CN111837119A - A Sound Signal Separation Method Based on Semi-Non-Negative Matrix Decomposition - Google Patents

Abstract

A method of sound signal separation with semi-non-negative matrix factorization, comprising: calculating a fourier transform result of the single-channel mixed sound signal and calculating a frequency spectrum thereof (S1); performing semi-nonnegative matrix factorization (S2) on the frequency spectrum of the mixed signal; obtaining respective initial spectra of the source signals from the spectra of the mixed signals (S3); performing semi-nonnegative matrix factorization (S4) on an initial spectrum of the source signal; obtaining a frequency spectrum of the source signal according to the frequency spectrum of the mixed signal, the characteristic matrix and the coefficient matrix corresponding to the frequency spectrum of the mixed signal, and the characteristic matrix and the coefficient matrix corresponding to the source signal (S5); obtaining a fourier transform result of the source signal from the fourier transform result of the mix signal and the frequency spectrum of the source signal (S6); the source signal is separated from the single-channel mixed sound signal by performing an inverse fourier transform on the fourier transform result of the source signal to obtain the source signal (S7). The method can be used for separating single-channel mixed sound signals formed by mixing source sound signals which are overlapped in frequency domain and are not necessarily independent.

Description

A Sound Signal Separation Method Based on Semi-Non-Negative Matrix Decomposition

technical field

The invention relates to the technical field of single-channel mixed sound signal separation, in particular to a sound signal separation method based on semi-non-negative matrix decomposition.

Background technique

Acoustic technology has been widely researched and applied in the fields of medical diagnosis, product quality inspection, equipment condition monitoring, mechanical performance test, and acoustic event classification. Because the sound field of its application environment may be complex, the collected sound signal is often a mixed signal of target sound and environmental noise. Therefore, it is generally necessary to first extract the target sound from the mixed sound signal for subsequent signal processing and analysis. In addition, in view of the limitations of size, equipment cost, installation problems and other conditions, it is possible to install only one sound sensor or it is better to install one sound sensor, which requires extracting the target from the single-channel mixed sound signal collected by a single microphone sound signal. Single-channel mixed sound signal separation is a common method for solving the above tasks.

The Chinese invention patent "Method and Device for Separation of Underdetermined Sound Signals Based on Hilbert Transform" applied by the Third Design and Research Institute of Machinery Industry proposes to use Hilbert transform to separate underdetermined sound signals. Not suitable for frequency domain aliasing. The Chinese invention patent "Multi-vehicle acoustic signal separation method based on particle filtering in wireless sensor network" and the Chinese invention patent applied by Shandong University "Based on the joint approximate diagonalization blind source separation algorithm" "Equipment fault sound detection method" is to separate the sound for the multi-channel mixed sound signal collected by the microphone array.

The paper "Blind Source Separation Method for Single-Channel Signals Based on Variational Mode Decomposition" published by Wang Kang et al. from Anhui University of Science and Technology proposed a blind source separation method for single-channel signals based on variational modal decomposition: first, the variational mode decomposition method was used. Decomposition realizes the dimension-raising of the single-channel observation signal, estimates the number of source signals, and then performs blind source separation of the signal. This method involves dimension-raising operations (that is, mapping a single-channel signal to a multi-channel signal), and is not suitable for the case of frequency domain aliasing. The paper "Single-channel same-frequency mixed signal low-complexity blind separation algorithm based on SIC" published by Guo Yiming et al. of PLA University of Information Engineering uses oversampling to construct multi-channel conditions, and then constructs a channel matrix, and uses continuous interference cancellation algorithm to achieve single-channel synchronization. Blind separation of frequency mixed signals. This method also involves mapping a single-channel signal into a multi-channel signal and then performing signal separation, which is greatly affected by the time delay difference and the oversampling multiple of the received signal, and there is a demodulation blind spot. The paper "Blind Separation Algorithm for Single-Channel Communication Signals" published by Yang Hailan et al. of Jiangnan University presents a blind source separation algorithm for single-channel communication signals based on Hilbert-Huang transform and independent component analysis. This method is not suitable for the case of frequency domain aliasing. The paper "Blind Source Separation of Single-Channel Mechanical Signals Based on Shift-Invariant Sparse Coding" published by Zhu Huijie et al. of PLA University of Science and Technology proposed a single-channel blind source separation method based on shift-invariant sparse coding for mechanical signals with recurring features. In the algorithm, the source signal is regarded as the convolution of multiple bases and coefficients, which can adaptively learn matching bases and sparse coefficients by using the signal's own characteristics according to the statistical distribution of the signal. This method targets mechanical signals that feature recurring patterns.

SUMMARY OF THE INVENTION

In view of this, it is necessary to propose a sound signal separation method based on semi-non-negative matrix decomposition to solve the above problems. The method firstly obtains the initial estimated spectrum from the spectrum of the single-channel mixed sound signal according to the main frequency band of the source sound signal, and then decomposes the initial estimated spectrum of the source signal into an initial feature matrix and an initial coefficient matrix based on semi-nonnegative matrix decomposition. The correlation between the coefficient matrices of the signal obtains the final characteristic matrix and coefficient matrix of the source signal, so as to obtain the spectrum of the source signal, and then performs inverse Fourier transform to obtain the source signal, and finally realizes the separation of single-channel mixed sound signals.

To achieve the above object, the present invention adopts the following technical solutions:

A sound signal separation method based on semi-non-negative matrix decomposition, comprising the following steps:

S1. The single-channel mixed sound signal S is formed by mixing several independent sound signals S ¹ , S ² , ..., ^Sn , calculate the Fourier transform result F of S, and calculate the spectrum X according to F;

S2. Perform semi-non-negative matrix decomposition on X to obtain feature matrix W and coefficient matrix H;

S3. Obtain the respective initial estimated spectrums of the sound signals S ¹ , S ² , ..., ^Sn according to X

分别进行半非负矩阵分解，得到对应的特征矩阵

和系数矩阵

S4, yes

Perform semi-non-negative matrix decomposition respectively to get the corresponding eigenmatrix

and coefficient matrix

获得声音信号S¹,S²,…,Sⁿ各自的频谱X¹,X²,…,Xⁿ；S5. According to X, W, H, and

Obtain the respective frequency spectra X ¹ , X ² ,..., X ⁿ of the sound signals S ¹ , S ² ,...,S ⁿ ;

S6. According to the Fourier transform result F and the frequency spectrum X ¹ , X ² ,...,X ⁿ , obtain the respective Fourier transform results F ¹ , F ² ,..., F ⁿ of the sound signals S ¹ , S ² ,..., ^Sn ;

^S7 . ^Perform inverse Fourier transform ^{on F 1} , F ² , . ¹ , S ² ,…,S ⁿ .

Further, the single-channel mixed sound signal in S1 means that the mixed sound signal is collected by only one sound collector.

Further, the single-channel mixed sound signal S in S1 is formed by mixing several independent sound signals S ¹ , S ² , . . . , Sn , where the value of ⁿ is 2 or 3.

Further, in S2, semi-non-negative matrix decomposition is performed on X to obtain a feature matrix W and a coefficient matrix H, and the steps are as follows:

S21. Construct the objective function Γ of the semi-nonnegative matrix factorization

S22. Initialize the coefficient matrix H, and the values of all its elements are random numbers between (0, 1);

S23. Calculate the initial value of the feature matrix W as

W=XH(H ^T H) ^-1 (2)

迭代更新系数矩阵H中的元素；S24, iteratively update the feature matrix W and the coefficient matrix H alternately: first iteratively update W once, and then iteratively update H once, so that W and H are iteratively updated successively in a cycle; using the formula W=XH(H ^T H) ^-1 ( 3) Iteratively update the elements in the feature matrix W, using the formula

Iteratively update the elements in the coefficient matrix H;

S25. Set the minimum value Γ _min of the objective function Γ of the semi-nonnegative matrix decomposition, set the maximum number of iterations E _max , and calculate the value of the objective function Γ after each iteration update is completed. When the value of the objective function Γ is less than Γ _min or When the number of iterations reaches the maximum number of iterations E _max , the iteration is stopped, and the final feature matrix W and coefficient matrix H are obtained;

表示矩阵的Frobenius范数；X为频谱；W为特征矩阵；H为系数矩阵；H^T为H的转置；(H^TH)^-1为H^TH的逆矩阵；X^T为X的转置；W^T为W的转置；(X^TW)⁺为X^TW中的正值元素；(X^TW)^-为X^TW中的负值元素；(W^TW)⁺为W^TW中的正值元素；(W^TW)^-为W^TW中的负值元素。In formulas (1), (2), (3) and (4),

Represents the Frobenius norm of the matrix; ^X is the frequency spectrum; W is the characteristic matrix; H is the coefficient matrix; H ^T is the transpose of H; (H ^T H) ^-1 is the inverse matrix of H ^T H; Set; W ^T is the transpose of W; (X ^T W) ⁺ is the positive value element in X ^T W; (X ^T W) ^- is the negative value element in X ^T W; (W ^T W) ⁺ is W Positive ^{-valued elements in TW; (W T W} ) ^- are negative-valued elements in W TW ^.

按如下步骤进行：Further, in S3, the respective initial estimated spectrums of the sound signals S ¹ , S ² ,..., ^Sn are obtained according to X

Proceed as follows:

S31. The respective main frequency bands of the sound signals S ¹ , S ² ,...,S ⁿ are f ₁ , f ₂ ,..., f _n ;

S32. Use the part of X corresponding to the frequency bands f ₁ , f ₂ ,..., f _n as the respective initial estimated spectrums of the sound signals S ¹ , S ² ,..., ^Sn

分别进行半非负矩阵分解，得到对应的特征矩阵

和系数矩阵

按如下步骤进行：Further, S4 pairs

Perform semi-non-negative matrix decomposition respectively to get the corresponding eigenmatrix

and coefficient matrix

Proceed as follows:

S41. Construct the objective function Γ ⁱ (i=1,2,...,n) of semi-nonnegative matrix decomposition

其所有元素的值为(0,1)之间的随机数；S42, initialization coefficient matrix

The value of all its elements is a random number between (0,1);

的初始值为S43. Calculate the feature matrix

The initial value is

和系数矩阵

交替迭代更新：先迭代更新一次

然后迭代更新一次

如此循环往复的先后迭代更新

和

利用公式

迭代更新特征矩阵

中的元素，利用公式

迭代更新系数矩阵

中的元素；S44, the feature matrix

and coefficient matrix

Alternate iterative update: first iterative update once

Then iteratively update once

Iterative update in this way

and

Use the formula

Iteratively update the feature matrix

elements in , using the formula

Iteratively update the coefficient matrix

elements in;

设定最大迭代次数

每次迭代更新完成后计算目标函数Γⁱ的值，当目标函数Γⁱ的值小于

或者迭代次数达到最大迭代次数

时，则停止迭代，得到最终的特征矩阵

和系数矩阵

S45. Set the minimum value of the objective function Γ ⁱ (i=1,2,...,n) of the semi-nonnegative matrix decomposition

Set the maximum number of iterations

Calculate the value of the objective function Γ ⁱ after each iteration update is completed, when the value of the objective function Γ ⁱ is less than

Or the number of iterations reaches the maximum number of iterations

When , stop the iteration and get the final feature matrix

and coefficient matrix

表示矩阵的Frobenius范数；

表示初始估计频谱

表示特征矩阵表示系数矩阵

的转置；

为

的逆矩阵；

为

的转置；

为

的转置；

为

中的正值元素；

为

中的负值元素；

为

中的正值元素；

为

中的负值元素。In formulas (5), (6), (7) and (8),

represents the Frobenius norm of the matrix;

represents the initial estimated spectrum

Represents the feature matrix Represents the coefficient matrix

transpose of ;

for

The inverse matrix of ;

for

transpose of ;

for

transpose of ;

for

positive-valued elements in ;

for

Negative elements in ;

for

positive-valued elements in ;

for

Negative elements in .

获得声音信号S¹,S²,…,Sⁿ各自的频谱X¹,X²,…,Xⁿ，按如下步骤进行：Further, S5 is based on X, W, H, and

To obtain the respective frequency spectra X ¹ , X ² ,..., X ⁿ of the sound signals S ¹ , S ² ,...,S ⁿ , follow the steps below:

表示系数矩阵

是维度为M的行向量；S51, H=[h ₁ ; h ₂ ;...;h _c ], h _k (k=1, 2,..., c) is a row vector of dimension M, which is represented by

Represents the coefficient matrix

is a row vector of dimension M;

计算

与h_k的相关系数

因此可以计算出

的每一行与h_k的相关系数

然后选出

中的最大值，记为最大相关系数

S52. According to the formula

calculate

Correlation coefficient with h _k

So it can be calculated

The correlation coefficient of each row with h _k

then choose

The maximum value in , denoted as the maximum correlation coefficient

的每一行与H的每一行的最大相关系数，记为

S53, according to step S52, calculate

The maximum correlation coefficient between each row of H and each row of H, denoted as

的每一行与H的每一行的最大相关系数，记为Q＝[q¹；q²；…；qⁿ]，qⁱ(i＝1,2,…,n)是维度为c的行向量，Q是一个n行c列的矩阵；S54, according to step S53, calculate respectively

The maximum correlation coefficient between each row of H and each row of H is denoted as Q=[q ¹ ; q ² ;...;q ⁿ ], q ⁱ (i=1,2,...,n) is a row vector of dimension c , Q is a matrix with n rows and c columns;

S55. The characteristic matrices of the respective frequency spectra X ¹ , X ² ,..., X ⁿ of the sound signals S ¹ , S ² ,..., ^Sn are W ¹ , W ² ,..., W ⁿ , and the coefficient matrices are H ¹ , H ² ,…,H ⁿ ;

S56. If in the kth column (k=1,2,...,c) of Q, the ith row (i=1,2,...,n) has the largest value, then the kth row of the coefficient matrix H is h _k is assigned to H ⁱ , and the k- ^th column of the feature matrix W=[w ₁ , w ₂ , . . . , _wn ], that is, w _k is assigned to Wi ;

S57, calculate the maximum value of each column in Q, and execute according to step S56, thereby obtaining characteristic matrices W ¹ , W ² ,...,W ⁿ and coefficient matrices H ¹ ,H ² ,...,H ⁿ ;

S58, according to the formula X ⁱ =W ⁱ H ^iT (i=1,2,...,n) (10), calculate and obtain the respective frequency spectra X ¹ , X ² ,..., of the sound signals S ¹ , S ² ,...,S ⁿ X ⁿ ;

In formulas (9) and (10), h _k ^T is the transposition of h _k ; H ^iT is the transposition of H ⁱ ; X ⁱ (i=1,2,...,n) represents the spectrum X ¹ , X ² ,...,X ⁿ ; Wi ( ⁱ =1,2,...,n) represents the characteristic matrix W ¹ ,W ² ,...,W ⁿ ;H ⁱ (i=1,2,...,n) represents the coefficient matrix H ¹ , H ² ,…,H ⁿ .

Further, in S6, according to the Fourier transform result F and the frequency spectrum X ¹ , X ² ,...,X ⁿ , the respective Fourier transform results F ¹ , F ² ,...,F of the sound signals S ¹ , S ² ,...,S ⁿ are obtained ⁿ , proceed as follows:

是p行q列矩阵，初始化Fⁱ为零矩阵； ^S61 . Use ^{F i} ( ^{i = 1} , ² , .

is a matrix with p rows and q columns, and initializes F ⁱ as a zero matrix;

是p行q列的矩阵；S62. F ^{= {} F _rk } _p×q is a matrix with p rows and q columns, and X ⁱ (i=1, ² , . X ¹ , X ² ,...,X ⁿ ,

is a matrix with p rows and q columns;

S63. Compare the sizes of the elements in the rth row (r=1, 2,...,p) of the kth (k=1, 2,...,q) column of each of X ¹ , X ² ,..., X ⁿ , if X ⁱ (i=1,2,...,n) where the element in the rth row and the kth column is the largest, then

即获得声音信号S¹,S²,…,Sⁿ各自的傅立叶变换结果F¹,F²,…,Fⁿ。S64. Execute according to step S63, traverse all elements in X ¹ , X ² ,..., X ⁿ , to obtain

That ^is , the Fourier transform results F ¹ , F ² , . . . , F ⁿ of the sound signals S ¹ , S ² , .

The beneficial effects of the present invention are:

The present invention can be used to separate single-channel mixed sound signals which are mixed from source sound signals that overlap in frequency domain and are not necessarily independent of each other.

Description of drawings

In order to illustrate the technical solutions in the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings used in the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained from these drawings without creative effort.

Fig. 1 is the working flow chart of a kind of sound signal separation method based on semi-non-negative matrix decomposition of the present invention;

Fig. 2 is the original heart sound signal diagram of the present invention;

Fig. 3 is the original lung sound signal diagram of the present invention;

Fig. 4 is the mixed signal diagram of original heart sound signal and original lung sound signal of the present invention;

FIG. 5 is a comparison diagram of the separated signal of the present invention and the original signal.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be further clearly and completely described below with reference to the embodiments of the present invention. It should be noted that the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Example

As shown in Figure 1, the present invention provides a method for separating sound signals based on semi-non-negative matrix decomposition, comprising the following steps:

S1. The single-channel mixed sound signal S is formed by mixing several independent sound signals S ¹ , S ² , ..., ^Sn , calculate the Fourier transform result F of S, and calculate the spectrum X according to F;

S2. Perform semi-non-negative matrix decomposition on X to obtain feature matrix W and coefficient matrix H;

S3. Obtain the respective initial estimated spectrums of the sound signals S ¹ , S ² , ..., ^Sn according to X

分别进行半非负矩阵分解，得到对应的特征矩阵

和系数矩阵

S4, yes

Perform semi-non-negative matrix decomposition respectively to get the corresponding eigenmatrix

and coefficient matrix

获得声音信号S¹,S²,…,Sⁿ各自的频谱X¹,X²,…,Xⁿ；S5. According to X, W, H, and

Obtain the respective frequency spectra X ¹ , X ² ,..., X ⁿ of the sound signals S ¹ , S ² ,...,S ⁿ ;

S6. According to the Fourier transform result F and the frequency spectrum X ¹ , X ² ,...,X ⁿ , obtain the respective Fourier transform results F ¹ , F ² ,..., F ⁿ of the sound signals S ¹ , S ² ,..., ^Sn ;

^S7 . ^Perform inverse Fourier transform ^{on F 1} , F ² , . ¹ , S ² ,…,S ⁿ .

In this embodiment, the single-channel mixed sound signal in S1 means that the mixed sound signal is collected by only one sound collector.

In this embodiment, the single-channel mixed sound signal S in S1 is formed by mixing a plurality of independent sound signals S ¹ , S ² , . . . , Sn , where the value of ⁿ is generally 2 or 3.

In this embodiment, the semi-non-negative matrix decomposition is performed on X in S2 to obtain the feature matrix W and the coefficient matrix H, and the steps are as follows:

S21. Construct the objective function Γ of the semi-nonnegative matrix factorization

S22. Initialize the coefficient matrix H, and the values of all its elements are random numbers between (0, 1);

S23. Calculate the initial value of the feature matrix W as

W=XH(H ^T H) ^-1 (2)

迭代更新系数矩阵H中的元素；S24, iteratively update the feature matrix W and the coefficient matrix H alternately: first iteratively update W once, and then iteratively update H once, so that W and H are iteratively updated successively in a cycle; using the formula W=XH(H ^T H) ^-1 ( 3) Iteratively update the elements in the feature matrix W, using the formula

Iteratively update the elements in the coefficient matrix H;

S25. Set the minimum value Γ _min of the objective function Γ of the semi-nonnegative matrix decomposition, set the maximum number of iterations E _max , and calculate the value of the objective function Γ after each iteration update is completed. When the value of the objective function Γ is less than Γ _min or When the number of iterations reaches the maximum number of iterations E _max , the iteration is stopped, and the final feature matrix W and coefficient matrix H are obtained.

表示矩阵的Frobenius范数；X为频谱；W为特征矩阵；H为系数矩阵；H^T为H的转置；(H^TH)^-1为H^TH的逆矩阵；X^T为X的转置；W^T为W的转置；(X^TW)⁺为X^TW中的正值元素；(X^TW)^-为X^TW中的负值元素；(W^TW)⁺为W^TW中的正值元素；(W^TW)^-为W^TW中的负值元素。In formulas (1), (2), (3) and (4),

Represents the Frobenius norm of the matrix; ^X is the frequency spectrum; W is the characteristic matrix; H is the coefficient matrix; H ^T is the transpose of H; (H ^T H) ^-1 is the inverse matrix of H ^T H; Set; W ^T is the transpose of W; (X ^T W) ⁺ is the positive value element in X ^T W; (X ^T W) ^- is the negative value element in X ^T W; (W ^T W) ⁺ is W Positive ^{-valued elements in TW; (W T W} ) ^- are negative-valued elements in W TW ^.

按如下步骤进行：In this embodiment, in S3, the respective initial estimated spectrums of the sound signals S ¹ , S ² , ..., ^Sn are obtained according to X

Proceed as follows:

S31. The respective main frequency bands of the sound signals S ¹ , S ² ,...,S ⁿ are f ₁ , f ₂ ,..., f _n ;

S32. Use the part of X corresponding to the frequency bands f ₁ , f ₂ ,..., f _n as the respective initial estimated spectrums of the sound signals S ¹ , S ² ,..., ^Sn

分别进行半非负矩阵分解，得到对应的特征矩阵

和系数矩阵

按如下步骤进行：In this embodiment, in S4, the

Perform semi-non-negative matrix decomposition respectively to get the corresponding eigenmatrix

and coefficient matrix

Proceed as follows:

S41. Construct the objective function Γ ⁱ (i=1,2,...,n) of semi-nonnegative matrix decomposition

其所有元素的值为(0,1)之间的随机数；S42, initialization coefficient matrix

The value of all its elements is a random number between (0,1);

的初始值为S43. Calculate the feature matrix

The initial value is

和系数矩阵

交替迭代更新：先迭代更新一次

然后迭代更新一次

如此循环往复的先后迭代更新

和

利用公式

迭代更新特征矩阵

中的元素，利用公式

迭代更新系数矩阵

中的元素；S44, the feature matrix

and coefficient matrix

Alternate iterative update: first iterative update once

Then iteratively update once

Iterative update in this way

and

Use the formula

Iteratively update the feature matrix

elements in , using the formula

Iteratively update the coefficient matrix

elements in;

设定最大迭代次数

每次迭代更新完成后计算目标函数Γⁱ的值，当目标函数Γⁱ的值小于

或者迭代次数达到最大迭代次数

时，则停止迭代，得到最终的特征矩阵

和系数矩阵

S45. Set the minimum value of the objective function Γ ⁱ (i=1,2,...,n) of the semi-nonnegative matrix decomposition

Set the maximum number of iterations

Calculate the value of the objective function Γ ⁱ after each iteration update is completed, when the value of the objective function Γ ⁱ is less than

Or the number of iterations reaches the maximum number of iterations

When , stop the iteration and get the final feature matrix

and coefficient matrix

表示矩阵的Frobenius范数；

表示初始估计频谱

表示特征矩阵

表示系数矩阵

为

的转置；

为

的逆矩阵；

为

的转置；

为

的转置；

为

中的正值元素；

为

中的负值元素；

为

中的正值元素；

为

中的负值元素。In formulas (5), (6), (7) and (8),

represents the Frobenius norm of the matrix;

represents the initial estimated spectrum

Represents the feature matrix

Represents the coefficient matrix

for

transpose of ;

for

The inverse matrix of ;

for

transpose of ;

for

transpose of ;

for

positive-valued elements in ;

for

Negative elements in ;

for

positive-valued elements in ;

for

Negative elements in .

获得声音信号S¹,S²,…,Sⁿ各自的频谱X¹,X²,…,Xⁿ，按如下步骤进行：In this embodiment, according to X, W, H, and

To obtain the respective frequency spectra X ¹ , X ² ,..., X ⁿ of the sound signals S ¹ , S ² ,...,S ⁿ , follow the steps below:

表示系数矩阵

是维度为M的行向量；S51, H=[h ₁ ; h ₂ ;...;h _c ], h _k (k=1, 2,..., c) is a row vector of dimension M, which is represented by

Represents the coefficient matrix

is a row vector of dimension M;

计算

与h_k的相关系数

因此可以计算出

的每一行与h_k的相关系数

然后选出

中的最大值，记为最大相关系数

S52. According to the formula

calculate

Correlation coefficient with h _k

So it can be calculated

The correlation coefficient of each row with h _k

then choose

The maximum value in , denoted as the maximum correlation coefficient

的每一行与H的每一行的最大相关系数，记为

S53, according to step S52, calculate

The maximum correlation coefficient between each row of H and each row of H, denoted as

的每一行与H的每一行的最大相关系数，记为Q＝[q¹；q²；…；qⁿ]，qⁱ(i＝1,2,…,n)是维度为c的行向量，Q是一个n行c列的矩阵；S54, according to step S53, calculate respectively

The maximum correlation coefficient between each row of H and each row of H is denoted as Q=[q ¹ ; q ² ;...;q ⁿ ], q ⁱ (i=1,2,...,n) is a row vector of dimension c , Q is a matrix with n rows and c columns;

S55. The characteristic matrices of the respective frequency spectra X ¹ , X ² ,..., X ⁿ of the sound signals S ¹ , S ² ,..., ^Sn are W ¹ , W ² ,..., W ⁿ , and the coefficient matrices are H ¹ , H ² ,…,H ⁿ ;

S56. If in the kth column (k=1,2,...,c) of Q, the ith row (i=1,2,...,n) has the largest value, then the kth row of the coefficient matrix H is h _k is assigned to H ⁱ , and the k- ^th column of the feature matrix W=[w ₁ , w ₂ , . . . , _wn ], that is, w _k is assigned to Wi ;

S57, calculate the maximum value of each column in Q, and execute according to step S56, thereby obtaining characteristic matrices W ¹ , W ² ,...,W ⁿ and coefficient matrices H ¹ ,H ² ,...,H ⁿ ;

S58, according to the formula X ⁱ =W ⁱ H ^iT (i=1,2,...,n) (10), calculate and obtain the respective frequency spectra X ¹ , X ² ,..., of the sound signals S ¹ , S ² ,...,S ⁿ X ⁿ .

In formulas (9) and (10), h _k ^T is the transposition of h _k ; H ^iT is the transposition of H ⁱ ; X ⁱ (i=1,2,...,n) represents the spectrum X ¹ , X ² ,...,X ⁿ ; Wi ( ⁱ =1,2,...,n) represents the characteristic matrix W ¹ ,W ² ,...,W ⁿ ;H ⁱ (i=1,2,...,n) represents the coefficient matrix H ¹ , H ² ,…,H ⁿ .

In this embodiment, in S6, according to the Fourier transform result F and the frequency spectrum X ¹ , X ² ,...,X ⁿ , the respective Fourier transform results F ¹ , F ² of the sound signals S ¹ , S ² ,..., ^Sn are obtained, …,F ⁿ , proceed as follows:

是p行q列矩阵，初始化Fⁱ为零矩阵(矩阵中的元素的值全为0)； ^S61 . Use ^{F i} ( ^{i = 1} , ² , .

is a matrix of p rows and q columns, and initializes F ⁱ to a zero matrix (the values of the elements in the matrix are all 0);

是p行q列的矩阵；S62. F ^{= {} F _rk } _p×q is a matrix with p rows and q columns, and X ⁱ (i=1, ² , . X ¹ , X ² ,...,X ⁿ ,

is a matrix with p rows and q columns;

S63. Compare the sizes of the elements in the rth row (r=1, 2,...,p) of the kth (k=1, 2,...,q) column of each of X ¹ , X ² ,..., X ⁿ , if X ⁱ (i=1,2,...,n) where the element in the rth row and the kth column is the largest, then

即获得声音信号S¹,S²,…,Sⁿ各自的傅立叶变换结果F¹,F²,…,Fⁿ。S64. Execute according to step S63, traverse all elements in X ¹ , X ² ,..., X ⁿ , to obtain

That ^is , the Fourier transform results F ¹ , F ² , . . . , F ⁿ of the sound signals S ¹ , S ² , .

In this embodiment, the effect of the present invention can be further illustrated by the following experiments:

1) Experimental data

The experimental data comes from a piece of heart sound signal and a piece of lung sound signal published on the Internet. The sampling frequency of the signal is 2000Hz, and the duration of the signal is 5 seconds. Mix the two to get a single-channel mixed sound signal. The main frequency band of the heart sound signal is known to be ≤100Hz, and the main frequency band of the lung sound signal is known to be ≥300Hz. The original heart sound signal is shown in Figure 2, the original lung sound signal is shown in Figure 3, and the mixed signal of the original heart sound signal and the original lung sound signal is shown in Figure 4.

2) Experimental conditions

也设为10^-4，最大迭代次数E_max设为500次，最大迭代次数

也设为500次。The experimental program of the present invention is written using Matlab9.2.0 software. The minimum value Γ _min of the objective function Γ is set to 10 ^-4 , and the minimum value of the objective function Γ ⁱ (i=1,2,...,n)

Also set to 10 ^-4 , the maximum number of iterations E _max is set to 500 times, the maximum number of iterations

Also set to 500 times.

3) Experimental results

计算分离出的信号与原信号的归一化均方误差NMSE。于公式(11)中，s表示原始信号(在本发明的实验中，s为心音信号或肺音信号)，

表示分离出的信号(在本发明的实验中，

为分离出的心音信号或肺音信号)。分离出的信号与原始信号对比如图5所示，归一化均方误差NMSE结果如表1所示。The normalized mean squared error NMSE (Normalized Mean Squared Error) between the separated signal and the original signal is used as the evaluation index of the separation effect of the present invention, and the smaller the index, the better. The mixed sound signal is separated by the present invention, and then according to the formula

Calculate the normalized mean square error NMSE between the separated signal and the original signal. In formula (11), s represents the original signal (in the experiment of the present invention, s is the heart sound signal or the lung sound signal),

represents the separated signal (in the experiments of the present invention,

is the isolated heart sound signal or lung sound signal). The comparison between the separated signal and the original signal is shown in Figure 5, and the normalized mean square error NMSE results are shown in Table 1.

Table 1

The above-mentioned embodiment only represents an embodiment of the present invention, and its description is relatively specific and detailed, but it should not be construed as a limitation on the patent scope of the present invention. It should be pointed out that for those skilled in the art, without departing from the concept of the present invention, several modifications and improvements can be made, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention should be subject to the appended claims.

Claims (8)

1. a sound signal separation method based on semi-non-negative matrix decomposition, is characterized in that, this method comprises the following steps: S1. The single-channel mixed sound signal S is formed by mixing several independent sound signals S ¹ , S ² , ..., ^Sn , calculate the Fourier transform result F of S, and calculate the spectrum X according to F; S2. Perform semi-non-negative matrix decomposition on X to obtain feature matrix W and coefficient matrix H; S3. Obtain the respective initial estimated spectrums of the sound signals S ¹ , S ² , ..., ^Sn according to X

S4, yes

Perform semi-non-negative matrix decomposition respectively to get the corresponding eigenmatrix

and coefficient matrix

S5. According to X, W, H, and

Obtain the respective frequency spectra X ¹ , X ² ,..., X ⁿ of the sound signals S ¹ , S ² ,...,S ⁿ ; S6. According to the Fourier transform result F and the frequency spectrum X ¹ , X ² ,...,X ⁿ , obtain the respective Fourier transform results F ¹ , F ² ,..., F ⁿ of the sound signals S ¹ , S ² ,..., ^Sn ; ^S7 . ^Perform inverse Fourier transform ^{on F 1} , F ² , . ¹ , S ² ,…,S ⁿ . 2 . The sound signal separation method based on semi-non-negative matrix decomposition according to claim 1 , wherein the single-channel mixed sound signal in S1 means that the mixed sound signal is collected by only one sound collector. 3 . 3. The sound signal separation method based on semi-non-negative matrix decomposition according to claim 1, wherein the single-channel mixed sound signal S described in S1 is composed of several independent sound signals S ¹ , S ² , . . . S A mixture of ⁿ , where the value of n is 2 or 3. 4. the sound signal separation method based on semi-non-negative matrix decomposition according to claim 1, is characterized in that, in S2, X is carried out semi-non-negative matrix decomposition, obtain characteristic matrix W and coefficient matrix H, carry out according to the following steps: S21. Construct the objective function Γ of the semi-nonnegative matrix factorization

S22. Initialize the coefficient matrix H, and the values of all its elements are random numbers between (0, 1); S23. Calculate the initial value of the feature matrix W as W=XH(H ^T H) ^-1 (2) S24, iteratively update the feature matrix W and the coefficient matrix H alternately: first iteratively update W once, and then iteratively update H once, so that W and H are iteratively updated successively in a cycle; using the formula W=XH(H ^T H) ^-1 ( 3) Iteratively update the elements in the feature matrix W, using the formula

Iteratively update the elements in the coefficient matrix H; S25. Set the minimum value Γ _min of the objective function Γ of the semi-nonnegative matrix decomposition, set the maximum number of iterations E _max , and calculate the value of the objective function Γ after each iteration update is completed. When the value of the objective function Γ is less than Γ _min or When the number of iterations reaches the maximum number of iterations E _max , the iteration is stopped, and the final feature matrix W and coefficient matrix H are obtained; In formulas (1), (2), (3) and (4),

Represents the Frobenius norm of the matrix; ^X is the frequency spectrum; W is the characteristic matrix; H is the coefficient matrix; H ^T is the transpose of H; (H ^T H) ^-1 is the inverse matrix of H ^T H; Set; W ^T is the transpose of W; (X ^T W) ⁺ is the positive value element in X ^T W; (X ^T W) ^- is the negative value element in X ^T W; (W ^T W) ⁺ is W Positive ^{-valued elements in TW; (W T W} ) ^- are negative-valued elements in W TW ^. 5. The sound signal separation method based on semi-non-negative matrix decomposition according to claim 1, wherein in S3, the respective initial estimated spectrums of the sound signals S ¹ , S ² , ..., ^Sn are obtained according to X in S3

Proceed as follows: S31. The respective main frequency bands of the sound signals S ¹ , S ² ,...,S ⁿ are f ₁ , f ₂ ,..., f _n ; S32. Use the part of X corresponding to the frequency bands f ₁ , f ₂ ,..., f _n as the respective initial estimated spectrums of the sound signals S ¹ , S ² ,..., ^Sn

6. the sound signal separation method based on semi-non-negative matrix decomposition according to claim 1, is characterized in that, in S4, to

Perform semi-non-negative matrix decomposition respectively to get the corresponding eigenmatrix

and coefficient matrix

Proceed as follows: S41. Construct the objective function Γ ⁱ (i=1,2,...,n) of semi-nonnegative matrix decomposition

S42, initialization coefficient matrix

The value of all its elements is a random number between (0,1); S43. Calculate the feature matrix

The initial value is

S44, the feature matrix

and coefficient matrix

Alternate iterative update: first iterative update once

Then iteratively update once

Iterative update in this way

and

Use the formula

Iteratively update the feature matrix

elements in , using the formula

Iteratively update the coefficient matrix

elements in; S45. Set the minimum value of the objective function Γ ⁱ (i=1,2,...,n) of the semi-nonnegative matrix decomposition

Set the maximum number of iterations

Calculate the value of the objective function Γ ⁱ after each iteration update is completed, when the value of the objective function Γ ⁱ is less than

Or the number of iterations reaches the maximum number of iterations

When , stop the iteration and get the final feature matrix

and coefficient matrix

In formulas (5), (6), (7) and (8),

represents the Frobenius norm of the matrix;

represents the initial estimated spectrum

Represents the feature matrix

Represents the coefficient matrix

for

transpose of ;

for

The inverse matrix of ;

for

transpose of ;

for

transpose of ;

for

positive-valued elements in ;

for

Negative elements in ;

for

positive-valued elements in ;

for

Negative elements in . 7. the sound signal separation method based on semi-non-negative matrix decomposition according to claim 1, is characterized in that, according to X, W, H in S5, and

To obtain the respective frequency spectra X ¹ , X ² ,..., X ⁿ of the sound signals S ¹ , S ² ,...,S ⁿ , follow the steps below: S51, H=[h ₁ ; h ₂ ;...;h _c ], h _k (k=1, 2,..., c) is a row vector of dimension M, which is represented by

Represents the coefficient matrix

is a row vector of dimension M; S52. According to the formula

calculate

Correlation coefficient with h _k

So it can be calculated

The correlation coefficient of each row with h _k

then choose

The maximum value in , denoted as the maximum correlation coefficient

S53, according to step S52, calculate

The maximum correlation coefficient between each row of H and each row of H, denoted as

S54, according to step S53, calculate respectively

The maximum correlation coefficient between each row of H and each row of H is denoted as Q=[q ¹ ; q ² ;...;q ⁿ ], q ⁱ (i=1,2,...,n) is a row vector of dimension c , Q is a matrix with n rows and c columns; S55. The characteristic matrices of the respective frequency spectra X ¹ , X ² ,..., X ⁿ of the sound signals S ¹ , S ² ,..., ^Sn are W ¹ , W ² ,..., W ⁿ , and the coefficient matrices are H ¹ , H ² ,…,H ⁿ ; S56. If in the kth column (k=1,2,...,c) of Q, the ith row (i=1,2,...,n) has the largest value, then the kth row of the coefficient matrix H is h _k is assigned to H ⁱ , and the k- ^th column of the feature matrix W=[w ₁ , w ₂ , . . . , _wn ], that is, w _k is assigned to Wi ; S57, calculate the maximum value of each column in Q, and execute according to step S56, thereby obtaining characteristic matrices W ¹ , W ² ,...,W ⁿ and coefficient matrices H ¹ ,H ² ,...,H ⁿ ; S58, according to the formula X ⁱ =W ⁱ H ^iT (i=1,2,...,n) (10) to obtain the respective frequency spectra X ¹ , X ² ,..., of the sound signals S ¹ , S ² ,...,S ⁿ X ⁿ ; In formulas (9) and (10), h _k ^T is the transposition of h _k ; H ^iT is the transposition of H ⁱ ; X ⁱ (i=1,2,...,n) represents the spectrum X ¹ , X ² ,...,X ⁿ ; Wi ( ⁱ =1,2,...,n) represents the characteristic matrix W ¹ ,W ² ,...,W ⁿ ;H ⁱ (i=1,2,...,n) represents the coefficient matrix H ¹ , H ² ,…,H ⁿ . 8. The sound signal separation method based on semi-non-negative matrix decomposition according to claim 1, wherein in S6, according to Fourier transform result F and frequency spectrum X ¹ , X ² ,..., X ⁿ , obtain sound signal S ¹ ,S ² ,...,S ⁿ The Fourier transform results F ¹ ,F ² ,...,F ⁿ of each are carried out according to the following steps: ^S61 . Use ^{F i} ( ^{i = 1} , ² , .

is a matrix with p rows and q columns, and initializes F ⁱ as a zero matrix; S62. F ^{= {} F _rk } _p×q is a matrix with p rows and q columns, and X ⁱ (i=1, ² , . X ¹ , X ² ,...,X ⁿ ,

is a matrix with p rows and q columns; S63. Compare the sizes of the elements in the rth row (r=1, 2,...,p) of the kth (k=1, 2,...,q) column of each of X ¹ , X ² ,..., X ⁿ , if X ⁱ (i=1,2,...,n) where the element in the rth row and the kth column is the largest, then

S64. Execute according to step S63, traverse all elements in X ¹ , X ² ,..., X ⁿ , to obtain

That ^is , the Fourier transform results F ¹ , F ² , . . . , F ⁿ of the sound signals S ¹ , S ² , .

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