BayesianEnhancementofSpeechSignals

BayesianEnhancementofSpeechSignals - overlapping successive...

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Bayesian Enhancement of Speech Signals Jeremy Reed
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Outline Speech Model Bayes application MCMC algorithm Results
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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 = - + = p i t i t i t e x a x 1
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Speech Model • x 1 are corrupted or “bad” samples Prior for e ~N(0, σ e 2 ) Prior, p( a , σ e 2 )=p( a , σ e 2 )~IG(σ e 2 ; α e , β e ) – α e , β e 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 Xa x Ax e 1 - = =
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Speech Model v t is the channel noise v t ~ N(0, σ v 2 ) Inverse Gamma for prior on σ v 2 Can use different distribution if have prior knowledge on the channel’s characteristics t t t v x y + =
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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 ( 29 ( 29 ( 29 ( 29 ( 29 y θ θ x θ x y y θ x p p p p p , , =
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Algorithm Window audio segment of T samples,
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Unformatted text preview: overlapping successive windows by p samples Assign initial values to a , v 2 , and e 2 by using values from last p samples of previous windows For first window, inferences for these parameters drawn from p( x , | y ) Algorithm Perform Gibbs sampling for unknown parameters: ( 29 ( 29 ( 29 1 2 , , ,- = X X a y x a e MAP p N p ( 29 + -+ = Ax A x y x 2 1 , 2 , , 2 e e e p T IG p ( 29 ( 29 ( 29 --+ + = y x y x y x ' 2 1 , 2 1 , , 2 e v v IG p ( 29 ( 29 1 2 , ,-- = e MAP p T N p x y x Algorithm R v is the covariance matrix for the corrupted samples and assumed diag( v 2 ) ( 29 1 1 x X X X a =-MAP ( 29 y R Ay A x v 1 2---= e MAP 1 2-+ = v R A A e Results 440 Hz Sine Wave Results - Speech...
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BayesianEnhancementofSpeechSignals - overlapping successive...

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