CN108231084B - Improved wavelet threshold function denoising method based on Teager energy operator - Google Patents

Improved wavelet threshold function denoising method based on Teager energy operator Download PDF

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CN108231084B
CN108231084B CN201711260681.5A CN201711260681A CN108231084B CN 108231084 B CN108231084 B CN 108231084B CN 201711260681 A CN201711260681 A CN 201711260681A CN 108231084 B CN108231084 B CN 108231084B
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罗元
谭琴
张毅
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Chongqing University of Post and Telecommunications
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    • G—PHYSICS
    • G10—MUSICAL INSTRUMENTS; ACOUSTICS
    • G10L—SPEECH ANALYSIS OR SYNTHESIS; SPEECH RECOGNITION; SPEECH OR VOICE PROCESSING; SPEECH OR AUDIO CODING OR DECODING
    • G10L21/00—Processing of the speech or voice signal to produce another audible or non-audible signal, e.g. visual or tactile, in order to modify its quality or its intelligibility
    • G10L21/02—Speech enhancement, e.g. noise reduction or echo cancellation
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Abstract

The invention requests to protect an improved wavelet threshold function denoising method based on a Teager energy operator, and relates to the field of voice signal denoising; by improving the soft and hard threshold denoising function, a new threshold function is provided, and the function not only can overcome the pseudo Gibbs effect caused by the discontinuity of the hard threshold function, but also can overcome the problem of constant deviation after the soft threshold function is denoised. The invention has great improvement on signal-to-noise ratio and mean square error.

Description

Improved wavelet threshold function denoising method based on Teager energy operator
Technical Field
The invention belongs to the field of voice signal denoising, and particularly relates to an improved wavelet threshold function denoising method based on a Teager energy operator.
Background
Speech signals often contain noise during acquisition or propagation, wherein the noise seriously affects the subsequent work of signal processing and analysis. Therefore, denoising of speech signals is the most fundamental and important task in the field of signal processing.
The traditional denoising method mainly comprises linear filtering and nonlinear filtering, such as median filtering, Wiener filtering, kalman filtering and the like. The disadvantages of these methods are that it is difficult to reflect the non-stationary characteristics and correlation of the signal while removing noise. In recent years, wavelet transformation is widely applied to signal denoising processing by the characteristic of multi-resolution, can show good signal local characteristics in both time domain and frequency domain, can effectively extract transient information in signals, is suitable for carrying out detailed analysis on non-stationary signals, and obtains better denoising effect. The wavelet threshold denoising is the most used wavelet analysis in denoising application because of simple realization and small calculation amount, and can effectively remove noise and reserve an original voice signal, thereby better improving the signal-to-noise ratio and mean square error of the signal.
The most important in the wavelet threshold denoising process is the selection of the threshold and the threshold function. If the threshold value is too small, the denoising is insufficient, and part of noise is reserved; if the threshold is selected too large, excessive denoising will occur, and weak feature components in the signal will be mistaken for noise and eliminated. The denoising method of the hard threshold and the soft threshold proposed by Donoho and Johnstone is widely applied in practice and achieves better effect, but the discontinuity of the hard threshold function causes the reconstruction signal to easily generate pseudo Gibbs effect; the soft threshold function, although continuous, always has a constant deviation between the estimated value and the actual value. If the threshold value is too small, the denoising is insufficient, and part of noise is reserved; if the threshold is selected too large, excessive denoising occurs, and weak characteristic components in the signal are mistakenly considered as noise to be eliminated, so that part of useful information is lost in the signal. Therefore, in order to obtain better denoising effect, it is important to select an appropriate threshold and a threshold function.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. The improved wavelet threshold function denoising method based on the Teager energy operator can improve the signal-to-noise ratio of a noisy signal and reduce the mean square error. The technical scheme of the invention is as follows:
a wavelet threshold function denoising method based on a Teager energy operator is disclosed, and comprises the following steps:
s1, collecting a section of voice signal, and adding noises with different signal-to-noise ratios to the collected voice signal to obtain a voice signal with noises;
s2, carrying out five-layer discrete wavelet decomposition on the noisy speech signal obtained in the step S1 to obtain wavelet decomposition coefficients of each layer;
s3, calculating a Teager energy operator for each layer of wavelet decomposition coefficients obtained in the step S2 to obtain the Teager energy operator value of the wavelet coefficients;
s4, passing the Teager energy operator in the step S3 through a 32-bit Hamming window, then carrying out normalization processing on the value of the Hamming window, and calculating a threshold value in the denoising process;
s5, denoising the noisy speech signal by adopting an improved threshold function according to the threshold in the step S4; the improvement is as follows: the continuity, the progressiveness and the constant deviation of the common threshold function are improved;
and S6, reconstructing the wavelet decomposition coefficient to obtain a denoised voice signal.
Further, step S2 is to perform discrete wavelet decomposition on the noisy speech signal to obtain wavelet coefficients of each layer, where the discrete wavelet decomposition includes:
firstly, defining a wavelet function psi (t), and performing translation and expansion operations on the wavelet function psi (t) to obtain a cluster of wavelet functions psi a, b (t):
Figure GDA0003136990500000021
a > 0, b ∈ R, a denotes a scale factor b denotes a translation factor, a denotes0And b0All represent the expansion step size, j represents the scale of wavelet decomposition;
discretizing a and b respectively as follows:
a＝a0 j,b＝ka0 jb0 j,k∈Z,a0≠1
after discretization, a cluster of discrete wavelet functions psi can be obtainedj,k(t)：
Figure GDA0003136990500000031
The discrete wavelet transformed wavelet coefficients of signal f (t) can be expressed as:
Figure GDA0003136990500000032
Wψrepresents the orthogonal wavelet transform, f represents the speech signal, t represents time, and k represents the number of nodes.
Further, the calculation step of calculating the Teager energy operator in step S3 is as follows:
first, the continuous form of the nonlinear energy operator is defined as:
Figure GDA0003136990500000033
in the formula (I), the compound is shown in the specification,
Figure GDA0003136990500000034
is the continuous Teager energy operator TEO, x (t) represents a continuous speech signal, when x (n) is a discrete speech signal:
Figure GDA0003136990500000035
n represents a discretized point in time;
the TEO value is calculated for the wavelet decomposition coefficients: w is aj,m(k) Representing wavelet coefficients T after wavelet decompositionj,m(k) Values representing the Teager energy operators for each layer;
Figure GDA0003136990500000036
further, the method for calculating the threshold in step S4 is as follows:
smoothing the obtained TEO value, and making it pass through a Hamming window with length of 32 points to obtain M ═ T ═ H, H is Hamming window, T represents Tj,m(k) The shorthand of (1) represents the value of each layer of Teager energy operator; and normalizing M to obtain M':
Figure GDA0003136990500000037
so that its adaptive threshold can be represented by the expression:
THj,m(k)＝λj,m(1-αjM'j,m(k))
in the formula, λj,mRepresenting a threshold, j, m respectively representing the mth subband of the jth layer, αjAre adjustment parameters based on the respective layers.
Further, the
Figure GDA0003136990500000041
Wherein N isj,mFor the length of the mth subband at the jth layer, σ j, m represents the standard deviation of gaussian noise:
Figure GDA0003136990500000042
mean represents the median estimate.
Further, in step S5, the improved threshold function is:
Figure GDA0003136990500000043
wherein λ is a threshold value, n is a positive integer, wherein,
Figure GDA0003136990500000044
corresponding to a threshold value which can be automatically adjusted whenj,kWhen | ≧ λ,
Figure GDA0003136990500000045
with | wj,kThe value of l is increasing continuously and the number of the columns,
Figure GDA0003136990500000046
is continuously decreased, and when | wj,kIf λ is less than | is set to 0, a smooth transition region is formed between the noise and the signal.
Further, in step S6, the calculation method for performing wavelet reconstruction on the signal to obtain the denoised signal includes:
Figure GDA0003136990500000047
where C is a constant independent of the original signal, where Cj,k(t)＝＜f(t),
Figure GDA0003136990500000048
Figure GDA0003136990500000049
To indicate psij,k(t)Complex conjugation of (a). The invention has the following advantages and beneficial effects:
firstly, the wavelet coefficient after wavelet decomposition is calculated by Teager energy operator, so that the difference between the noise wavelet coefficient and the signal wavelet coefficient is increased, and the adaptive selection of the threshold value is facilitated; and then, improving a common soft and hard threshold denoising function, and providing a new threshold function, wherein the function not only can overcome the pseudo Gibbs effect caused by the discontinuity of the hard threshold function, but also can overcome the problem of constant deviation after the soft threshold function is denoised.
The invention provides an improved threshold function denoising method based on a Teager energy operator, aiming at the problems of aliasing phenomenon of signal and noise wavelet coefficients, discontinuity of a threshold function at a threshold value, constant deviation of a wavelet coefficient estimated value and an original value and the like in a denoising process. Firstly, calculating a Teager energy operator for a wavelet coefficient, increasing the difference between a signal and noise, and facilitating the selection of a threshold value; and then the wavelet coefficient is quantized by the improved threshold function, so that the problems of pseudo Gibbs effect caused by the discontinuity of the hard threshold function and constant deviation caused by the soft threshold function are effectively avoided. The improved denoising method has the advantages that the denoising effect is greatly improved, the signal-to-noise ratio is greatly improved, the distortion of the voice signal is avoided while denoising is carried out to the maximum degree, and the practicability is high in the actual processing process of the voice signal.
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FIG. 1 is a flow chart of an improved wavelet threshold function denoising method based on a Teager energy operator according to a preferred embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
as shown in FIG. 1, the invention provides an improved threshold function denoising method based on Teager energy operator, which comprises the following steps:
s1, collecting a section of voice signal by using Cool Edit Pro, and adding noises with different signal-to-noise ratios to the collected voice signal to obtain a voice signal with noises;
s2, calculating Teager energy operators for the wavelet decomposition coefficients of the layers obtained in the step S2 to obtain TEO values of the wavelet decomposition coefficients; (concrete procedure)
The discrete wavelet decomposition comprises the following steps:
first, we define a wavelet function ψ (t), and perform translation and expansion operations on it to obtain a cluster of wavelet functions ψ a, b (t):
Figure GDA0003136990500000061
a＞0,b∈R
we discretize a, b separately as:
a＝a0j,b＝ka0jb0 j,k∈Z,a0≠1
after discretization, a cluster of discrete wavelet functions psi can be obtainedj,k(t)：
Figure GDA0003136990500000062
The discrete wavelet transformed wavelet coefficients of signal f (t) can be expressed as:
Figure GDA0003136990500000063
s3, calculating Teager energy operators for the wavelet decomposition coefficients of the layers obtained in the step S2 to obtain TEO values of the wavelet decomposition coefficients;
first, we define the continuous form of the nonlinear energy operator as:
Figure GDA0003136990500000064
in the formula (I), the compound is shown in the specification,
Figure GDA0003136990500000065
is the continuous Teager energy operator TEO, x (t) represents a continuous speech signal, then when x (n) is a discrete speech signal:
Figure GDA0003136990500000066
the TEO value is calculated for the wavelet decomposition coefficients:
Figure GDA0003136990500000067
s4, calculating a threshold value in the denoising process;
smoothing the obtained TEO values, passing them through a hamming window of 32 points in length to obtain M ═ T × H, where × represents the convolution and H is the hamming window, and normalizing M to obtain M':
Figure GDA0003136990500000071
so that its adaptive threshold can be represented by the expression:
THj,m(k)＝λj,m(1-αjM′j,m(k))
wherein j and m respectively represent the m-th sub-band of the j layer, and alphajThe method can reduce the threshold value of the low frequency band and increase the threshold value of the high frequency band based on the adjustment parameters of each layer, and can remove more noise. In the formula (I), the compound is shown in the specification,
Figure GDA0003136990500000072
wherein the content of the first and second substances,Nj,mis the length of the mth subband of the jth layer. σ j, m represents the standard deviation of gaussian noise:
Figure GDA0003136990500000073
s5, the step of improving the threshold function is:
for the commonly used threshold functions, soft and hard threshold functions are:
Figure GDA0003136990500000074
Figure GDA0003136990500000075
equation (1) represents a hard threshold function, and equation (2) represents a soft threshold function. The voice denoised by the hard threshold function usually has great concussion, and a large amount of noise remains; the wavelet coefficient processed by the soft threshold function has constant deviation with the original wavelet coefficient, so that part of useful high-frequency components are lost, and voice distortion is caused.
In order to overcome the disadvantages of the above two functions, the present invention proposes an improved threshold function:
Figure GDA0003136990500000076
in the formula, lambda is a threshold value, and n is a positive integer. Wherein the content of the first and second substances,
Figure GDA0003136990500000081
corresponding to a threshold value that can be automatically adjusted. When | wj,kWhen | ≧ λ,
Figure GDA0003136990500000082
with | wj,kThe value of l is increasing continuously and the number of the columns,
Figure GDA0003136990500000083
the constant deviation problem in the soft threshold processing process is avoided by continuously reducing the soft threshold. And when | wj,kWhen the value is less than lambda, the value is not simply set to 0, but a smooth transition region is formed between noise and a signal, and the oscillation possibly generated by direct truncation in a hard threshold value is avoided.
And S6, performing wavelet reconstruction to obtain a denoised voice signal.
Figure GDA0003136990500000084
Where c is a constant independent of the original signal, where
Figure GDA0003136990500000085
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.

Claims (6)

1. An improved wavelet threshold function denoising method based on a Teager energy operator is characterized by comprising the following steps:
s1, collecting a section of voice signal, and adding noises with different signal-to-noise ratios to the collected voice signal to obtain a voice signal with noises;
s2, carrying out five-layer discrete wavelet decomposition on the noisy speech signal obtained in the step S1 to obtain wavelet decomposition coefficients of each layer;
s3, calculating a Teager energy operator for each layer of wavelet decomposition coefficients obtained in the step S2 to obtain the Teager energy operator value of the wavelet coefficients;
s4, passing the Teager energy operator in the step S3 through a 32-bit Hamming window, then carrying out normalization processing on the value of the Hamming window, and calculating a threshold value in the denoising process;
s5, denoising the noisy speech signal by adopting an improved threshold function according to the threshold in the step S4; the improvement is as follows: the continuity, the progressiveness and the constant deviation of the common threshold function are improved; in step S5, the improved threshold function is:
Figure FDA0003110524050000011
wherein λ is a threshold value, n is a positive integer, wherein,
Figure FDA0003110524050000012
corresponding to a threshold value which can be automatically adjusted whenj,kWhen | ≧ λ,
Figure FDA0003110524050000013
with | wj,kThe value of l is increasing continuously and the number of the columns,
Figure FDA0003110524050000014
is continuously decreased, and when | wj,kWhen the value is less than lambda, a smooth transition region is formed between noise and a signal instead of 0;
and S6, performing wavelet reconstruction on the signal subjected to the denoising processing of S5 to obtain a denoised voice signal.
2. The improved wavelet threshold function denoising method based on Teager' S energy operator as claimed in claim 1, wherein said step S2 performs discrete wavelet decomposition on the noisy speech signal to obtain wavelet coefficients of each layer, the discrete wavelet decomposition step is:
firstly, defining wavelet function psi (t), and making it undergo the processes of translation and expansion operation to obtain a cluster of wavelet functions psia,b(t)：
Figure FDA0003110524050000021
a denotes a scale factor b denotes a translation factor, a0And b0All represent an extension stepLength, j, represents the scale of the wavelet decomposition;
discretizing a and b respectively as follows:
a＝a0 j,b＝ka0 jb0 j,k∈Z,a0≠1
after discretization, a cluster of discrete wavelet functions psi can be obtainedj,k(t)：
Figure FDA0003110524050000022
The discrete wavelet transformed wavelet coefficients of signal f (t) can be expressed as:
Figure FDA0003110524050000023
Wψrepresents the orthogonal wavelet transform, f represents the speech signal, t represents time, and k represents the number of nodes.
3. The method for denoising the wavelet threshold function based on the Teager energy operator as claimed in claim 2, wherein the step of calculating the Teager energy operator in the step S3 is:
first, the continuous form of the nonlinear energy operator is defined as:
Figure FDA0003110524050000024
in the formula (I), the compound is shown in the specification,
Figure FDA0003110524050000025
is the continuous Teager energy operator TEO, x (t) represents a continuous speech signal, when x (n) is a discrete speech signal:
Figure FDA0003110524050000026
n represents a discretized point in time;
the TEO value is calculated for the wavelet decomposition coefficients: w is aj,m(k) Representing wavelet coefficients T after wavelet decompositionj,m(k) Values representing the Teager energy operators for each layer;
Figure FDA0003110524050000027
4. the improved wavelet threshold function denoising method based on Teager energy operator as claimed in claim 3, wherein the threshold value calculating method in step S4 is:
smoothing the obtained TEO value, and making it pass through a Hamming window with length of 32 points to obtain M ═ T ═ H, H is Hamming window, T represents Tj,m(k) The shorthand of (1) represents the value of each layer of Teager energy operator; and normalizing M to obtain M':
Figure FDA0003110524050000031
so that its adaptive threshold can be represented by the expression:
THj,m(k)＝λj,m(1-αjM'j,m(k))
in the formula, λj,mRepresenting a threshold, j, m respectively representing the mth subband of the jth layer, αjAre adjustment parameters based on the respective layers.
5. The Teager energy operator-based improved wavelet threshold function denoising method of claim 4, wherein said method comprises
Figure FDA0003110524050000032
Wherein N isj,mFor the length of the mth subband at the jth layer, σ j, m represents the standard deviation of gaussian noise:
Figure FDA0003110524050000033
mean represents the median estimate.
6. The Teager energy operator-based improved wavelet threshold function denoising method of claim 1, wherein in step S6, the calculation method for performing wavelet reconstruction on the signal to obtain the denoised signal comprises:
Figure FDA0003110524050000034
where c is a constant independent of the original signal, where
Figure FDA0003110524050000035
Figure FDA0003110524050000036
To indicate psij,k(t)Complex conjugation of (a).
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