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Bayesian Enhancement of Speech Signals

Bayesian Enhancement of Speech Signals. Jeremy Reed. Outline. Speech Model Bayes application MCMC algorithm Results. Speech Model. Predict current speech sample from p previous samples (AR process) Justified by physics Lossless acoustic tubes Time for vocal tract to change shape

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Bayesian Enhancement of Speech Signals

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  1. Bayesian Enhancement of Speech Signals Jeremy Reed

  2. Outline • Speech Model • Bayes application • MCMC algorithm • Results

  3. Speech Model • Predict current speech sample from p previous samples (AR process) • Justified by physics • Lossless acoustic tubes • Time for vocal tract to change shape • Use a window of T samples for short-time analysis

  4. Speech Model • x1 are corrupted or “bad” samples • Prior for e~N(0, σe2) • Prior, p(a, σe2)=p(a, σe2)~IG(σe2; αe, βe) • αe, βe chosen to be broad enough to incorporate a (approach Jeffrey’s Prior) • AR coefficients are normal with ML mean and variance related to error and samples

  5. Speech Model • vt is the channel noise • vt~ N(0, σv2) • Inverse Gamma for prior on σv2 • Can use different distribution if have prior knowledge on the channel’s characteristics

  6. Bayesian Speech Enhancement • x is the clean speech sequence • y is x plus additive noise, v • θ is a vector containing the parameters of the speech and noise

  7. Algorithm • Window audio segment of T samples, overlapping successive windows by p samples • Assign initial values to a, σv2, and σe2 by using values from last p samples of previous windows • For first window, inferences for these parameters drawn from p(x,θ|y)

  8. Algorithm • Perform Gibbs sampling for unknown parameters:

  9. Algorithm • Rv is the covariance matrix for the corrupted samples and assumed diag(σv2)

  10. Results – 440 Hz Sine Wave

  11. Results - Speech

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