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<p>Blind Source Separation (BSS) addresses the recovery of unknown source signals from observed mixtures without prior knowledge of the mixing process. Independent Component Analysis (ICA) is a fundamental approach that linearly estimates statistically independent components. However, conventional ICA methods exhibit performance degradation in the presence of additive white Gaussian noise (AWGN) or quasi-Gaussian sources. Furthermore, optimization-based formulations impose substantial computational burden due to iterative search procedures and parameter tuning, limiting their suitability for real-time applications. This paper presents a fully analytical, deterministic BSS framework based on direct kurtosis maximization with closed-form estimation of optimal separation angles. By leveraging the sinusoidal variation of kurtosis under pairwise rotations and an amplitude-based selection rule, the method achieves separation with at most three rotations per signal pair, eliminating the need for adaptive optimization and ensuring numerical stability. The framework is validated on synthetic deterministic signals, grayscale images, speech, and electroencephalographic (EEG) recordings. Deterministic signals achieve normalized signal-to-distortion ratios (NSDR) above 90&#xa0;dB, speech signals reach approximately 30&#xa0;dB, and EEG data maintain approximately 14&#xa0;dB despite weak non-Gaussianity. Experiments under noisy and limited-sample conditions demonstrate robust performance with short data records, while mutual information and fourth-order cross-cumulant analyses verify global statistical independence. Wavelet-based denoising is examined in preprocessing and postprocessing configurations, with post-separation denoising consistently outperforming preprocessing. Overall, the proposed framework provides a fast, accurate, and scalable alternative to optimization-driven ICA methods, making it suitable for real-time and large-scale applications.</p>

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An Efficient Geometric Framework for Blind Source Separation of Stationary and Non-Stationary Signals through Analytical Rotation Estimation

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • El Mouataz Billah Smatti,
  • Djemai Arar

摘要

Blind Source Separation (BSS) addresses the recovery of unknown source signals from observed mixtures without prior knowledge of the mixing process. Independent Component Analysis (ICA) is a fundamental approach that linearly estimates statistically independent components. However, conventional ICA methods exhibit performance degradation in the presence of additive white Gaussian noise (AWGN) or quasi-Gaussian sources. Furthermore, optimization-based formulations impose substantial computational burden due to iterative search procedures and parameter tuning, limiting their suitability for real-time applications. This paper presents a fully analytical, deterministic BSS framework based on direct kurtosis maximization with closed-form estimation of optimal separation angles. By leveraging the sinusoidal variation of kurtosis under pairwise rotations and an amplitude-based selection rule, the method achieves separation with at most three rotations per signal pair, eliminating the need for adaptive optimization and ensuring numerical stability. The framework is validated on synthetic deterministic signals, grayscale images, speech, and electroencephalographic (EEG) recordings. Deterministic signals achieve normalized signal-to-distortion ratios (NSDR) above 90 dB, speech signals reach approximately 30 dB, and EEG data maintain approximately 14 dB despite weak non-Gaussianity. Experiments under noisy and limited-sample conditions demonstrate robust performance with short data records, while mutual information and fourth-order cross-cumulant analyses verify global statistical independence. Wavelet-based denoising is examined in preprocessing and postprocessing configurations, with post-separation denoising consistently outperforming preprocessing. Overall, the proposed framework provides a fast, accurate, and scalable alternative to optimization-driven ICA methods, making it suitable for real-time and large-scale applications.