Cramér-Rao-Induced bound for interference-to-signal ratio achievable through non-Gaussian independent component extraction

Kautský, Václav; Koldovsky, Zbynek; Tichavský, Petr

doi:10.1109/camsap.2017.8313097

Cited by 6 publications

(4 citation statements)

References 12 publications

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“…A formal confirmation of this bound for the real-valued case has been proven recently in [5] through computing the CRLB for the ICE mixing model, that is, assuming that the mixing matrix is structured as described by (2) and that the background signals are Gaussian.…”

Section: Performance Boundsmentioning

confidence: 81%

“…( 3) is just a particular choice that guarantees that Ba = 0. The ICE formulation enables us to compute the CRLB as we did in [5] for the realvalued case and Gaussian background. The contribution here compared to [5] is that the bound is derived for the complex-valued case and it involves also the non-Gaussian background.…”

Section: Problem Statementmentioning

confidence: 99%

“…ICA has been used for blind separation of convolutive mixtures in the frequency domain [6], where the mixture is transformed into a set of complexvalued instantaneous mixtures (one mixture per frequency). The problem, called Frequency-Domain ICA (FDICA), is formally described by (5), however, m plays the role of the frequency bin index. When ICA is applied separately to each mixture, the indeterminacy of the order of separated component gives rise to the permutation problem [15] (the separated frequency components must be reordered in order to separate the signals in the frequency domain).…”

Section: Problem Statementmentioning

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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Section: Performance Boundsmentioning

confidence: 81%

Section: Problem Statementmentioning

confidence: 99%

Section: Problem Statementmentioning

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

View full text Add to dashboard Cite

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“…In ICE/IVE, the mixing matrix is assumed to have a special parameterization involving only the mixing and separating vectors corresponding to the SOI. It was shown that this structure is sufficient for the BSE task under the standard mixing models without bringing any limitation in terms of the achievable accuracy given by the Cramér-Rao bound [25], 1 The formal descriptions of the mixing models (3) and (2) coincide. Therefore, we will accept a convention that t denotes the index of a time instant or interval, while k stands for the index of the mixture.…”

Section: Blind Source Extractionmentioning

confidence: 99%

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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Orthogonally-Constrained Extraction of Independent Non-Gaussian Component from Non-Gaussian Background Without ICA

Koldovsky

Tichavský

2018

Latent Variable Analysis and Signal Separation

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Cramér-Rao-Induced bound for interference-to-signal ratio achievable through non-Gaussian independent component extraction

Cited by 6 publications

References 12 publications

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

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

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

Orthogonally-Constrained Extraction of Independent Non-Gaussian Component from Non-Gaussian Background Without ICA

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