Graph signal blind source separation method in white noise environment
By introducing blind compression functions and graph smoothing regularization into the blind source separation method, the problem of unstable signal separation performance under strong white noise is solved, and high-precision signal separation and robustness improvement are achieved in high-noise environments.
Patent Information
- Application Number
- CN202511642903.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-11
- Publication Date
- 2026-02-03
AI Technical Summary
In strong white noise environments, existing technologies struggle to balance the separation performance and robustness of blind source separation methods, especially under high noise conditions where signal separation quality deteriorates and becomes unstable.
A blind compression function is used for nonlinear noise suppression preprocessing. Combined with the joint diagonalization optimization of the graph Laplacian matrix and smoothing regularization, an optimization objective function is constructed. The separation matrix is then iteratively optimized using the Givens rotation algorithm.
High-precision and robust signal separation was achieved in high-noise environments, improving the stability and convergence efficiency of the separation matrix and significantly enhancing separation performance.
Smart Images
Figure CN121456665A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application belongs to the technical field of signal processing, and particularly relates to a robust blind source separation method combining a graph signal smoothness prior and joint diagonalization solving in an additive white noise (AWGN) environment, which is suitable for speech separation, electroencephalogram / sensor network signal separation and other data scenarios with a graph structure prior. BACKGROUND
[0002] In signal processing and communication systems, blind source separation (BSS) technology is widely used to recover original independent signals from mixed signals. This method does not require or only requires a small amount of prior knowledge, and can separate the mixed signals under the condition of mutual superposition of multiple source signals, so it has important value in the fields of speech recognition, medical signal analysis, radar / sounder processing and financial data modeling.
[0003] Blind source separation (BSS) aims to recover mutually independent or weakly correlated source signals from observed signals. The classical method relies on reliable estimation of high-order statistics (such as fourth-order cumulants) and whitening preprocessing. However, under strong white noise conditions, the cumulant estimation bias increases, the whitening is unstable, and the diagonalization target degenerates, resulting in a significant decrease in separation performance. On the other hand, many real data naturally obey graph smoothness or network coupling prior (such as multi-sensor array, EEG channel, and microphone array). Existing methods often do not explicitly use the graph prior to constrain the solving process of the separation matrix, resulting in a contradiction between the diagonalization target and the noise suppression target in the white noise scene, and the separation quality and robustness are difficult to balance. SUMMARY
[0004] The present application aims to overcome the problem of degradation of graph signal separation performance in the prior art under strong white noise environment, and proposes a graph signal blind source separation method that combines blind compression non-linear noise suppression and smooth regularization joint diagonalization optimization to achieve high robustness and high precision source signal recovery.
[0005] The method first introduces a blind compression function in signal preprocessing to perform non-linear noise suppression in a sample-by-sample processing manner; then uses a graph Laplacian matrix to describe the structural dependence relationship between signals, and realizes high-precision solving of the separation matrix by constructing an optimization objective function and combining smooth regularization constraints. Compared with existing methods, the present scheme has significant advantages in noise robustness, convergence efficiency and small sample adaptability.
[0006] To achieve the above purpose, the technical scheme adopted by the present application is a graph signal blind source separation method in a white noise environment, comprising the following steps:
[0007] Step one: obtain a noisy observation graph signal ;
[0008] Step two: nonlinear noise suppression preprocessing, apply blind compression function to each node sample of graph signal matrix
[0009] ,
[0010] get compressed signal matrix , for suppressing high amplitude noise interference; wherein is compression factor, for compressing large amplitude samples while preserving structural information and phase relationship, to suppress the destruction of noise to high-order statistics and graph correlation; is exponential function, that is, exponential operation with natural constant as base.
[0011] Step three: de-meaning and whitening, de-mean and whiten to get whitened data satisfying covariance is unit matrix
[0012] Step four: graph Laplacian matrix construction, construct adjacency matrix based on node relationship of graph signal, calculate degree matrix D, and then get smoothing operator from
[0013] Step five: joint diagonalization modeling of smoothing regularization, maximize joint objective to obtain separation matrix , input whitened data , construct graph autocorrelation matrix set and square symmetric FastICA term, introduce graph smoothing matrix to build optimization objective:
[0014]
[0015] wherein is defined as:
[0016]
[0017] wherein function is a nonlinear non-quadratic function satisfying , the function has twice continuous differentiability, suitable for normalized Gaussian random variable , defined as:
[0018]
[0019] is smoothing matrix; weight parameter is used to balance the two parts of the objective function, the first part focuses on graph correlation, and the second part pays attention to non-Gaussianity; To smooth the regularization weight, control the smoothness of the prior, and increase when the noise level is less than or equal to 15dB To improve robustness. To be the separation matrix.
[0020] Iterative optimization: use the iterative joint diagonalization algorithm based on Givens rotation to optimize the objective function, and rotate the update of the two vectors of each row of , so that the objective function Monotonically increases. When the objective function increment of adjacent iterations is less than the threshold Or the number of iterations reaches the upper limit , terminate the optimization to obtain the final solution of the separation matrix .
[0021] Step six: source reconstruction, get the estimated source signal from .
[0022] The beneficial effects of the present application: compared with the traditional ICA method, the present application effectively reduces the interference of noise on high-order moments by adding a blind compression function before separation; at the same time, the graph smoothing regularization term , the graph structure consistency of the signal is maintained during the separation process.
[0023] The experimental results show that under the conditions of 5dB, 15dB and 25dB noise levels, the average output SNR of the present application is improved by about 1-5dB compared with the traditional method, the separation matrix converges more stably, and has stronger noise resistance and generalization ability.
[0024] In summary, the present application introduces a joint modeling mechanism of nonlinear noise suppression and smoothing regularization based on the traditional graph signal blind source separation framework, and realizes stable signal separation in a high-noise environment. By performing blind compression processing before whitening, the interference of noise on high-order moment estimation is effectively weakened, and the separability of the source signal is improved; at the same time, the smoothing regularization term guides the separation matrix to maintain the graph structure consistency during the optimization process, thereby establishing a cooperative constraint between the spatial domain and the statistical domain of the signal. This method not only has higher robustness and separation accuracy under strong white noise conditions, but also is superior to traditional ICA and FastICA algorithms in convergence speed and stability, and has high engineering application value and promotion potential. BRIEF DESCRIPTION OF DRAWINGS
[0025] Figure 1 It is a graph signal blind source separation method flow chart in white noise environment;
[0026] Figure 2 It is a frame diagram of a graph signal blind source separation method in white noise environment; DETAILED DESCRIPTION
[0027] The technical solution of the present invention will be further described in detail below with reference to the embodiments.
[0028] like Figure 1 As shown in this embodiment, a method for separating blind sources of graph signals in a white noise environment includes the following steps:
[0029] Step 1: Source signal generation process in this embodiment: Construction A number of independent source signals that follow a non-Gaussian distribution. From the GMA model:
[0030]
[0031] Generate the observation map signal S. Where M is the order. It is an N-order identity matrix. Let y be the scalar coefficient, and y be the newly generated graph signal defined on graph G. The number of source signals K=4, order M=1, and the number of graph signal nodes N=250, 500, and 1000 were set, and comparative experiments were conducted under these three node sets. The four independent components under each node set followed t-distribution, uniform distribution, exponential distribution, and Gaussian distribution with 5 degrees of freedom, respectively. The graph smoothing coefficient θ for each independent component was set to 0.04, 0.08, 0.16, and 0.32, respectively. All independent components shared the same graph structure. The four signals were stacked row-wise to obtain the source signal matrix S. Then, a 4*4 mixing matrix was randomly generated. Generate mixed signals Generate Gaussian white noise The input SNR was set to three levels: 5dB, 15dB, and 25dB, to obtain the noisy signal. .
[0032] Step 2: Nonlinear noise suppression, for Apply a blind compression function to each element , The compressed graph signal matrix is obtained. This function compresses high-amplitude samples while preserving the signal polarity and structure, reducing the impact of noise on the fourth-order cumulant estimation.
[0033] Step 3: Whitening, calculate the covariance matrix S, and then... Perform row-by-row mean removal and use Left multiplication yields the whitening matrix. This achieves decorrelation and unit variance normalization to ensure numerical stability for subsequent orthogonal separation.
[0034] Step 4: Graph construction, constructing an adjacency matrix based on the graph signal node relationships. Calculate the degree matrix D, and then... The smoothing operator is obtained.
[0035] Step five: optimization to whiten data based on the auto-correlation matrix of the basis graph :
[0036]
[0037] symmetric square FastICA term:
[0038]
[0039] graph smoothing matrix :
[0040]
[0041] and define the objective function:
[0042]
[0043] Optimization is performed using the Givens rotation algorithm to update U, and when the objective function increment of adjacent iterations is less than the threshold or the number of iterations reaches the upper limit , the optimization is terminated to obtain the final solution of the separation matrix .
[0044] Step six: source signal reconstruction, from to obtain the estimated source signal.
[0045] Steps one to six constitute a complete graph signal blind source separation experiment process. To verify the stability and reliability of the algorithm performance, repeat the experiment H=500 times under each set of node number and input signal-to-noise ratio, and calculate the signal-to-noise ratio (SNR) index of the separation signal obtained in each experiment. The average SNR value of 500 experiments is taken as the evaluation standard of separation performance.
Claims
1. A method for blind source separation of graphical signals in white noise environment, characterized by, Comprising the steps of: Step one, obtaining a noisy observation map signal ; Step two, to Apply blind compression transform element-wise to get the graph signal matrix ; A nonlinear denoising pre-processing is applied on the graph signal, blindly compressing the observation of each sample node in the graph signal domain, defining a function: (1) wherein represents the sample value corresponding to a certain node on the graph, is a compression factor, used to compress the large value samples while preserving the structure information and phase relationship, so as to suppress the damage of noise to high-order statistics and graph correlation; by applying to all samples on the graph one by one, a compressed graph signal matrix is obtained, which is used for subsequent whitening and joint diagonalization; Step three, calculate sample covariance , get whitened data , achieve decorrelation and unit variance normalization to meet the numerical stability of subsequent orthogonal separation; Step four, constructing the graph Laplacian matrix : the construction method is to construct the adjacency matrix based on the node relationship of the graph signal , and then obtain the smoothing operator, is a degree matrix; Step five, smooth regularized joint diagonalization modeling, maximizing the joint objective to obtain the separation matrix ; Step six, source reconstruction, from The estimated source signal is obtained.
2. The method of blind source separation of graphical signals in white noise environment according to claim 1, characterized in that: The joint diagonalization modeling of the smoothing regularization in step five, maximizing the joint objective to solve the separation matrix, specifically comprising: 2.1, Objective function construction: based on whitened data , construct the set of graph autocorrelation matrices and square symmetric FastICA terms, and introduce a graph smoothing matrix , get the following optimization objective function:
3. Wherein is defined as:
4. where the function is a nonlinear non-quadratic function satisfying with twice continuous differentiability, applicable to standardized Gaussian random variables defined as:
5. is a smoothing matrix; weight parameter is used to balance two parts of the objective function, the first part focuses on the graph correlation, the second part concerns the non-Gaussianity; is a smoothing regularization weight, controls the smoothing prior strength, increases when the noise level is less than or equal to 15dB to improve robustness; is a to-be-solved separation matrix; 2.2, constraint setting: requirements satisfy the orthogonal constraint , to ensure the orthogonality and numerical stability between different separation vectors; 2.3, Iterative optimization method: the iterative joint diagonalization algorithm based on Givens rotation is adopted to update the two-by-two row vectors by rotation, so that the objective function monotonically increases; monotonically increases; 2.4, Convergence criterion: terminate optimization when the objective function increment of adjacent iterations is less than a threshold or the number of iterations reaches an upper limit , resulting in a final solution of the separation matrix .