REMOVING NOISE FROM SPEECH
Method for removing noise from a digital speech waveform, including receiving the digital speech waveform having the noise contained therein, segmenting the digital speech waveform into one or more frames, each frame having a clean portion and a noisy portion, extracting a feature component from each frame, creating an nonlinear speech distortion model from the feature components, creating a statistical noise model by making a Piecewise Linear Approximation (PLA) of the nonlinear speech distortion model, determining the clean portion of each frame using the statistical noise model, a log power spectra of each frame, and a model of a digital speech waveform recorded in a noise controlled environment, and constructing a clean digital speech waveform from each clean portion of each frame.
1 . A method for removing noise from a digital speech waveform, comprising:
receiving the digital speech waveform having the noise contained therein;
segmenting the digital speech waveform into one or more frames, each frame having a clean portion and a noisy portion;
extracting a feature component from each frame;
creating a nonlinear speech distortion model from the feature components;
creating a statistical noise model by making a Piecewise Linear Approximation (PLA) of the nonlinear speech distortion model;
determining the clean portion of each frame using the statistical noise model, a log power spectra of each frame, and a model of a digital speech waveform recorded in a noise controlled environment; and
constructing a clean digital speech waveform from each clean portion of each frame.
2 . The method of claim 1 , wherein the model is a Gaussian Mixture Model (GMM).
3 . The method of claim 1 , wherein the frames comprise 32 milliseconds of speech and are positioned such that two consecutive frames half over-laps each other.
4 . The method of claim 1 , wherein extracting the feature component comprises:
computing a Discrete Fourier Transform (DFT) of each frame y f (k) such that
y
f
(
k
)
=
∑
l
=
0
L
-
1
y
t
(
l
)
h
(
l
)
-
j2π
kl
/
L
k
=
0
,
1
,
…
,
L
-
1
where k is a frequency bin index, h(l) denotes a window function, y t (l) denotes a l th speech sample in a current frame of the digital speech waveform in a time domain, the frame y f (k) denotes the digital speech spectra in a k th frequency bin, and L represents a frame length;
representing each frame y f (k) with a complex number comprising a magnitude component and a phase component; and
calculating a log power spectra of each frame y f (k) such that:
y 1 ( k )=log| y f ( k )| 2 k= 0, 1, . . . , K− 1
where
K
=
L
2
+
1
,
and |y f (k)| is the magnitude component.
5 . The method of claim 1 , wherein creating the nonlinear speech distortion model comprises:
modeling the digital speech waveform in a log power spectra domain such that:
exp( y 1 )=exp( x 1 )+exp( n 1 )
where y 1 , represents a log power spectra of the digitial speech waveform, x 1 represents a log power spectra of a clean portion of the digital speech waveform, and n 1 represents a log power spectra of a noisy portion of the digital speech waveform;
modeling the log power spectra of the noisy portion n 1 statistically as a Gaussian Probability Density Function (PDF) with a mean vector μ n and a diagonal covariance matrix ;
determining a sample mean μ n and a sample covariance from the feature components of a first ten frames; and
calculating the nonlinear speech distortion model using the sample mean μ n and the sample covariance
6 . The method of claim 5 , wherein creating the statistical noise model comprises:
determining a maximum likelihood (ML) estimation of the mean vector μ n and the diagonal covariance matrix using a Expectation-Maximization (EM) algorithm such that:
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where
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where p y (y t l |m) represents a Probability Density Function (PDF) of the digital speech waveform's feature component y t l , for an m th component of a mixture of densities, where E n [(n t l |y t l ,m)] and E n [(n t l (n t l ) T |y t l ,m)] are relevant conditional expectations, and where t is a frame index; and
using the Piecewise Linear Approximation (PLA) of the nonlinear speech distortion model to calculate p y (y t l |m),
E n [(n t l |y t l ,m), and E n [(n t l (n t l ) T |y t l ,m).
7 . The method of claim 6 , wherein the clean portion of each frame is represented in the log power spectra domain.
8 . The method of claim 7 , wherein determining the clean portion of each frame comprises:
using a minimum mean-squared error (MMSE) estimation of the log power spectra of the clean portion of the digital speech waveform x l such that:
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]
where E x [(x t l |y t l ,m)] is a conditional expectation of the log power spectra of the clean portion of the digital speech waveform x t l given the log power spectra of the digital speech waveform y t l for the m th component of the mixture of densities; and
using the Piecewise Linear Approximation (PLA) of the nonlinear speech distortion model to calculate E x [(x t l |y t l ,m)].
9 . The method of claim 7 , wherein constructing the clean digital speech waveform comprises:
using each log power spectra of the clean portion of the digital speech waveform and a phase component corresponding thereto as inputs in a wave reconstruction function such that:
{circumflex over (x)} f ( k )=exp{ {circumflex over (x)} t ( k )/2}exp{ j∠y f ( k )}
where ∠y f (k) is the phase component from the digital speech waveform to create a reconstructed spectra from each log power spectra;
converting each reconstructed spectra of the clean portion of the digital speech; waveform to a time domain using an Inverse Discrete Fourier Transform (IDFT) such that:
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^
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(
l
)
=
1
L
∑
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=
0
L
-
1
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(
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j2π
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/
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;
and
synthesizing the digital speech waveform using a traditional overlap-add procedure.
10 . A computer-readable medium having stored thereon computer-executable instructions which, when executed by a computer, cause the computer to:
receive the digital speech waveform having the noise contained therein;
segment the digital speech waveform into one or more frames, each frame having a clean portion and a noisy portion represented in a log power spectra domain;
extract a feature component from each frame;
create a nonlinear speech distortion model from the feature components;
create a statistical noise model by making a Piecewise Linear Approximation (PLA) of the nonlinear speech distortion model to derive one or more terms in an Expectation-Maximization (EM) algorithm;
determine the clean portion of each frame using the statistical noise model, a log power spectra of each frame, and a Gaussian Mixture Model (GMM) model of a digital speech waveform recorded in a noise controlled environment; and
construct a clean digital speech waveform from each clean portion of each frame.
11 . The computer-readable medium of claim 10 , wherein the frames comprise 32 milliseconds of speech and are positioned such that two consecutive frames half over-laps each other.
12 . The computer-readable medium of claim 10 , wherein the computer-executable instructions to create the nonlinear speech distortion model are configured to:
model the digital speech waveform in the log power spectra domain such that:
exp( y 1 )=exp( x 1 )+exp( n 1 )
where y 1 , represents a log power spectra of the digitial speech waveform, x 1 represents a log power spectra of a clean portion of the digital speech waveform, and n 1 represents a log power spectra of a noisy portion of the digital speech waveform;
model the log power spectra of the noisy portion n 1 statistically as a Gaussian Probability Density Function (PDF) with a mean vector μ n and a diagonal covariance matrix
determine a sample mean μ n and a sample covariance from the feature components of a first ten frames; and
calculate the nonlinear speech distortion model using the sample mean μ n and the sample covariance
13 . The computer-readable medium of claim 12 , wherein the computer-executable instructions to create the statistical noise model are configured to:
determine a maximum likelihood (ML) estimation of the mean vector μ n and the diagonal covariance matrix using a Expectation-Maximization (EM) algorithm such that:
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where
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|
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)
∑
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(
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|
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)
where p y (y t l |m) represents a Probability Density Function (PDF) of the digital speech waveform's feature component y t l , for an m th component of a mixture of densities, where E n [(n t l |y t l ,m)] and E n [(n t l (n t l ) T |y t l ,m)] are relevant conditional expectations, and where t is a frame index; and
use the Piecewise Linear Approximation (PLA) of the nonlinear speech distortion model to derive one or more detailed formulas to calculate p y (y t l |m), E n [(n t l |y t l ,m), and E n [(n t l (n t l ) T |y t l ,m).
14 . The computer-readable medium of claim 12 , wherein the computer-executable instructions to construct the clean digital speech waveform are configured to:
use each log power spectra of the clean portion of the digital speech waveform and a phase component corresponding thereto as inputs in a wave reconstruction function such that:
{circumflex over (x)} f ( k )=exp{ {circumflex over (x)} l ( k )/2}exp{ j∠y f ( k )}
where ∠y f (k) is the phase component from the digital speech waveform to create a reconstructed spectra from each log power spectra;
convert each reconstructed spectra of the clean portion of the digital speech waveform to a time domain using an Inverse Discrete Fourier Transform (IDFT) such that:
x
^
t
(
k
)
=
1
L
∑
k
=
0
L
-
1
x
^
f
(
k
)
j2π
kl
/
L
;
and
synthesizing the digital speech waveform using a traditional overlap-add procedure.
15 . A computer system, comprising:
a processor; and
a memory comprising program instructions executable by the processor to:
receive the digital speech waveform having the noise contained therein;
segment the digital speech waveform into one or more frames, each frame having 32 milliseconds of speech, being positioned such that two consecutive frames half over-laps each other, and each frame having a clean portion and a noisy portion and the frames;
extract a feature component from each frame;
create a nonlinear speech distortion model from the feature components;
create a statistical noise model by making a Piecewise Linear Approximation (PLA) of the nonlinear speech distortion model;
determine the clean portion of each frame using the statistical noise model, a log power spectra of each frame, and a model of a digital speech waveform recorded in a noise controlled environment; and
construct a clean digital speech waveform from each clean portion of each frame.
16 . The computer system of claim 15 , wherein the model is a Gaussian Mixture Model (GMM).
17 . The computer system of claim 15 , wherein the frames comprise 32 milliseconds of speech and are positioned such that two consecutive frames half over-laps each other.
18 . The computer system of claim 15 , wherein the program instructions executable the processor to extract the feature component comprise program instructions executable by the processor to:
compute a Discrete Fourier Transform (DFT) of each frame y f (k) such that
y
f
(
k
)
=
∑
l
=
0
L
-
1
y
t
(
l
)
h
(
l
)
-
j2π
kl
/
L
k
=
0
,
1
,
…
,
L
-
1
where k is a frequency bin index, h(l) denotes a window function, y t (l) denotes a l th speech sample in a current frame of the digital speech waveform in a time domain, the frame y f (k) denotes the digital speech spectra in a k th frequency bin, and L represents a frame length;
represent each frame y f (k) with a complex number comprising a magnitude component and a phase component; and
calculate a log power spectra of each frame y f (k) such that:
y l ( k )=log| y f ( k )| 2 k= 0, 1 , . . . , K− 1
where
K
=
L
2
+
1
,
and |y f (k)| is the magnitude component.
19 . The computer system of claim 15 , wherein the program instructions executable the processor to create the nonlinear speech distortion model comprise program instructions executable by the processor to:
model the digital speech waveform in a log power spectra domain such that:
exp( y 1 )=exp( x 1 )+exp( n 1 )
where y 1 represents a log power spectra of the digitial speech waveform, x 1 represents a log power spectra of a clean portion of the digital speech waveform, and n 1 represents a log power spectra of a noisy portion of the digital speech waveform;
model the log power spectra of the noisy portion n 1 statistically as a Gaussian Probability Density Function (PDF) with a mean vector μ n and a diagonal covariance matrix
determine a sample mean μ n and a sample covariance from the feature components of a first ten frames; and
calculate the nonlinear speech distortion model using the sample mean μ n and the sample covariance
20 . The computer system of claim 19 , wherein the program instructions executable the processor to create the statistical noise model comprise program instructions executable by the processor to:
determine a maximum likelihood (ML) estimation of the mean vector μ n and the diagonal covariance matrix using a Expectation-Maximization (EM) algorithm such that:
μ
_
n
=
∑
t
=
0
T
-
1
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=
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where
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|
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=
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p
y
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t
l
|
m
)
∑
l
=
1
M
ω
l
p
y
(
y
t
l
|
l
)
where p y (y t l |m) represents a Probability Density Function (PDF) of the digital speech waveform's feature component y t l , for an m th component of a mixture of densities, where E n [(n t l |y t l ,m)] and E n [(n t l (n t l ) T |y t l ,m)] are relevant conditional expectations, and where t is a frame index; and
use the Piecewise Linear Approximation (PLA) of the nonlinear speech distortion model to derive one or more detailed formulas to calculate p y (y t l |m), E n [(n t l |y t l ,m), and E n [(n t l (n t l ) T |y t l ,m).