Independent component analysis (ICA) is a popular technique for demixing multichannel data. The performance of a typical ICA algorithm strongly depends on the presence of additive noise, the actual distribution of source signals, and the estimated number of non-Gaussian components. Often, a linear mixing model is assumed and source signals are extracted by data whitening followed by a sequence of plane (Jacobi) rotations. In this article, we develop a novel algorithm, based on the quaternionic factorization of rotation matrices and the Newton-Raphson iterative scheme. Unlike conventional rotational techniques such as the JADE algorithm, our method exploits 4×4 rotation matrices and uses approximate negentropy as a contrast function. Consequently, the proposed method can be adjusted to a given data distribution (e.g., super-Gaussians) by selecting a suitable non-linear function that approximates the negentropy. Compared to the widely used, the symmetric FastICA algorithm, the proposed method does not require an orthogonalization step and is more accurate in the presence of multiple Gaussian sources.

独立分量分析（ICA）是一种用于混合多通道数据的流行技术。典型ICA算法的性能在很大程度上取决于附加噪声的存在，源信号的实际分布以及估计的非高斯分量。通常，采用线性混合模型，并通过数据白化和随后的一系列平面（Jacobi）旋转来提取源信号。在本文中，我们基于旋转矩阵的四元数分解和Newton-Raphson迭代方案，开发了一种新颖的算法。与传统的旋转技术（例如JADE算法）不同，我们的方法利用4×4旋转矩阵，并使用近似负熵作为对比函数。因此，建议的方法可以调整为给定的数据分布（例如，通过选择合适的非线性函数来近似负熵。与广泛使用的对称FastICA算法相比，该方法不需要正交化步骤，并且在存在多个高斯源的情况下更加准确。