Efficient Full-Rank Spatial Covariance Estimation Using Independent Low-Rank Matrix Analysis for Blind Source Separation

Kubo, Yasunori; Takamune, Norihiro; Kitamura, Daichi; Saruwatari, Hiroshi

doi:10.23919/eusipco.2019.8903026

Cited by 16 publications

(28 citation statements)

References 21 publications

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“…We also investigate the computational cost and convergence speed of each variant and compare four methods of initializing the spatial models. In a speech enhancement experiment, we show the superiority of rank-constrained FastMNMF over a conventional ILRMA-based method that sequentially estimates the rank-1 SCMs of directional speech and the full-rank SCMs of diffuse noise in different steps [22].…”

Section: Mnmf Fastmnmf1 Fastmnmf2mentioning

confidence: 95%

Fast Multichannel Nonnegative Matrix Factorization With Directivity-Aware Jointly-Diagonalizable Spatial Covariance Matrices for Blind Source Separation

Sekiguchi

Bando

Nugraha

et al. 2020

IEEE/ACM Trans. Audio Speech Lang. Process.

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This paper describes a computationally-efficient blind source separation (BSS) method based on the independence, lowrankness, and directivity of the sources. A typical approach to BSS is unsupervised learning of a probabilistic model that consists of a source model representing the time-frequency structure of source images and a spatial model representing their interchannel covariance structure. Building upon the low-rank source model based on nonnegative matrix factorization (NMF), which has been considered to be effective for inter-frequency source alignment, multichannel NMF (MNMF) assumes source images to follow multivariate complex Gaussian distributions with unconstrained full-rank spatial covariance matrices (SCMs). An effective way of reducing the computational cost and initialization sensitivity of MNMF is to restrict the degree of freedom of SCMs. While a variant of MNMF called independent low-rank matrix analysis (ILRMA) severely restricts SCMs to rank-1 matrices under an idealized condition that only directional and lessechoic sources exist, we restrict SCMs to jointly-diagonalizable yet full-rank matrices in a frequency-wise manner, resulting in FastMNMF1. To help inter-frequency source alignment, we then propose FastMNMF2 that shares the directional feature of each source over all frequency bins. To explicitly consider the directivity or diffuseness of each source, we also propose rankconstrained FastMNMF that enables us to individually specify the ranks of SCMs. Our experiments showed the superiority of FastMNMF over MNMF and ILRMA in speech separation and the effectiveness of the rank constraint in speech enhancement.

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Section: Mnmf Fastmnmf1 Fastmnmf2mentioning

confidence: 95%

Fast Multichannel Nonnegative Matrix Factorization With Directivity-Aware Jointly-Diagonalizable Spatial Covariance Matrices for Blind Source Separation

Sekiguchi

Bando

Nugraha

et al. 2020

IEEE/ACM Trans. Audio Speech Lang. Process.

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show abstract

“…and the demixing matrix Wi can also jointly diagonalize the first term of the right-hand side of (14), as in (13). Therefore, the jointdiagonalization matrix Qi can be approximated by Wi estimated in ILRMA.…”

Section: Motivation and Strategymentioning

confidence: 99%

“…In this paper, we only consider a determined situation (M = N ). If M < N , i.e., underdetermined situations, the demixing matrix Wi cannot strictly diagonalize the first term of the right-hand side of (14). However, we can still apply this method in this case because the demixing matrix Wi leads to the separated signals being independent of each other to some extent, i.e., WiGinW H i (n = 1, .…”

Section: Motivation and Strategymentioning

confidence: 99%

“…The demixing matrix Wi is not an accurate solution of FastMNMF because we cannot ignore the second term of the right-hand side of (14) in the full-rank spatial covariance case. Therefore, the weight parameter of the regularizer, λim, should become smaller in the latter part of the iterations and this annealing-like approach improves the separation accuracy.…”

Section: Scheduling Of Weight Parameter Of Regularizermentioning

confidence: 99%

“…To accelerate the parameter estimation, Ito and Nakatani have proposed FastMNMF [13], which is an improved algorithm of MNMF under the assumption of jointly diagonalizable spatial covariance matrices. It has been reported that, although the computation time of the algorithm is greatly reduced, its source-separation performance is still sensitive to the parameter initialization and not always improved (indeed, it is almost the same as that of the original MNMF) [14]. In addition, the physical meaning of the joint-diagonalization process in FastMNMF is unclear; consequently, prior information cannot be introduced into the parameter optimization to achieve further improvement.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Regularized Fast Multichannel Nonnegative Matrix Factorization with ILRMA-Based Prior Distribution of Joint-Diagonalization Process

Kamo

Kubo

Takamune

et al. 2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Self Cite

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In this paper, we address a convolutive blind source separation (BSS) problem and propose a new extended framework of FastMNMF by introducing prior information for joint diagonalization of the spatial covariance matrix model. Recently, FastMNMF has been proposed as a fast version of multichannel nonnegative matrix factorization under the assumption that the spatial covariance matrices of multiple sources can be jointly diagonalized. However, its sourceseparation performance was not improved and the physical meaning of the joint-diagonalization process was unclear. To resolve these problems, we first reveal a close relationship between the jointdiagonalization process and the demixing system used in independent low-rank matrix analysis (ILRMA). Next, motivated by this fact, we propose a new regularized FastMNMF supported by IL-RMA and derive convergence-guaranteed parameter update rules. From BSS experiments, we show that the proposed method outperforms the conventional FastMNMF in source-separation accuracy with almost the same computation time.

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Effects of Shear Layer Characteristics on Acoustic Propagation and Source Localization

et al. 2019

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The shear layer characteristics of an open-jet acoustic wind tunnel are of key importance on measurements of aeroacoustics. The effects of thickness, spreading angle and strength of shear layer on acoustic propagation and source localization are investigated through the mean/spreading shear layer with a self-similar velocity distribution. Based on the shear flow, the acoustic propagation is computed by the linearized Euler equations via a source term, and then source localization is obtained from beamforming technique combined with the theory of Amiet. Results show that the numerical method can precisely capture the refraction and reflection after sound traversing shear layer. The thickness, spreading angle and strength of the shear layer exerts little effects on the refracted region where sound wave nearly vertical incident, while mainly influence the corresponding up/downstream region in terms of phase change. Increment of thickness, spreading angle and strength of the shear layer increases the acoustic difference between the shear layer with and without thickness, and produces a larger error of source localization downstream of the actual position.

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Efficient Full-Rank Spatial Covariance Estimation Using Independent Low-Rank Matrix Analysis for Blind Source Separation

Cited by 16 publications

References 21 publications

Fast Multichannel Nonnegative Matrix Factorization With Directivity-Aware Jointly-Diagonalizable Spatial Covariance Matrices for Blind Source Separation

Fast Multichannel Nonnegative Matrix Factorization With Directivity-Aware Jointly-Diagonalizable Spatial Covariance Matrices for Blind Source Separation

Regularized Fast Multichannel Nonnegative Matrix Factorization with ILRMA-Based Prior Distribution of Joint-Diagonalization Process

Effects of Shear Layer Characteristics on Acoustic Propagation and Source Localization

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