Methods for Independent Component/Vector Extraction

We have recently revised the problem of Blind Source Extraction (BSE) where the goal is to extract one source of interest (SOI) from an observed mixture of signals, compared to Blind Source Separation (BSS) where the goal is to separate the mixture into all individual signal contained in it. We are focused on approaches based on independence, namely, on the assumption that the SOI is statistically independent of the other background signals.

We call our approach Independent Component Extraction (ICE). ICE has many things in common with Independent Component Analysis (ICA) and is related also to the Multidimensional ICA (also known as Independent Subspace Analysis). We decided to call it differently because ICE fits well with ICA (BSE generally involves also methods that do not perform signal extraction based on signals’ independence), but also because we plan to develop more generalizations that go beyond the standard ICA. For example, Independent Vector Extraction is an extension of ICE to the joint extraction of sources from a set of mixtures. IVE is thus a BSE variant of Independent Vector Analysis (IVA).

This page will collect our software outputs, that is, algorithms, codes of simulations, examples, etc.

Software outputs of Z. Koldovský and V. Kautský, “Quick Algorithms for Independent Vector Extraction and Analysis Based on Exact Newton-Raphson Optimization, ” arXiv:1910.10242[eess.SP]:

Quick algorithms for real-valued and complex-valued ICE/IVE, that is, QuickIVE-1 (Newton-Raphson optimization-based algorithm for ICE/IVE), QuickIVE-2 (Newton-Raphson optimization-based algorithm for ICE/IVE including the CSV mixing model extension assuming piecewise determined mixing models with constant separating vectors), and QuickIVA-1 a QuickIVA-2 for ICA/IVA (based on the symmetric and parallel extraction by QuickIVE-1 a QuickIVE-2, resp.): here

Software outputs of Z. Koldovský and P. Tichavský, “Gradient Algorithms for Complex Non-Gaussian Independent Component/Vector Extraction, Question of Convergence, ” submitted. arXiv:1803.10108[eess.SP]:

Gradient ICE Algorithms: here

Gradient IVE Algorithms (including a piloted version): here

Simulation of BSE comparing various ICE, IVE, BSE, ICA algorithms: here