On the Cramér-Rao Bound for Estimating the Mixing Matrix in Noisy Sparse Component Analysis

Zayyani, Hadi; Babaie‐Zadeh, Massoud; Haddadi, Farzan; Jutten, Christian

doi:10.1109/lsp.2008.2003989

Cited by 8 publications

(2 citation statements)

References 16 publications

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“…The UBSS problem is more common and challenging, and has become a research hotspot in recent years [7][8][9][10]. Sparse component analysis (SCA) is one of the methods to solve the UBSS problem [11][12][13][14]. If the source signals are sufficiently sparse, the received signals are characterised by line clustering.…”

Section: Introductionmentioning

confidence: 99%

Mixing matrix estimation in UBSS based on homogeneous polynomials

Bin

2018

IET signal process.

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An algorithm is proposed for mixing matrix estimation in underdetermined blind source separation (UBSS) based on homogeneous polynomials representation, in order to blindly identify a mixing matrix in the case where the source signal is insufficiently sparse. First, the observed signal subspaces (hyperplanes) are identified by polynomial fitting, differentiation, and spectral clustering. Then, the intersection lines between clustering planes are estimated by using normal vectors of each subspace, which are finally proved to be column vectors of the mixing matrix up to scaling and ordering. Based on the algebraicgeometric theory, the proposed algorithm can improve the accuracy of mixing matrix estimation, without being influenced by convergence. Simulation results indicate that the proposed algorithm has higher estimation accuracy than traditional algorithms. Additionally, the single-source and multi-source points of the source signal can be detected simultaneously, which increases the robustness of the algorithm.

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Section: Introductionmentioning

confidence: 99%

Mixing matrix estimation in UBSS based on homogeneous polynomials

Bin

2018

IET signal process.

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“…We compute BCRB for both non-blind and blind CS, where in the latter, we do not know the measurement matrix in advance. In a related direction of research, a CRB is obtained for mixing matrix estimation in Sparse Component Analysis (SCA) [8].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Cramér-Rao Bound for Noisy Non-Blind and Blind Compressed Sensing

Zayyani,

Babaie-Zadeh,

Jutten

2010

Preprint

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In this paper, we address the theoretical limitations in reconstructing sparse signals (in a known complete basis) using compressed sensing framework. We also divide the CS to non-blind and blind cases. Then, we compute the Bayesian Cramer-Rao bound for estimating the sparse coefficients while the measurement matrix elements are independent zero mean random variables. Simulation results show a large gap between the lower bound and the performance of the practical algorithms when the number of measurements are low.

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A Mixing Matrix Estimation Algorithm for the Time-Delayed Mixing Model of the Underdetermined Blind Source Separation Problem

Chen

Gao

et al. 2018

Circuits Syst Signal Process

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On the Cramér-Rao Bound for Estimating the Mixing Matrix in Noisy Sparse Component Analysis

Cited by 8 publications

References 16 publications

Mixing matrix estimation in UBSS based on homogeneous polynomials

Mixing matrix estimation in UBSS based on homogeneous polynomials

Bayesian Cramér-Rao Bound for Noisy Non-Blind and Blind Compressed Sensing

A Mixing Matrix Estimation Algorithm for the Time-Delayed Mixing Model of the Underdetermined Blind Source Separation Problem

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