arXiv subjects

Václav Kautský

Publications and source records attributed to Václav Kautský.

5 recordsLinked to original sources

arXiv2022

Dynamic Independent Component Extraction with Blending Mixing Vector: Lower Bound on Mean Interference-to-Signal Ratio

This paper deals with dynamic Blind Source Extraction (BSE) from where the mixing parameters characterizing the position of a source of interest (SOI) are allowed to vary over time. We present a new source extraction model called CvxCSV which is a parameter-reduced modification of the recent Constant Separation Vector (CSV) mixing model. In CvxCSV, the mixing vector evolves as a convex combination of its initial and final values. We derive a lower bound on the achievable mean interference-to-signal ratio (ISR) based on the Cramér-Rao theory. The bound reveals advantageous properties of CvxCSV compared with CSV and compared with a sequential BSE based on independent component extraction (ICE). In particular, the achievable ISR by CvxCSV is lower than that by the previous approaches. Moreover, the model requires significantly weaker conditions for identifiability, even when the SOI is Gaussian.

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arXiv2022

Double Nonstationarity: Blind Extraction of Independent Nonstationary Vector/Component from Nonstationary Mixtures -- Algorithms

In this article, nonstationary mixing and source models are combined for developing new fast and accurate algorithms for Independent Component or Vector Extraction (ICE/IVE), one of which stands for a new extension of the well-known FastICA. This model allows for a moving source-of-interest (SOI) whose distribution on short intervals can be (non-)circular (non-)Gaussian. A particular Gaussian source model assuming tridiagonal covariance matrix structures is proposed. It is shown to be beneficial in the frequency-domain speaker extraction problem. The algorithms are verified in simulations. In comparison to the state-of-the-art algorithms, they show superior performance in terms of convergence speed and extraction accuracy.

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arXiv2021

Algorithm for Independent Vector Extraction Based on Semi-Time-Variant Mixing Model

A new algorithm for dynamic independent vector extraction is proposed. It is based on the mixing model where mixing parameters related to the source-of-interest (SOI) are time-variant while the separating parameters are time-invariant. A contrast function based on the quasi-likelihood approach is optimized using the Newton-Raphson approach. The update is computed without imposing the orthogonal constraint, and the orthogonality is enforced afterward. This yields an algorithm that is significantly faster than gradient-based algorithms while different from fixed-point methods, which are even faster. We show advantageous properties of the proposed algorithm compared to the fixed-point methods in an on-line processing regime where stable convergence to the SOI is the important issue. The effectiveness of the method is demonstrated in a speech extraction experiment with a dense microphone array.

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arXiv2021

Dynamic Independent Component/Vector Analysis: Time-Variant Linear Mixtures Separable by Time-Invariant Beamformers

A novel extension of Independent Component and Independent Vector Analysis for blind extraction/separation of one or several sources from time-varying mixtures is proposed. The mixtures are assumed to be separable source-by-source in series or in parallel based on a recently proposed mixing model that allows for the movements of the desired source while the separating beamformer is time-invariant. The popular FastICA algorithm is extended for these mixtures in one-unit, symmetric and block-deflation variants. The algorithms are derived within a unified framework so that they are applicable in the real-valued as well as complex-valued domains, and jointly to several mixtures, similar to Independent Vector Analysis. Performance analysis of the one-unit algorithm is provided; it shows its asymptotic efficiency under the given mixing and statistical models. Numerical simulations corroborate the validity of the analysis, confirm the usefulness of the algorithms in separation of moving sources, and show the superior speed of convergence and ability to separate super-Gaussian as well as sub-Gaussian signals.

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arXiv2019

Cramér-Rao Bounds for Complex-Valued Independent Component Extraction: Determined and Piecewise Determined Mixing Models

This paper presents Cramér-Rao Lower Bound (CRLB) for the complex-valued Blind Source Extraction (BSE) problem based on the assumption that the target signal is independent of the other signals. Two instantaneous mixing models are considered. First, we consider the standard determined mixing model used in Independent Component Analysis (ICA) where the mixing matrix is square and non-singular and the number of the latent sources is the same as that of the observed signals. The CRLB for Independent Component Extraction (ICE) where the mixing matrix is re-parameterized in order to extract only one independent target source is computed. 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 bring new results for the complex domain. Also, the CRLB for ICE is shown to coincide with that for ICA when the non-Gaussianity of background is taken into account. %unless the assumed sources' distributions are misspecified. Second, we extend the CRLB analysis to piecewise determined mixing models. Here, 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. However, 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 bounds for the BSE problem.

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