提出新型非线性盲源分离方法，提升复杂信号分解精度与抗噪能力。
Deep Deterministic Nonlinear ICA via Total Correlation Minimization with Matrix-Based Entropy Functional
- 基于矩阵熵函数直接优化独立性，无需变分近似或对抗训练
- 在模拟信号、高光谱图像等4类任务中实现高精度成分分离
- 适合需要强鲁棒性的复杂信号处理场景，如脑功能成像分析
盲源分离，尤其是通过独立成分分析（ICA）方法，在各类信号处理领域广泛应用，因其完全数据驱动的特性，可减少对先验假设的依赖。然而，传统ICA方法依赖线性混合假设，难以捕捉复杂非线性关系，且在噪声环境下鲁棒性不足。本文提出深度确定性非线性独立成分分析（DDICA），一种基于深度神经网络的新框架，以解决上述问题。DDICA采用矩阵基熵函数，直接通过随机梯度下降优化独立性准则，避免了变分近似或对抗机制。该方法简化了训练流程，增强了抗噪能力。我们在多种应用场景中验证了其有效性与泛化能力，包括模拟信号混合、高光谱图像解混、初级视觉感受野建模以及静息态功能磁共振成像（fMRI）数据分析。实验结果表明，DDICA在多个任务中均能高精度分离独立成分。这些发现表明，DDICA为多样化的信号处理任务提供了稳健且通用的盲源分离解决方案。
原文摘要 · Abstract (English)
Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains for disentangling underlying components from observed mixed signals, owing to its fully data-driven nature that minimizes reliance on prior assumptions. However, conventional ICA methods rely on an assumption of linear mixing, limiting their ability to capture complex nonlinear relationships and to maintain robustness in noisy environments. In this work, we present deep deterministic nonlinear independent component analysis (DDICA), a novel deep neural network-based framework designed to address these limitations. DDICA leverages a matrix-based entropy function to directly optimize the independence criterion via stochastic gradient descent, bypassing the need for variational approximations or adversarial schemes. This results in a streamlined training process and improved resilience to noise. We validated the effectiveness and generalizability of DDICA across a range of applications, including simulated signal mixtures, hyperspectral image unmixing, modeling of primary visual receptive fields, and resting-state functional magnetic resonance imaging (fMRI) data analysis. Experimental results demonstrate that DDICA effectively separates independent components with high accuracy across a range of applications. These findings suggest that DDICA offers a robust and versatile solution for blind source separation in diverse signal processing tasks.
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