain blind source separation (BSS) can be resolved. Based on the results of experiments using real data in a simulated medium, it has been concluded that compared to conventional frequency domain BSS methods, both objective and subjective results are improved when the proposed algorithm is used.

scholarly journals Inertia-Constrained Pixel-by-Pixel Nonnegative Matrix Factorisation: A Hyperspectral Unmixing Method Dealing with Intra-Class Variability

2018 ◽  
Vol 10 (11) ◽  
pp. 1706 ◽  
Author(s):  
Charlotte Revel ◽  
Yannick Deville ◽  
Véronique Achard ◽  
Xavier Briottet ◽  
Christiane Weber
Keyword(s):  
Blind Source Separation ◽  
Hyperspectral Image ◽  
Source Separation ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Real Data ◽  
Mixing Model ◽  
Data Set ◽  
Linear Mixing Model ◽  
New Formulation

Blind source separation is a common processing tool to analyse the constitution of pixels of hyperspectral images. Such methods usually suppose that pure pixel spectra (endmembers) are the same in all the image for each class of materials. In the framework of remote sensing, such an assumption is no longer valid in the presence of intra-class variability due to illumination conditions, weathering, slight variations of the pure materials, etc. In this paper, we first describe the results of investigations highlighting intra-class variability measured in real images. Considering these results, a new formulation of the linear mixing model is presented leading to two new methods. Unconstrained pixel-by-pixel NMF (UP-NMF) is a new blind source separation method based on the assumption of a linear mixing model, which can deal with intra-class variability. To overcome the limitations of UP-NMF, an extended method is also proposed, named Inertia-constrained Pixel-by-pixel NMF (IP-NMF). For each sensed spectrum, these extended versions of NMF extract a corresponding set of source spectra. A constraint is set to limit the spreading of each source’s estimates in IP-NMF. The proposed methods are first tested on a semi-synthetic data set built with spectra extracted from a real hyperspectral image and then numerically mixed. We thus demonstrate the interest of our methods for realistic source variabilities. Finally, IP-NMF is tested on a real data set and it is shown to yield better performance than state of the art methods.

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