An Innovative Nonlinear Bounded Component Analysis Algorithm Based on Multivariate Nonlinear Chirp Mode Decomposition

In complex and diverse practical application scenarios, the challenge of blind source separation under underdetermined and nonlinear conditions is often encountered. To address this challenge, this paper proposes an innovative underdetermined nonlinear bounded component analysis method. This method first employs Multivariate Nonlinear Chirp Mode Decomposition (MNCMD) to process and reconstruct the observed signals, transforming the original underdetermined problem into a positive definite problem. Subsequently, Gaussianization techniques are introduced as a means of nonlinear compensation, successfully converting the nonlinear model into an analyzable linear model, laying a solid foundation for subsequent signal separation. Finally, the signal is separated by the bounded component analysis method, which does not require the source signals to be independent of each other. To validate the effectiveness and superiority of the proposed algorithm, detailed simulation experiments were designed and implemented. The experimental results demonstrate that compared to traditional underdetermined blind source separation algorithms, the algorithm presented in this paper exhibits significant advantages in terms of universality, convergence speed, separation accuracy, and robustness. Furthermore, this paper successfully applies the algorithm to the blind extraction of fetal electrocardiogram (FECG) signals from real datasets. The experimental results show that the algorithm can rapidly and effectively extract clearer and more accurate FECG signals, demonstrating its great potential and value in practical applications.