Speech Enhancement Under Low SNR Conditions Via Noise Estimation Using Sparse and Low-Rank NMF with Kullback–Leibler Divergence

Sun, Meng; Li, Yinan; Gemmeke, Jort F.; Zhang, Xiongwei

doi:10.1109/taslp.2015.2427520

Cited by 82 publications

(41 citation statements)

References 28 publications

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“…where is the potential of H defined by Equation (27). The form of the admissible set  ad, follows from the representation using Lagrange multipliers.…”

Section: Reformulating the Optimization Problem As A Function Of Randmentioning

confidence: 99%

Physics‐constrained non‐Gaussian probabilistic learning on manifolds

Soize

Ghanem

2019

Numerical Meth Engineering

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Summary An extension of the probabilistic learning on manifolds (PLoM), recently introduced by the authors, has been presented: In addition to the initial data set given for performing the probabilistic learning, constraints are given, which correspond to statistics of experiments or of physical models. We consider a non‐Gaussian random vector whose unknown probability distribution has to satisfy constraints. The method consists in constructing a generator using the PLoM and the classical Kullback‐Leibler minimum cross‐entropy principle. The resulting optimization problem is reformulated using Lagrange multipliers associated with the constraints. The optimal solution of the Lagrange multipliers is computed using an efficient iterative algorithm. At each iteration, the Markov chain Monte Carlo algorithm developed for the PLoM is used, consisting in solving an Itô stochastic differential equation that is projected on a diffusion‐maps basis. The method and the algorithm are efficient and allow the construction of probabilistic models for high‐dimensional problems from small initial data sets and for which an arbitrary number of constraints are specified. The first application is sufficiently simple in order to be easily reproduced. The second one is relative to a stochastic elliptic boundary value problem in high dimension.

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“…where is the potential of H defined by Equation (27). The form of the admissible set  ad, follows from the representation using Lagrange multipliers.…”

Section: Reformulating the Optimization Problem As A Function Of Randmentioning

confidence: 99%

Physics‐constrained non‐Gaussian probabilistic learning on manifolds

Soize

Ghanem

2019

Numerical Meth Engineering

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“…The residual norm is minimized by seeking for a rank-one approximation [12]. The approximation is based on computing the singular value decomposition (SVD) [13].…”

Section: ) Sparse Codingmentioning

confidence: 99%

Speech Enhancement Based on Sparse Representation Using Joint Dictionary

Wei¹,

Liu²,

Chen³

et al. 2018

Proceedings of the 2018 International Conference on Computer Science, Electronics and Communication Engineering (CSECE 2018)

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A new speech denoising method that aims for processing corrupted speech signal which is based on the sparse representation theory of speech signal. In this paper, we train a composite dictionary consisting of the concatenation of the speech dictionary and the noise dictionary by using the K-SVD algorithm. Noise is divided into structured and unstructured noise in this paper. For structured noise, we train speech and noise dictionary firstly, and then according to the different coherence between speech and noise, we use LARC algorithm with a suitably chosen residual coherence threshold to realize the separation of the speech and the noise. For unstructured noise, we only need speech dictionary to extract the clean speech from corrupted speech. Experiments indicate that the proposed method gives better enhancement results in terms of quality measures of speech. The proposed method outperforms the universal dictionary speech enhancement algorithm.

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“…1 is only describing a basic separation system to help focus on the selection of the divergence cost function to be used under the sparse and lowrank framework. The obtained performance can, however, be further improved through techniques such as adopting a universal speech dictionary [23], imposing temporal continuity to the sparse matrix [24], using an information fusion strategy [25], or a combination with autocorrelation [26]. The use of these techniques for performance improvement is beyond the scope of this paper, and will be explored in future works.…”

Section: Unsupervised Speech Separationmentioning

confidence: 99%

Robust Non-negative Matrix Factorization with β-Divergence for Speech Separation

Li¹,

Zhang²,

Sun³

2017

ETRI J

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This paper addresses the problem of unsupervised speech separation based on robust non‐negative matrix factorization (RNMF) with β‐divergence, when neither speech nor noise training data is available beforehand. We propose a robust version of non‐negative matrix factorization, inspired by the recently developed sparse and low‐rank decomposition, in which the data matrix is decomposed into the sum of a low‐rank matrix and a sparse matrix. Efficient multiplicative update rules to minimize the β‐divergence‐based cost function are derived. A convolutional extension of the proposed algorithm is also proposed, which considers the time dependency of the non‐negative noise bases. Experimental speech separation results show that the proposed convolutional RNMF successfully separates the repeating time‐varying spectral structures from the magnitude spectrum of the mixture, and does so without any prior training.

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Speech Enhancement Under Low SNR Conditions Via Noise Estimation Using Sparse and Low-Rank NMF with Kullback–Leibler Divergence

Cited by 82 publications

References 28 publications

Physics‐constrained non‐Gaussian probabilistic learning on manifolds

Physics‐constrained non‐Gaussian probabilistic learning on manifolds

Speech Enhancement Based on Sparse Representation Using Joint Dictionary

Robust Non-negative Matrix Factorization with β-Divergence for Speech Separation

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