Source signal sparsity enhancement based on local maximum synchronous extraction transform algorithm for mixed matrix estimation in UBSS

To address the issues of suboptimal sparsity and the tendency of clustering algorithms to converge to local optima in the estimation of the mixing matrix within underdetermined blind source separation (UBSS) systems, a novel mixing matrix estimation algorithm based on source signal sparsity is proposed. Firstly, the principle of underdetermined mixing matrix estimation leveraging source sparsity is derived. Building upon this foundation, improvements are made from enhancement of signal sparsity and optimization of the clustering algorithm. To overcome the limited sparse representation capability of conventional time–frequency (TF) transformation methods, a source signal sparsity enhancement algorithm based on the Local Maximum Synchroextracting Transform (LMSET) is proposed. This method rearranges the TF coefficients by detecting local maxima in the frequency direction, thereby achieving a more desirable TF resolution and enhanced signal sparsity. Furthermore, to mitigate the sensitivity of the Fuzzy C-Means (FCM) algorithm to initial cluster centers and its propensity for local optima, a robust FCM algorithm optimized by the PID(Proportional-integral-Derivative)-based Search Algorithm (PSA) is adopted. Simulation results demonstrate that the proposed algorithm achieves a superior TF representation and enhances the sparsity of source signals across various environments. Compared to traditional algorithms, the estimation accuracy of the mixing matrix is increased by 19.8%, effectively improving the performance of mixing matrix estimation in underdetermined blind source separation systems.