Mixing Matrix Identification Method in Underdetermined Blind Source Separation Based on Tensor Regularized Decomposition

Abstract

The invention discloses a mixing matrix identification method in underdetermined blind source separation based on tensor canonical decomposition, which mainly solves the problem that the prior art is restricted by specific conditions when estimating the mixing matrix. The implementation steps are: (1) Sampling the source signal to obtain the observation data; (2) Using the fourth-order cumulant of the observation data to calculate the fourth-order covariance matrix under different time delays; The fourth-order covariance matrix is ​​expanded into the form of a third-order tensor; (4) the tensor canonical decomposition is performed on the third-order tensor to obtain the Khatri‑Rao product matrix of the mixed matrix to be identified; (5) the method of eigenvalue decomposition is used for the The product matrix is ​​processed to obtain an estimate of the mixing matrix. The invention has the advantage of high recognition accuracy, and can be used for underdetermined blind source separation of source signals in the fields of voice, communication, radar and biomedicine under the condition of time-frequency aliasing.

Description

technical field [0001] The invention belongs to the technical field of communication, and in particular relates to a method for identifying a mixing matrix, which can be used in underdetermined blind source separation of source signals in the fields of voice, communication, radar and biomedicine under the condition of time-frequency aliasing. Background technique [0002] Blind source separation (BSS) refers to the purpose of separating the source signal only through the observation signal received by the sensor under the condition of unknown transmission channel and source signal. This method has been widely used in speech signal processing, image processing, radar, Communications and biomedicine and other fields. As a classic algorithm of blind source separation, independent component analysis (ICA) and its extended algorithms are mostly used to solve the problem under the condition that the number of observed signals is equal to or greater than the number of source signal...

AI Technical Summary

Problems solved by technology

Some scholars take advantage of the sparsity of the signal and use the clustering method to identify the mixing matrix. When the source signal does not meet the sparsity in the time domain, they use tools such as Fourier transform or wavelet transform to transform the signal into a sparse frequency domain. , and then use the method of clustering or potential function to identify the mixing matrix, for example, NgutyenLin-Trung, ABelouchrani, KarimA-M. In the case of uniform aliasing, the performance of this method is not ideal

Some scholars use time-frequency methods, for example, Lu Fengbo, Huang Zhitao, Peng Geng, etc., "Undetermined Blind Aliasing Separation Based on Time-Frequency Distribution", Journal of Electronics, 2011, 39(9), pp.2067-2072, the The method performs time-frequency processing on the observed signal, and then extracts the self-source time-frequency points of the signal, uses the self-source time-frequency points to construct a tensor model and decomposes the model by tensor regularization, so as to complete the identification of the mixing matrix, but in the frequency domain In the case of serious overlap, the extraction of time-frequency points from the source is not ideal, so it will affect the recognition performance of the mixing matrix; some scholars use the statistical characteristics of the signal, such as DeLathauwerL, CastaingJ, CardosoJ, "Fourth-order cumulant- basedblindidentificationofunderdeterminedmixtures",IEEETransactionsonSignalProcessing,2007,55(6),pp.2965-2973, this method does not require the source signal to meet the sparse characteristics, only requires the source signal to be a statistically independent non-Gaussian signal, in the actual process, this condition is often easy Satisfied, but in the process of solving the algorithm, it is necessary to assume that the source signal has the same sign of kurtosis, that is, the numerical statistic reflecting the distribution characteristics of the vibration signal, which is a normalized fourth-order central moment, while the source signal prior In the case of insufficient knowledge, this condition is often difficult to meet, thus affecting the recognition accuracy of the mixing matrix

Images