Speech enhancement using a mixture-maximum model

Burshtein, David; Gannot, Sharon

doi:10.1109/tsa.2002.803420

Cited by 83 publications

(58 citation statements)

References 20 publications

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“…The frame index t is omitted for simplicity. We rewrite the full model as (11) where (8) and p(s) is the mixture probability.…”

Section: Two Signal Estimation Approachesmentioning

confidence: 99%

“…SuperGaussian priors, including Gaussian, Laplacian, and Gamma densities, have been used to model the real part and imaginary part of the frequency components [10], and the MMSE estimator used for signal estimation. The log-spectra of speech has often been explicitly and accurately modeled by the Gaussian mixture model (GMM) [11]- [13]. The GMM clusters similar log-spectra together and represents them by a mixture component.…”

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confidence: 99%

“…The family of GMM has the ability to model any distribution given a sufficient number of mixtures [20], although a small number of mixtures is often enough. However, because signal estimation is intractable, MIXMAX [11] and Taylor expansion [12], [13] are used. Speech enhancement using the log-spectral domain models offers better spectral estimation and is more suitable for speech recognition.…”

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confidence: 99%

“…The idea is to specify the relation between the log-spectra and frequency coefficients stochastically. We modeled the log-spectra using a GMM following [11]- [13], where each mixture captures the spectra of similar phonemes. The frequency coefficients obey a Gaussian density whose covariances are the exponentials of the log-spectra.…”

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confidence: 99%

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Speech Enhancement Using Gaussian Scale Mixture Models

Hao¹,

Lee²,

Sejnowski³

2010

IEEE Trans. Audio Speech Lang. Process.

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This paper presents a novel probabilistic approach to speech enhancement. Instead of a deterministic logarithmic relationship, we assume a probabilistic relationship between the frequency coefficients and the log-spectra. The speech model in the log-spectral domain is a Gaussian mixture model (GMM). The frequency coefficients obey a zero-mean Gaussian whose covariance equals to the exponential of the log-spectra. This results in a Gaussian scale mixture model (GSMM) for the speech signal in the frequency domain, since the log-spectra can be regarded as scaling factors. The probabilistic relation between frequency coefficients and logspectra allows these to be treated as two random variables, both to be estimated from the noisy signals. Expectation-maximization (EM) was used to train the GSMM and Bayesian inference was used to compute the posterior signal distribution. Because exact inference of this full probabilistic model is computationally intractable, we developed two approaches to enhance the efficiency: the Laplace method and a variational approximation. The proposed methods were applied to enhance speech corrupted by Gaussian noise and speech-shaped noise (SSN). For both approximations, signals reconstructed from the estimated frequency coefficients provided higher signal-to-noise ratio (SNR) and those reconstructed from the estimated log-spectra produced lower word recognition error rate because the log-spectra fit the inputs to the recognizer better. Our algorithms effectively reduced the SSN, which algorithms based on spectral analysis were not able to suppress. Index TermsGaussian scale mixture model (GSMM); Laplace method; speech enhancement; variational approximation

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“…The frame index t is omitted for simplicity. We rewrite the full model as (11) where (8) and p(s) is the mixture probability.…”

Section: Two Signal Estimation Approachesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Speech Enhancement Using Gaussian Scale Mixture Models

Hao¹,

Lee²,

Sejnowski³

2010

IEEE Trans. Audio Speech Lang. Process.

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“…The developed HMM with gain adaptation has been applied to the speech enhancement [14] and to the recognition of clean and noisy speech [15]. In contrast to the frequency-domain models [12]- [15], the density of log-spectral amplitudes is modeled by a Gaussian mixture model (GMM) with parameters trained on the clean signals [16]- [18]. Spectrally similar signals are clustered and represented by their mixture components.…”

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confidence: 99%

Speech Enhancement, Gain, and Noise Spectrum Adaptation Using Approximate Bayesian Estimation

Hao

Attias²,

Nagarajan³

et al. 2009

IEEE Trans. Audio Speech Lang. Process.

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Abstract-This paper presents a new approximate Bayesian estimator for enhancing a noisy speech signal. The speech model is assumed to be a Gaussian mixture model (GMM) in the log-spectral domain. This is in contrast to most current models in frequency domain. Exact signal estimation is a computationally intractable problem. We derive three approximations to enhance the efficiency of signal estimation. The Gaussian approximation transforms the log-spectral domain GMM into the frequency domain using minimal Kullback-Leiber (KL)-divergency criterion. The frequency domain Laplace method computes the maximum a posteriori (MAP) estimator for the spectral amplitude. Correspondingly, the log-spectral domain Laplace method computes the MAP estimator for the log-spectral amplitude. Further, the gain and noise spectrum adaptation are implemented using the expectation-maximization (EM) algorithm within the GMM under Gaussian approximation. The proposed algorithms are evaluated by applying them to enhance the speeches corrupted by the speech-shaped noise (SSN). The experimental results demonstrate that the proposed algorithms offer improved signal-to-noise ratio, lower word recognition error rate, and less spectral distortion.Index Terms-Approximate Bayesian estimation, Gaussian mixture model (GMM), speech enhancement.

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