Blind source separation/extraction (BSS/BSE) methods are widely applicable, from wireless communication to cosmic explorations. They are subsets of blind signal processing, used in original source waveform estimation, without relying on transmission media characteristics or exploiting pilot or training signals.

Independent component analysis (ICA) is a well-known technology for the implementation of BSS/BSE. With ICA, detecting all components via forcing independency constraints is the objective; however, the paper discusses subsets of ICA where the extraction of one independent component, the source of interest (SOI), is preferred.

This is a typical, well-structured classical scientific paper. The introduction explains “one independent component” separation and its contrast with ICA. It briefly expresses many variants of ICA and their drawbacks, and especially concern with the Gaussianity. In describing the contribution of the paper, as the main trend, independent component extraction (ICE) is defined. By introducing a re-parametrization mechanism, permutation ambiguity and region of convergence (ROC) detection are counted as reasons for deviated SOI extraction. The optimized automatic selection of parameters for the gradient algorithms and independent vector extraction (IVE) technique is proposed to combat the impairments.

Developing their ideas, the details of forming ICE by matrix-based notations and using the ICA lemmas are presented. Single target column decomposition is featured by considering the mixing matrix; next, the paper analyzes the ambiguity of the solution, related statistical discussions, the influence of background signal Gaussinity, and the avoidance of orthogonality constraints in ICE. The following section provides two algorithms: an orthogonal constrained gradient-ascent ICE algorithm and an ICE algorithm for the automatic selection of an optimization parameter. Along with designing the algorithms, the related theoretical math is sufficiently considered.

Independent vector analysis (IVA) is introduced, which is an extension of ICE, with the main aim of separating the *K* independent vector component. IVE is the ICE version of IVA, which, by re-parametrization of each mixing matrix, tries to extract just one favorite independent vector component. After related theoretical discussion, the gradient algorithm for IVE is presented. In the simulation, the efficiency of the proposed ICE and IVE algorithms, along with other available ones, are compared.

The idea of a single independent source and a single IVE is definitely relevant to numerous practical applications. The authors could present a well-developed monograph. It is a good paper, definitely beneficial to scientists interested in the latest findings about BSS/BSE.