An underdetermined blind source separation method based on improved single-source-point detection

Abstract

The application discloses an underdetermined blind source separation method based on improved single-source-point detection, first, the method uses the cosine angle criterion of the real part and the imaginary part of the time-frequency matrix array vector to preliminarily extract a single-source-point from a mixed signal; then, the presence or absence of the linear relationship between the single-source-point and an abnormal point is used to remove the abnormal point, so as to reduce the influence of the abnormal point on the single-source-point detection, thereby improving the estimation accuracy of the mixed matrix; then, the K-means algorithm is used to cluster the obtained single-source-points, so as to obtain an estimated mixed matrix; finally, the least square method is used to restore the source signal. The method provided by the application not only considers the absolute direction of the real part and the imaginary part in the single-source-point, but also considers the linear relationship between different single-source-points to remove the abnormal point, so that the estimation accuracy of the mixed matrix can be improved, the noise resistance of the method is enhanced, and finally high-quality restored signals are obtained.

Description

Technical Field

[0001] This invention belongs to the field of signal and information processing, and specifically relates to an underdetermined blind source separation method based on improved single-source point detection. Background Technology

[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. It is a typical source separation method widely used in various fields such as speech signal processing, biomedical signal processing, and wireless communication systems. In practical 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; this is known as an underdetermined blind source separation model. Therefore, addressing underdetermined blind source separation problems is more realistic.

[0003] Currently, sparse component analysis (SCI) is the mainstream technique for handling underdetermined blind source separation problems. SCI divides the underdetermined blind source separation problem into two steps: first, estimating the mixing matrix; and second, recovering the source signals based on the estimated mixing matrix. SCI-based methods require the signal to possess sparsity, meaning that the source signals are non-zero only at a few moments in the time domain or other domains. If, at a certain moment, the mixed signal has exactly one dominant source signal, while the sampled values ​​of other source signals are close to zero, then the signal point obtained at that moment is considered a single-source point. Single-source points are key to enhancing the sparsity of the mixed signal, and the accuracy of the single-source point detection algorithm affects the accuracy of the mixing matrix estimation. Specifically, the quality of source signal recovery depends on the accuracy of the mixing matrix estimation, and the accuracy of single-source point detection directly affects the accuracy of the mixing matrix estimation.

[0004] Currently, most single-source point detection methods involve one-time screening. Among them, methods that only consider each time-frequency point are highly efficient and perform well in high signal-to-noise ratio environments, making them the mainstream single-source point detection methods, especially the cosine angle single-source point detection method. However, these methods are prone to false detection of outliers, leading to a decrease in the accuracy of the mixing matrix estimation. Their effectiveness is severely reduced when faced with noise interference. These outliers, generated by false detections, directly affect the clustering results, reducing the accuracy of the mixing matrix estimation and thus limiting the quality of source signal recovery. In the face of noise interference, methods that utilize the linear relationship between single-source points to screen for outliers often exhibit better noise resistance. Methods that only consider each time-frequency point cannot effectively remove outliers and do not utilize the linear relationship between different single-source points. Therefore, the estimated mixing matrix has low accuracy, poor noise resistance, and insufficient source signal separation quality. Summary of the Invention

[0005] The purpose of this invention is to provide an underdetermined blind source separation method based on improved single-source point detection, which improves the accuracy of the cosine angle single-source point detection algorithm, thereby improving the accuracy of the mixing matrix estimation and obtaining a higher quality separated signal.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

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

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

[0009] S2: Integrate the time-frequency domain mixing matrix 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 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 directions of the real and imaginary parts of each column vector in S. Column vectors that are lower than the threshold Δθ are the initial single-source points.

[0011] S4: Perform low-energy point removal and normalization on the preliminary single-source points detected in S3;

[0012] S5: Perform linear relationship detection on the data processed by S4. By comparing the angle between the directions of two normalized column vectors, determine whether two single source points belong to the same source signal. Column vectors below the threshold ε are considered as single source points, and those above the threshold ε are considered as outliers. Then, remove the outliers from the initial single source points 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 one-to-one with the column vectors of the mixture matrix, thus achieving the estimation of the mixture matrix.

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

[0015] Furthermore, in step S1, the time-domain mixed signal x received by each microphone... i The operations performed sequentially by (t) are as follows: using x(t) = [x1(t), x2(t), ..., x m (t)] T Let x represent the m-dimensional mixed signal received by m microphones. i (t) is the mixed signal received by the i-th microphone at time t. TThis represents the transpose operation; for a mixed signal x i (t) Performing a short-time Fourier transform yields the time-frequency domain complex matrix X of the mixed signal. i , where i = 1, 2, ..., m, and X i Let f represent a complex matrix with t columns.

[0016] Furthermore, in step S2, the complex matrix of each microphone obtained in step S1 is vectorized, specifically by transforming the time-frequency domain complex matrix X... i The first and last rows of the row vectors are concatenated to obtain a one-dimensional row vector s. 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 matrix S represents an observed signal.

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

[0018]

[0019] Where k = 1, 2, ..., K, K represents the number of column vectors in matrix S, Re[] represents the real part of the frequency domain vector, Im[] represents the imaginary part of the frequency domain vector, and · represents the absolute value. Δθ represents the filtering threshold; by using the angle difference between each column vector in matrix S, column vectors that are higher than the threshold Δθ are removed, and column vectors that are lower than the threshold Δθ are the initial single source points.

[0020] Furthermore, in step S4, low-energy points are removed and normalized from the initial single-source points. Low-energy points are time-frequency points with lower energy. Low-energy points affect the estimation of the mixing matrix, therefore they need to be removed. The screening threshold for low-energy points is... Where N represents the total number of initial single-source points, and ρ is a parameter, typically greater than or equal to 0.1. This invention uses a threshold of ρ times the average energy to remove low-energy points from the initial single-source points.

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

[0022]

[0023] Wherein, s1(p) represents the real part of the first mixed signal in S(p), and the time and frequency points can be normalized and symmetricized according to this formula.

[0024] Furthermore, in step S5, a linear relationship detection is performed on the data after low-energy point removal and normalization. The direction angle between 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 follows:

[0025] 1-S(i),S(j)<ε

[0026] Where · represents the scalar product, and ε is the filtering threshold. Column vectors below the threshold ε are considered single-source points, and column vectors above the threshold ε are considered outliers. Outliers in the initial single-source points are then removed to obtain the final single-source points.

[0027] This invention discloses an underdetermined blind source separation method based on improved single-source detection. This method not only possesses the high efficiency of cosine angle single-source detection but also the good noise resistance of linear single-source detection methods. The method first uses the cosine angle single-source method to filter out most non-single-source points. Then, low-energy point removal and normalization operations are performed to further reduce the number of time-frequency points that need to be processed. The time-frequency point mapping is then symmetricized, thus improving the efficiency of outlier removal using the linear single-source method. Experimental verification shows that the estimated mixing matrix obtained by this method is not only more accurate but also more robust, with lower time complexity and higher quality source signal recovery, effectively improving the accuracy of single-source detection methods. Attached Figure Description

[0028] Figure 1 This is a flowchart of an underdetermined blind source separation method based on improved single-source point detection in the embodiments;

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

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

[0031] Figure 4 The following is a diagram showing the results of hybrid matrix estimation under different signal-to-noise ratio environments in the example;

[0032] Figure 5 This is a waveform diagram of the source signal in the embodiment;

[0033] Figure 6 The image shows the recovered source signal waveform in the example. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with the embodiments and accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0035] Example:

[0036] An underdetermined blind source separation method based on improved single-source point detection is illustrated in the flowchart below. Figure 1 As shown.

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

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

[0039]

[0040] Where 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 time-domain mixed signal into a time-frequency domain mixed signal through short-time Fourier transform, and then perform single-source point screening on the time-frequency domain mixed signal. A single source point is 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 time-frequency domain mixed signal.

[0042] By performing a short-time Fourier transform on each observation signal, the time-frequency domain observation signal of each observation signal is obtained, and then the time-frequency domain observation signals of each observation signal are integrated into a row vector s. i (k), and finally integrated into a 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 in matrix S, column vectors with angle differences smaller than a preset threshold are retained as initial single sources. Here, Δθ is a judgment threshold, and this angle difference is generally set to a small value. In this embodiment, the value of Δθ is 1°.

[0044] In this embodiment, a preliminary scatter plot of a single source point is detected by calculating the included angle difference, such as... Figure 2 As shown;

[0045] Next, low-energy point removal and normalization operations are performed on the initial single-source points;

[0046] Linearity detection is performed on the data after low-energy point removal and normalization. The angle between the directions of two normalized column vectors is compared to determine whether two single-source points belong to the same source signal. Single-source points from the same source have similar normalized vector values. Therefore, column vectors below a threshold ε are considered single-source points, while those above the threshold ε are considered outliers. Outliers in the initial single-source point set are then removed to obtain the final single-source points. Here, 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 a single source point obtained after outlier removal is as follows: Figure 3 As shown; comparison Figure 2 and Figure 3 As can be seen, the present invention effectively removes abnormal points such as deviation points and interference points, making the distribution of the scatter plot of the normalized single source points more compact.

[0048] After single-source point detection is completed, K-means algorithm is used for clustering to obtain cluster centers. Each cluster center corresponds one-to-one with the column vector of the mixture matrix, and finally the mixture matrix is ​​estimated.

[0049] In this embodiment, the three acoustic signals are processed by a mixing matrix A to obtain two observation signals, wherein the mixing matrix A is:

[0050]

[0051] To quantitatively evaluate the estimation of each column vector of the estimated mixture matrix, a deviation angle is used to measure the deviation between the original mixture matrix and the corresponding column vector of the estimated mixture matrix. The formula for the deviation angle is as follows:

[0052]

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

[0054] To comprehensively evaluate the accuracy of the mixture matrix estimation, the normalized mean squared error (NMSE) is used as the evaluation metric. The formula for NMSE is as follows:

[0055]

[0056] In the formula, m and n represent the number of rows and columns of the mixing matrix, respectively, and a ij Let a represent the elements in the i-th row and j-th column of the original mixing matrix A. ij This represents the elements in the i-th row and j-th column of the estimated mixture matrix A. The smaller the NMSE value, the higher the accuracy of the mixture matrix estimation.

[0057] Table 1 shows a comparison of the accuracy of the mixture matrix estimated by the cosine angle single-source point detection method and the method proposed in this invention. As can be seen from the table, the method proposed in this invention improves the accuracy of each column of the mixture matrix by 14.20%, 30.93%, and 80.55% respectively, with an average improvement of 57.23%. This indicates that the proposed method can effectively remove outliers and improve the estimation accuracy of the mixture matrix. The method also improves the NMSE by 25.49%, indicating that the proposed method can obtain a more accurate estimated mixture matrix. The results of the deviation angle and NMSE demonstrate the correctness and effectiveness of the proposed method.

[0058] Table 1 Comparison of the accuracy of the estimated mixture matrix

[0059]

[0060] In this embodiment, to test the noise immunity of the proposed method, Gaussian white noise with different signal-to-noise ratios was added to the mixed signal. The mixing matrix was estimated 20 times for each noise level, and the average NMSE was recorded. The experimental results are as follows: Figure 4 As shown. From Figure 4 As can be seen from the data, the average NMSE of the method of the present invention is better than that of the cosine angle single-source detection method under each signal-to-noise ratio environment, which shows that the method of the present invention is superior to the cosine angle single-source 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 recovered by the method proposed in this invention are as follows: Figure 6 As shown, through Figure 5 and Figure 6 The comparison shows that the waveform of the source signal obtained by the method proposed in this invention is very similar to the waveform of the actual signal, indicating that this embodiment has high estimation accuracy.

Claims

1. A method for separating underdetermined blind sources based on improved single-source point detection, characterized in that, Includes the following steps: S1: Perform a short-time Fourier transform on the time-domain mixed signal received by each microphone to obtain the time-frequency domain mixing matrix; S2: Integrate the time-frequency domain mixing matrix 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 matrix S represents an observed signal; S3: Detect the angle difference between the absolute directions of the real and imaginary parts of each column vector in S using the cosine angle single-source point detection method. If the angle difference is below a threshold... The column vectors are the initial single source points; S4: Perform low-energy point removal and normalization on the preliminary single-source points detected in S3; S5: Perform linearity detection on the data processed by S4. Determine whether two single-source points belong to the same source signal by comparing the direction angle between two normalized column vectors. If the value is below a threshold... The column vectors are considered as single-source points, and those above the threshold Those are considered outliers, and then the outliers in the initial 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 one-to-one with the column vectors of the mixture matrix, thus achieving the estimation of the mixture matrix. S7: Using the estimated mixing matrix and the mixed signal in the time and frequency domains, the source signal of each source is recovered by the least squares method, and finally the source signal in the time domain is obtained by the short-time Fourier inverse transform.

2. The underdetermined blind source separation method based on improved single-source point detection according to claim 1, characterized in that: In step S3, the cosine angle single-source point detection method is used to calculate the angle difference between the absolute directions of the real and imaginary parts of each column vector of matrix S to screen preliminary single-source points. The cosine angle single-source point detection method is expressed as follows: Where k = 1, 2, ..., K, K represents the number of column vectors in matrix S, Re[] represents the real part of the frequency domain vector, and Im[] represents the imaginary part of the frequency domain vector. Represents absolute value. Indicates the filtering threshold; By using the angle difference between each column vector in matrix S, those exceeding the threshold will be... Column vector removal, below the threshold The column vectors are the initial single source points.

3. The underdetermined blind source separation method based on improved single-source point detection according to claim 1, characterized in that: In step S4, the initial single-source points undergo low-energy point removal and normalization processing, with the low-energy point screening threshold being [value missing]. Where N represents the initial total number of single-source points, This is a parameter, generally greater than or equal to 0.1; In step S4, normalization is represented as: Wherein, s1(p) represents the real part of the first mixed signal in S(p), and the time and frequency points can be normalized and symmetricized according to this formula.

4. The underdetermined blind source separation method based on improved single-source point detection according to claim 1, characterized in that: In step S5, linear relationship detection is performed on the data after low-energy point removal and normalization. The direction angle between two normalized column vectors is compared to determine whether two single-source points belong to the same source signal. The detection method is as follows: in, Represents scalar product. It's a filtering threshold; values ​​below the threshold... The column vectors are considered as single-source points, and those above the threshold The column vectors are considered outliers, and then the outliers in the initial single-source points are removed to obtain the final single-source points.

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