Underdetermined blind source separation method based on improved single source point detection

Abstract

The invention discloses an underdetermined blind source separation method based on improved single source point detection, and the method comprises the steps: firstly, carrying out the initial single source point extraction of a mixed signal through employing the cosine angle criterion of a real part and an imaginary part of a time-frequency matrix column vector; then, abnormal points are removed according to whether the linear relation between the single source points and the abnormal points exists or not, the influence of the abnormal points on single source point detection is reduced, and therefore the estimation precision of a hybrid matrix is improved; then, clustering is carried out on the obtained single source points by using a K-means algorithm, so that an estimated hybrid matrix is obtained; and finally, recovering a source signal by using a least square method. The method provided by the invention not only considers the absolute direction of the real part and the imaginary part in the single source point, but also considers the linear relation between different single source points to remove the abnormal points, so that the estimation precision of the hybrid matrix can be improved, the noise immunity of the method is enhanced, and finally, a high-quality recovery signal is obtained.

Description

Technical Field

[0001] The invention belongs to the field of signal and information processing, and in particular relates to an underdetermined blind source separation method based on improved single source point detection. Background Art

[0002] Blind source separation is a signal processing technique that aims to separate source signals from multiple mixed signals without prior information about these source signals. Blind source separation is a typical source separation method, which has been widely used in different fields such as speech signal processing, biomedical signal processing, and wireless communication systems. In actual engineering environments, due to cost constraints and environmental complexity, the number of sensors is often limited, and the number of observation channels is generally less than the number of source signals, which is an underdetermined blind source separation model. Therefore, it is more practical to deal with the underdetermined blind source separation problem.

[0003] At present, sparse component analysis is the mainstream technology for dealing with underdetermined blind source separation problems. Sparse component analysis divides the underdetermined blind source separation problem into two steps. The first step is to estimate the mixing matrix, and the second step is to restore the source signal based on the estimated mixing matrix. The method based on sparse component analysis requires that the signal is sparse, that is, the source signal has only a few non-zero values ​​in the time domain or other domains. If there is only one source signal that dominates the mixed signal at a certain moment, and the sampling values ​​of other source signals are close to zero, the signal point obtained at that moment is regarded as a single source point. The single source point is the key to enhancing the sparsity of the mixed signal, and the accuracy of the single source point detection algorithm will affect the accuracy of the mixing matrix estimation. Among them, the quality of source signal recovery depends on the accuracy of the mixing matrix estimation, and the accuracy of the single source point detection will directly affect the accuracy of the mixing matrix estimation.

[0004] At present, most single source point detection methods are one-time screening. Among them, the method that only considers each time-frequency point itself has high screening efficiency and good overall detection effect in a high signal-to-noise ratio environment. It is the current mainstream single source point detection method, especially the cosine angle single source point detection method. However, these methods are prone to misdetecting outliers, which reduces the accuracy of the mixed matrix estimation. In the face of noise interference, the effectiveness of these methods will be seriously reduced. These outliers are generated by false detection, which will directly affect the clustering results, reduce the estimation accuracy of the mixed matrix, and thus limit the quality of source signal recovery. In the face of noise interference, the method of using the linear relationship between single source points to screen single source points often has better noise resistance. The method that only considers each time-frequency point itself cannot effectively remove outliers and does not use the linear relationship between different single source points. Therefore, the estimated mixed matrix is ​​not accurate, has poor noise resistance, and the separation quality of the source signal is not high enough. Summary of the invention

[0005] The purpose of the present invention is to provide an underdetermined blind source separation method based on improved single source point detection, to improve the accuracy of the cosine angle single source point detection algorithm, and then to improve the accuracy of the mixing matrix estimation, so as to obtain a higher quality separation signal.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] An underdetermined blind source separation method based on improved single source point detection comprises the following steps:

[0008] S1: Perform short-time Fourier transform on the time-domain mixed signal received by each microphone to obtain a mixing matrix in the time-frequency domain;

[0009] S2: Integrate the mixing matrix in the time-frequency domain into a one-dimensional row vector, and integrate the row vectors of the received mixed signal into a matrix S, where each row vector of the matrix S represents an observed signal;

[0010] S3: Use the cosine angle single source point detection method to detect the angle difference between the absolute direction of the real part and the imaginary part of each column vector in S. The column vector below the threshold Δθ is the preliminary single source point;

[0011] S4: remove low-energy points and normalize the preliminary single source points detected in S3;

[0012] S5: Perform linear relationship detection on the data processed by S4, and judge whether two single source points belong to the same source signal by comparing the direction angles of two normalized column vectors. Column vectors below the threshold ε are regarded as single source points, and those above the threshold ε are regarded as abnormal points. Then, the abnormal points in the preliminary single source points are removed to obtain the final single source points.

[0013] S6: Use the K-means algorithm to cluster the final single source points to obtain cluster centers. Each cluster center corresponds to the column vector of the mixing matrix one by one, and finally the estimation of the mixing matrix is ​​realized;

[0014] S7: Using the estimated mixing matrix and the mixed signal in the time-frequency domain, each source signal is recovered by the least square method, and finally the source signal in the time domain is obtained by inverse short-time Fourier transform.

[0015] Furthermore, in step S1, the time domain mixed signal x received by each microphone is i (t) is to use x(t) = [x1(t), x2(t), …, x m (t)] T represents the m-dimensional mixed signal received by m microphones, x i (t) is the mixed signal received by the i-th microphone at time t, TRepresents the transpose operation; for the mixed signal x i (t) Performing short-time Fourier transform can obtain the time-frequency domain complex matrix X of the mixed signal i , where i = 1, 2, ..., m, where X i represents a complex matrix with f rows and t columns.

[0016] Furthermore, in step S2, the complex matrix of each microphone obtained in step S1 is vectorized. Specifically, the time-frequency domain complex matrix X i The row vectors of the first row are connected, and finally a one-dimensional row vector s is obtained. i (k), and then combine the row vectors obtained from each microphone into a matrix to obtain S = [s1(k), s2(k), …, s m (k)] T , where s m (k) represents the time-frequency domain row vector of the mixed signal received by the m-th microphone, and each row vector of the matrix S represents an observation signal.

[0017] Furthermore, in step S3, the angle difference between the absolute directions of the real and imaginary parts of each column vector of the matrix S is calculated by the cosine angle single source point detection method to screen the preliminary single source point. The cosine angle single source point detection method is expressed as:

[0018]

[0019] Where k = 1, 2, ..., K, K represents the number of column vectors of the matrix S, Re[] represents the real part of the frequency domain vector, Im[] represents the imaginary part of the frequency domain vector, · represents the absolute value, Δθ represents the screening threshold; through the angle difference of each column vector in the matrix S, the column vectors above the threshold Δθ are removed, and the column vectors below the threshold Δθ are the preliminary single source points.

[0020] Furthermore, in step S4, the preliminary single source points are subjected to low energy point removal and normalization processing. Low energy points are time-frequency points with low energy. Low energy points will affect the estimation of the mixing matrix, so they need to be removed. The screening threshold of low energy points is Wherein, N represents the total number of preliminary single source points, and ρ is a parameter, which is generally greater than or equal to 0.1. The present invention can remove low-energy points from the preliminary single source points by using ρ times the average energy as a threshold.

[0021] Furthermore, in step S4, the normalization process can be expressed as:

[0022]

[0023] Among them, s1(p) represents the real part value of the first mixed signal in S(p). According to this formula, the time-frequency points can be normalized and symmetric.

[0024] Furthermore, in step S5, a linear relationship detection is performed on the data after low-energy point removal and normalization processing, and the direction angles of the two normalized column vectors are compared to determine whether the two single source points belong to the same source signal. The detection method is expressed as:

[0025] 1-S(i),S(j)<ε

[0026] Here, · represents the scalar product, and ε is the screening threshold. Column vectors below the threshold ε are considered as single source points, and column vectors above the threshold ε are considered as outliers. Then, outliers in the preliminary single source points are removed to obtain the final single source points.

[0027] The present invention discloses an underdetermined blind source separation method based on improved single source point detection. This method not only has the advantage of high efficiency of cosine angle single source point detection, but also has the advantage of good noise resistance of linear single source point detection method. This method first uses the cosine angle single source point method to screen out most of the non-single source points, and then performs low-energy point removal and normalization operations to further reduce the time-frequency points that need to be processed, and symmetrizes the time-frequency point mapping, thereby improving the processing efficiency of removing abnormal points using the linear single source point method. Through experimental verification, the mixing matrix estimated by this method is not only more accurate, but also more robust, the time complexity of the algorithm is lower, the quality of source signal recovery is higher, and the accuracy of the single source point detection method is effectively improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flow chart of an underdetermined blind source separation method based on improved single source point detection in an embodiment;

[0029] Figure 2 It is a preliminary scatter plot of a single source point in the embodiment;

[0030] Figure 3 It is a scatter plot of a single source point after removing the outliers in the embodiment;

[0031] Figure 4 Result diagram of mixed matrix estimation under different signal-to-noise ratio environments in the embodiment;

[0032] Figure 5 It is the source signal waveform diagram in the embodiment;

[0033] Figure 6 4 is a waveform diagram of the source signal restored in the embodiment. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in combination with the embodiments and drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by the technicians in this field without making creative work are within the scope of protection of the present invention.

[0035] Example:

[0036] An underdetermined blind source separation method based on improved single source point detection, the flow chart is as follows Figure 1 shown.

[0037] In this embodiment, three sounds representing environmental information, namely, alarm sound, car horn sound and baby crying sound, are selected as source signals. The method of the present invention is applicable to both speech signals and non-speech signals that meet the sparsity requirement.

[0038] The mathematical model of underdetermined blind source separation is a linear instantaneous mixture model. Based on this, ignoring the noise signal, the mathematical model of underdetermined blind source separation can be expressed as:

[0039]

[0040] Among them, x(t) represents the observed signal, A represents the mixing matrix, y(t) represents the source signal, m represents the number of microphones, and n represents the number of source signals.

[0041] The observed signal has good sparsity in the time-frequency domain. It is necessary to transform the mixed signal in the time domain into a mixed signal in the time-frequency domain through short-time Fourier transform, and then screen the mixed signal in the time-frequency domain for single source points; a single source point refers to a time-frequency point where only one source signal exists or only one source signal plays a major role. These single source points correspond to a column vector of the mixed signal in the time-frequency domain.

[0042] By performing a short-time Fourier transform on each observation signal, the observation signal in the time-frequency domain of each observation signal is obtained, and then the observation signal in the time-frequency domain of each observation signal is integrated into a row vector s i (k), and finally integrated into the matrix S = [s1(k), s2(k), …, s m (k)] T .

[0043] By calculating the angle difference Δθ between the absolute directions of the real and imaginary parts of each column vector of the matrix S, the column vectors with an angle difference smaller than a preset value are retained as preliminary single sources, where Δθ is a judgment threshold, and the angle difference is generally set to a small value. In this embodiment, the value of Δθ is 1°.

[0044] In this embodiment, the scatter diagram of the preliminary single source point detected by calculating the angle difference is as follows: Figure 2 As shown;

[0045] Then, the preliminary single source points are subjected to low-energy point removal and normalization operations;

[0046] The linear relationship detection is performed on the data after low-energy point removal and normalization. By comparing the direction angles of the two normalized column vectors, it is determined whether the two single source points belong to the same source signal. The normalized vector values ​​of the single source points of the same source are equivalent. Therefore, the column vectors below the threshold ε are regarded as single source points, and the column vectors above the threshold ε are regarded as abnormal points. Then, the abnormal points in the preliminary single source points are removed to obtain the final single source points, where ε is the judgment threshold, which is generally set to a small value. In this embodiment, the value of ε is set to 0.00001.

[0047] In this embodiment, the final scatter plot of the single source point is obtained after the outliers are removed, as shown in FIG. Figure 3 shown; contrast Figure 2 and Figure 3 It can be seen that the present invention effectively removes abnormal points such as deviation points and interference points, making the scatter plot distribution of the normalized single source points more compact.

[0048] After completing the single source point detection, the K-means algorithm is used for clustering to obtain the cluster center. Each cluster center corresponds one-to-one to the column vector of the mixing matrix, and finally the estimation of the mixing matrix is ​​realized.

[0049] In this embodiment, three-way acoustic signals are mixed by a mixing matrix A to obtain two-way observation signals, where the mixing matrix A is:

[0050]

[0051] In order to quantitatively evaluate the estimation of each column vector of the estimated mixing matrix, the deviation angle is used to measure the deviation value of the corresponding column vector of the original mixing matrix and the estimated mixing matrix. The formula of the deviation angle is as follows:

[0052]

[0053] Among them, a i represents the i-th column vector of the original mixing matrix A, Represents the i-th column vector of the estimated mixing matrix A. The smaller the value of the deviation angle, the more accurate the estimation of the mixing matrix column vector is.

[0054] In order to evaluate the accuracy of the mixing matrix estimation as a whole, the normalized mean square error (NMSE) is used as the evaluation criterion. The formula of NMSE is as follows:

[0055]

[0056] Where m and n represent the number of rows and columns of the mixing matrix, respectively. ij Represents the element of the i-th row and j-th column of the original mixing matrix A, a ij Represents the elements of the ith row and jth column of the estimated mixing matrix A. The smaller the value of NMSE, the higher the accuracy of the mixing matrix estimation.

[0057] The comparison of the accuracy of the mixed matrix estimated by the cosine angle single source point detection method and the present invention is shown in Table 1. It can be seen from the table that each column of the mixed matrix estimated by the method proposed in the present invention is improved compared with the cosine angle single source point detection method. The deviation angle of each column is increased by 14.20%, 30.93% and 80.55% respectively, and the deviation angle is increased by 57.23% on average, indicating that the proposed method can effectively remove outliers and improve the estimation accuracy of the mixed matrix. The NMSE is improved by 25.49%, indicating that the proposed method can obtain a more accurate estimated mixed matrix. The results of the deviation angle and NMSE can show the correctness and effectiveness of the proposed method.

[0058] Table 1 Comparison of estimated mixing matrix accuracy

[0059]

[0060] In this example, in order to test the anti-noise performance of the method proposed in the present invention, Gaussian white noise with different signal-to-noise ratios is added to the mixed signal, and the mixing matrix under each signal-to-noise ratio noise condition is estimated 20 times, and the average NMSE under each noise level is recorded. The experimental results are shown in Figure 4 As shown. Figure 4 It can also be seen that under each signal-to-noise ratio environment, the average NMSE of the method of the present invention is better than the cosine angle single source point detection method, which shows that the method of the present invention is better than the cosine angle single source point detection method in terms of noise resistance.

[0061] In this embodiment, the actual waveforms of the three source signals are as follows: Figure 5 As shown, the waveforms of the three source signals restored by the method proposed in the present invention are as follows Figure 6 As shown, through Figure 5 and Figure 6 By comparison, it can be found that the waveform of the source signal obtained by the method proposed in the present invention is very similar to the waveform of the actual signal, which shows that this embodiment has a high estimation accuracy.

Claims

1. An underdetermined blind source separation method based on improved single source point detection, characterized in that: The following steps are involved: S1: Perform short-time Fourier transform on the time-domain mixed signal received by each microphone to obtain a mixing matrix in the time-frequency domain; S2: Integrate the mixing matrix in the time-frequency domain into a one-dimensional row vector, and integrate the row vectors of the received mixed signal into a matrix S, where each row vector of the matrix S represents an observed signal; S3: Use the cosine angle single source point detection method to detect the angle difference between the absolute direction of the real part and the imaginary part of each column vector in S. The column vector below the threshold Δθ is the preliminary single source point; S4: remove low-energy points and normalize the preliminary single source points detected in S3; S5: Perform linear relationship detection on the data processed by S4, and judge whether two single source points belong to the same source signal by comparing the direction angles of two normalized column vectors. Column vectors below the threshold ε are regarded as single source points, and those above the threshold ε are regarded as abnormal points. Then, the abnormal points in the preliminary single source points are removed to obtain the final single source points. S6: Use the K-means algorithm to cluster the final single source points to obtain cluster centers. Each cluster center corresponds to the column vector of the mixing matrix one by one, and finally the estimation of the mixing matrix is ​​realized; S7: Using the estimated mixing matrix and the mixed signal in the time-frequency domain, each source signal is recovered by the least square method, and finally the source signal in the time domain is obtained by inverse short-time Fourier transform.

2. The underdetermined blind source separation method based on improved single source point detection according to claim 1, characterized in that: In step S1, the time domain mixed signal x received by each microphone is i The operation performed on (t) is to use x(t)=[x1(t),x2(t),…,x m (t)] T represents the m-dimensional mixed signal received by m microphones, x i (t) is the mixed signal received by the i-th microphone at time t, T Represents the transpose operation; for the mixed signal x i (t) Perform short-time Fourier transform to obtain the time-frequency domain complex matrix X of the mixed signal i , where i = 1, 2, ..., m, Where X i represents a complex matrix with f rows and t columns.

3. The underdetermined blind source separation method based on improved single source point detection according to claim 1, characterized in that: In step S2, the complex matrix of each microphone obtained in step S1 is vectorized. Specifically, the time-frequency domain complex matrix X i The row vectors of the first row are connected, and finally a one-dimensional row vector s is obtained. i (k), and then combine the row vectors obtained from each microphone into a matrix to obtain S = [s1(k), s2(k), …, s m (k)] T , where s m (k) represents the time-frequency domain row vector of the mixed signal received by the m-th microphone, and each row vector of the matrix S represents an observation signal.

4. The underdetermined blind source separation method based on improved single source point detection according to claim 1, characterized in that: In step S3, the angle difference between the absolute directions of the real and imaginary parts of each column vector of the matrix S is calculated by the cosine angle single source point detection method to screen the preliminary single source point. The cosine angle single source point detection method is expressed as: Where k = 1, 2, ..., K, K represents the number of column vectors of the matrix S, Re[] represents the real part of the frequency domain vector, Im[] represents the imaginary part of the frequency domain vector, |·| represents the absolute value, Δθ represents the screening threshold; Through the angle difference of each column vector in the matrix S, the column vectors above the threshold Δθ are removed, and the column vectors below the threshold Δθ are the preliminary single source points.

5. The underdetermined blind source separation method based on improved single source point detection according to claim 1, characterized in that: In step S4, the preliminary single source points are subjected to low energy point removal and normalization processing, and the screening threshold of low energy points is Where N represents the total number of preliminary single source points, and ρ is a parameter, which is generally greater than or equal to 0.

1.

6. The underdetermined blind source separation method based on improved single source point detection according to claim 5, characterized in that: In step S4, the normalization is expressed as: Among them, s1(p) represents the real part value of the first mixed signal in S(p). According to this formula, the time-frequency points can be normalized and symmetric.

7. The underdetermined blind source separation method based on improved single source point detection according to claim 1, characterized in that: In step S5, a linear relationship detection is performed on the data after low-energy point removal and normalization processing, and the direction angle of two normalized column vectors is compared to determine whether two single source points belong to the same source signal. The detection method is expressed as: |1-<S(i),S(j)> |<ε Where <·> represents the scalar product, ε is the screening threshold, column vectors below the threshold ε are considered as single source points, and column vectors above the threshold ε are considered as outliers. Then, outliers in the preliminary single source points are removed to obtain the final single source points.

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