Block Coordinate Descent Algorithms for Auxiliary-Function-Based Independent Vector Extraction

• Published in: IEEE transactions on signal processing Vol. 69; pp. 3252 - 3267
• Main Authors: Ikeshita, Rintaro, Nakatani, Tomohiro, Araki, Shoko
• Format: Journal Article
• Language: English
• Published: New York IEEE 2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Blind source extraction; block coordinate descent method; Eigenvalues; generalized eigenvalue problem; independent component analysis; independent vector analysis; IP networks; Mathematical analysis; Noise measurement; Probabilistic logic; Random noise; Robustness (mathematics); Sensors; Signal processing algorithms; Source separation; Speech recognition; Transfer functions
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2021.3076884

In this paper, we address the problem of extracting all super-Gaussian source signals from a linear mixture in which (i) the number of super-Gaussian sources <inline-formula><tex-math notation="LaTeX">K</tex-math></inline-formula> is less than that of sensors <inline-formula><tex-math notation="LaTeX">M</tex-math></inline-formula>, and (ii) there are up to <inline-formula><tex-math notation="LaTeX">M - K</tex-math></inline-formula> stationary Gaussian noises that do not need to be extracted. To solve this problem, independent vector extraction (IVE) using a majorization minimization and block coordinate descent (BCD) algorithms has been developed, attaining robust source extraction and low computational cost. We here improve the conventional BCDs for IVE by carefully exploiting the stationarity of the Gaussian noise components. We also newly develop a BCD for a semiblind IVE in which the transfer functions for several super-Gaussian sources are given a priori. Both algorithms consist of a closed-form formula and a generalized eigenvalue decomposition. In a numerical experiment of extracting speech signals from noisy mixtures, we show that when <inline-formula><tex-math notation="LaTeX">K = 1</tex-math></inline-formula> in a blind case or at least <inline-formula><tex-math notation="LaTeX">K - 1</tex-math></inline-formula> transfer functions are given in a semiblind case, the convergence of our proposed BCDs is significantly faster than those of the conventional ones.