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.

翻译：盲源分离，特别是通过独立成分分析（ICA），因其完全数据驱动的特性最小化了对先验假设的依赖，被广泛应用于各种信号处理领域，以从观测到的混合信号中分离出潜在成分。然而，传统的ICA方法依赖于线性混合假设，限制了其捕捉复杂非线性关系以及在噪声环境中保持鲁棒性的能力。在本工作中，我们提出了深度确定性非线性独立成分分析（DDICA），这是一个新颖的基于深度神经网络的框架，旨在解决这些局限性。DDICA利用基于矩阵的熵函数，通过随机梯度下降直接优化独立性准则，从而绕过了对变分近似或对抗方案的需求。这带来了简化的训练过程以及对噪声更强的鲁棒性。我们在包括模拟信号混合、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）数据分析等一系列应用中验证了DDICA的有效性和泛化能力。实验结果表明，DDICA在多种应用中都能以高精度有效地分离独立成分。这些发现表明，DDICA为多样化的信号处理任务中的盲源分离提供了一个鲁棒且通用的解决方案。