A novel mixing matrix estimation method for underdetermined blind source separation based on sparse subspace clustering

It is essential to accurately estimate the mixing matrix and determine the number of source signals in the problem of underdetermined blind source separation. The problem is solved in this paper via sparse subspace clustering, which can be used to found low-dimensional data structures in observed data. To enhance the linear clustering characteristics of time-frequency points, the high energy points are reserved first, and the angle difference of real and imaginary portions is employed to screen single source points. After that, the time-frequency points are clustered using sparse subspace clustering, and the number of source signals is identified. Finally, the local density of eigenvectors is used to determine the mixing matrix. The proposed algorithm is capable of accurately estimating the mixing matrix. It has strong robustness and adaptable to a wide range of mixing circumstances. The proposed method's effectiveness is demonstrated by theoretical analysis and experimental data.