Orthogonal approach to independent component analysis using quaternionic factorization
- PDF / 2,400,924 Bytes
- 23 Pages / 595 x 794 pts Page_size
- 7 Downloads / 214 Views
(2020) 2020:39
EURASIP Journal on Advances in Signal Processing
RESEARCH
Open Access
Orthogonal approach to independent component analysis using quaternionic factorization Adam Borowicz Correspondence: [email protected] Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland
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. Keywords: BSS, ICA, Jacobi rotations, Negentropy, Quaternions
1 Introduction Blind source separation (BSS) problems occur in various engineering applications, including the multichannel speech enhancement, image restoration, analysis of electroencephalographic (EEG) signals, and telecommunications [1]. The BBS consists of recovering of unobservable source signals from their observed mixtures. Most often, the following linear model [2] of the observation vector is assumed: x = As,
(1)
where A ∈ Rn×d is an unknown mixing matrix and s is a random vector of d unknown source signals. Please note that there exist other models that can deal, for example, with spherical noise [3], under-determination, and mixture synchronization issues. In the under-determined case, the number of source signals is greater than the number of mixtures. Obviously, it makes the BSS problem ill-posed. In such cases, a concept of sparsity © The Author(s). 2020 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulatio
Data Loading...
