Bi-Dimensional BSS Using Multi-Statistical Properties Optimization

Diversity measures employed in blind source separation methods typically exploit single statistical properties such as independence, sparsity, or temporal structure. This limits their effectiveness when underlying sources exhibit diverse statistical behaviors, which results in suboptimal separation performance. Although some recent studies have explored multiple statistical properties through single or multi-objective optimization, most methods remain constrained to exploiting at most two properties. To address this limitation, we propose a unified statistical properties framework named bi-dimensional and multi-statistical (BDMS) for source separation that simultaneously exploits spatial regularization and multiple spatial statistical characteristics through unified temporal optimization. The proposed method integrates spatial regularization through adaptive soft thresholding and a unified temporal optimization framework combining three statistical diversity measures (kurtosis, spectral entropy, Hoyer sparsity) with reconstruction fidelity constraints. Spatial properties are integrated through magnitude-matched gradient descent with performance-based optimized weighting factors that systematically balance the contribution of each statistical measure and reconstruction fidelity. Additionally, domain-specific post-processing enhances robustness by including discrete cosine transform basis expansion for functional magnetic resonance imaging (fMRI) temporal smoothness. The proposed framework demonstrates superior separation accuracy and robustness to noise and strong spatiotemporal dependencies compared to single and dual-property methods and maintains computational efficiency. Experimental validation on synthetic and real fMRI datasets demonstrates 19.5% improvement in source recovery accuracy and 2.6 times faster execution time compared to SICA-EBM (dual property multi-objective framework) across four different experimental conditions. To ensure reproducibility, we provide the synthetic dataset and complete source code at https://github.com/usmankhalid06/BDMS