Browsing by Author "Tichavský, Petr"
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- ItemCramer-Rao Bounds for Complex-Valued Independent Component Extraction: Determined and Piecewise Determined Mixing Models(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA, 2020-01-01) Kautský,Václav; Koldovský, Zbyněk; Tichavský, Petr; Zarzoso, VicenteBlind source extraction (BSE) aims at recovering an unknown source signal of interest from the observation of instantaneous linear mixtures of the sources. This paper presents Cramer-Rao lower bounds (CRLB) for the complex-valued BSE problem based on the assumption that the target signal is independent of the other signals. The target source is assumed to be non-Gaussian or non-circular Gaussian while the other signals (background) are circular Gaussian or non-Gaussian. The results confirm some previous observations known for the real domain and yield new results for the complex domain. Also, the CRLB for independent component extraction (ICE) is shown to coincide with that for independent component analysis (ICA) when the non-Gaussianity of background is taken into account. Second, we extend the CRLB analysis to piecewise determined mixing models, where the observed signals are assumed to obey the determined mixing model within short blocks where the mixing matrices can be varying from block to block. This model has applications, for instance, when separating dynamic mixtures. Either the mixing vector or the separating vector corresponding to the target source is assumed to be constant across the blocks. The CRLBs for the parameters of these models bring new performance limits for the BSE problem.
- ItemFast And Accurate Methods Of Independent Component Analysis: A Survey(Kybernetika, 2011-01-01) Tichavský, Petr; Koldovský, ZbyněkThis paper presents a survey of recent successful algorithms for blind separation of determined instantaneous linear mixtures of independent sources such as natural speech or biomedical signals. These algorithms rely either on non-Gaussianity, nonstationarity, spectral diversity, or on a combination of them. Performance of the algorithms will be demonstrated on separation of a linear instantaneous mixture of audio signals (music, speech) and on artifact removal in electroencephalogram (EEG).
- ItemPerformance Bound for Blind Extraction of Non-gaussian Complex-valued Vector Component from Gaussian Background(2019-01-01) Kautský, Václav; Koldovský, Zbyněk; Tichavský, PetrIndependent Vector Extraction aims at the joint blind source extraction of K dependent signals of interest (SOI) from K mixtures (one signal from one mixture). Similarly to Independent Component/Vector Analysis (ICA/IVA), the SOIs are assumed to be independent of the other signals in the mixture. Compared to IVA, the (de-)mixing IVE model is reduced in the number of parameters for the extraction problem. The SOIs are assumed to be non-Gaussian or noncircular Gaussian, while the other signals are modeled as circular Gaussian. In this paper, a Cramér-Rao-Induced Bound (CRIB) for the achievable Interference-to-Signal Ratio (ISR) is derived for IVE. The bound is compared with similar bounds for ICA, IVA, and Independent Component Extraction (ICE). Numerical simulations show a good correspondence between the empirical results and the theory.