Orthogonal approach to independent component analysis using quaternionic factorization - Adam Borowicz (EURASIP Journal on Advances in Signal Processing, 2020)
Abstract 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.