Extraction of Independent Vector Component from Underdetermined Mixtures through Block-wise Determined Modeling

Koldovsky, Zbynek; Málek, Jiřı́; Janský, Jakub

doi:10.1109/icassp.2019.8683431

Cited by 14 publications

(13 citation statements)

References 15 publications

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“…There have been few time-varying mixing models considered in the previous BSS literature; see, e.g., [17], [18] for BSS models with a linearly changing mixing matrix. Recently, Piecewise Determined Mixing models (PDM) assume that the mixture is determined and locally obeys the standard mixing model within specified time intervals [19]. The mixing matrix can be changing from interval to interval, which approximates the dynamic mixing.…”

Section: B Mixing Models For Dynamic Conditionsmentioning

confidence: 99%

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Auxiliary Function-Based Algorithm for Blind Extraction of a Moving Speaker

Janský¹,

Koldovsky²,

Málek³

et al. 2020

Preprint

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Independent Vector Extraction (IVE) is a modification of Independent Vector Analysis (IVA) for Blind Source Extraction (BSE) to a setup in which only one source of interest (SOI) should be separated from a mixture of signals observed by microphones. The fundamental assumption is that the SOI is independent of the other signals. IVE shows reasonable results; however, its basic variant is limited to static sources. To extract a moving source, IVE has recently been extended by considering the Constant Separating Vector (CSV) mixing model. It enables us to estimate a separating filter that extracts the SOI from a wider spatial area through which the source has moved. However, only slow gradient-based algorithms were proposed in the pioneering papers on IVE and CSV. In this paper, we experimentally verify the applicability of the CSV mixing model and propose new IVE methods derived by modifying the auxiliary function-based algorithm for IVA. Piloted Variants are proposed as well for the methods with partially controllable global convergence. The methods are verified under reverberant and noisy conditions using model-based as well as real-world acoustic impulse responses. They are also verified within the CHiME-4 speech separation and recognition challenge. The experiments corroborate the applicability of the CSV mixing model for the blind moving source extraction as well as the improved convergence of the proposed algorithms.

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Section: B Mixing Models For Dynamic Conditionsmentioning

confidence: 99%

“…However, the number of parameters can further be reduced, e.g., by assuming that some parameters are constant over the intervals of data. This way, Constant Mixing/Separating Vector (CMV/CSV) models have been considered in [19]. 3 .…”

Section: Contributionmentioning

confidence: 99%

Auxiliary Function-Based Algorithm for Blind Extraction of a Moving Speaker

Janský¹,

Koldovsky²,

Málek³

et al. 2020

Preprint

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“…In this paper, we focus on the BSE problem where the SOI should be extracted based on the assumption of its independence from the background, a problem closely related to ICA. We compute Cramér-Rao Lower Bounds (CRLB) in order to analyze performance limitations of three mixing models, two of which were only recently considered in the literature [3]. The resulting bounds are compared between each other and also with the similar bound for the standard ICA.…”

Section: Problem Statementmentioning

confidence: 99%

“…CSV involves a moving SOI (varying mixing vector) under the assumption that a constant separating vector such that extracts the signal from all blocks exists. These models have been considered for the first time in [3], where they were applied to blind audio source extraction. This paper provides their theoretical analysis through the CRLB theory.…”

Section: Problem Statementmentioning

confidence: 99%

“…To validate the bounds for CMV and CSV, both are compared with empirical results achieved by block-wise versions of OGICE introduced in [3]. The methods will be jointly referred to as BOGICE (in [3], BOGICE a is the variant for CMV while BOGICE w is for CSV). It should be noted that no other methods for CMV/CSV currently exist in the literature to our best knowledge.…”

Section: Piecewise Determined Mixtures With Circular Gaussian Backgroundmentioning

confidence: 99%

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

Kautský,

Koldovský,

Tichavský

et al. 2019

Preprint

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This paper presents Cramér-Rao Lower Bound (CRLB) for the complexvalued 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 noncircular 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. 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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