Underdetermined blind source separation based on third-order cumulant and tensor compression

A method for Underdetermined Blind Source Separation is proposed using third-order cumulants and tensor compression. To effectively suppress symmetrical distributed noise, the third-order cumulant is considered. Additionally, the complexity of high-dimensional tensors can be reduced through high order singular value decomposition (HOSVD) for compression purposes. The method begins by calculating the third-order cumulant tensor for whitening signals at different time delays, and then stacks several cumulants into a fourth-order tensor. The HOSVD decomposition is applied to the fourth-order tensor, compressing the high-dimensional tensor into a low-dimensional core tensor. Next, the core tensor is further decomposed using the canonical polyadic decomposition, and the resulting factor matrices are fused to obtain an estimation of the mixed matrix. Finally, leveraging the signal independence, a matrix diagonalisation method is employed to recover the source signals. Theoretical analysis and simulation results demonstrate that the proposed method effectively suppresses the influence of Gaussian noise, reduces computational complexity, and saves computational time. Moreover, compared with five representative approaches, the proposed method achieves superior separation results. Specifically, for the 3 × 4 mixed model with a signal-to-noise ratio of 20 dB, the average relative error of speech signal and radio signal are −11.02 and −6.8 dB respectively.