Research On Underdetermined Blind Source Separation Algorithm Based On Sparse Component Analysis

The blind source separation technique refers to a technique of separating source signals by only mixing signals in the case where the source signals and the transmission channels are unknown.In actual life,it is often the case that the number of source signals is greater than the number of observation signals,that is,an underdetermined situation.For this situation,sparse component analysis is usually used to solve it.Therefore,the paper studies the underdetermined blind source separation technique of speech signals based on sparse component analysis.Firstly,the current clustering algorithm is susceptible to noise when the source signal is sufficiently sparse.An improved Laplacian potential function clustering algorithm is proposed to address this problem.Sufficiently sparse source signals mean that at each observation moment,only one source signal is active in most cases.At this time,the scatter plot of the observed signals exhibits the characteristic of linear clustering.Since the signals are not well sparse in the time domain,the sparseness is enhanced in the frequency domain.The signals are usually transformed to the frequency domain for processing.Due to the existence of stray points,the accuracy of the mixing matrix estimated in the later period is not good,so a method is proposed to detect single source points by using the difference between the real part vector and the imaginary part vector of the observation signals.Since the single source points near the origin affect the estimation effect of the mixing matrix,low energy point processing is required.When the signal-to-noise ratio is relatively low,the biases of the cluster centers estimated by the existing algorithms are large,which leads to low accuracy of the matrix estimated in the later stage.An improved Laplacian potential function is proposed in the paper,corrects the estimated clustering center,and obtains an estimation matrix.The simulation results show that the algorithm proposed in the paper has good performance in estimating the mixing matrix.Secondly,under the condition that the source signal is not sufficiently sparse,the estimation effect of the current clustering algorithm is not good due to the existence of noise and outliers.For this situation,the paper proposes an estimation algorithm based on hyperplane clustering.Insufficiently sparse source signals mean that at each observation moment,not only one source signal is active in most cases.At this time,the scatter plot of the observed signals has the characteristic of surface clustering,not linear clustering.Since the current clustering algorithms are sensitive to noise and outliers,they tend to fall into local optimal values when iterating out the clustering plane,making the estimated mixing matrix ineffective.So the paper first proposes a new distance measurement method to improve the kernel density function as the objective function,the adaptive gradient iterative method is derived to optimize the normal vector of the cluster hyperplane,and then the estimated normal vector is used to iterate out the column vector using the steepest rising method to obtain the mixing matrix.The simulation results show that the algorithm proposed in the paper improves the noise immunity when estimating the mixing matrix.Finally,an improved minimization l₁ norm algorithm is proposed to solve the problem that the reconstruction algorithm is seriously affected by noise.Firstly,perform preprocessing.Remove the zero vector in the observation signal vectors,the directions are unified,normalize the column vector and then calculate the direction of the observation signal and the column vector separately.Firstly,we can find the vector closest to the observed signal according to the length and angle of the vector,and then estimate the source signals.However,it is found that the reconstruction effect of the method is not good.On this basis,it considers changing the form of the mixing matrix and using the changed mixing matrix to estimate the source signals at a certain moment.And then estimate the source signals at all times.The simulation results illustrate the proposed algorithm can construct the source signal effectively and it is not affected by the number of source signals.