Sign-Enhanced Semidefinite Programming Algorithm and its Application to Independent Component Analysis

Abstract

Independent component analysis (ICA) is widely applied in remote sensing signal processing. Among various ICA algorithms, the modified semidefinite programming (MSDP) algorithm stands out. However, the efficacy and safety of MSDP depend on the distribution of data. Our research found that MSDP is better suited for handling data with a super-Gaussian distribution. As real-world data usually exhibit a combination of sub-Gaussian and super-Gaussian distributions, MSDP faces challenges in accurately extracting all independent components (ICs). To solve this problem, we conducted a comprehensive analysis of the MSDP algorithm and introduced an enhanced version, the sign-enhanced MSDP (SMSDP) algorithm. By incorporating the sign function into the projected Hessian matrix, SMSDP enables the algorithm to effectively extract ICs from data characterized by a mixture of sub-Gaussian and super-Gaussian distributions. Furthermore, we provided a detailed comparison with MSDP to illustrate why SMSDP can achieve more accurate eigenpairs. Some experiments have demonstrated the effectiveness of SMSDP. The experiments in blind separation of image/sound, radar clutter removal, and real hyperspectral feature extraction also show the superiority of SMSDP in improving the accuracy of IC extraction.