Blind Multichannel Deconvolution and Convolutive Extensions of Canonical Polyadic and Block Term Decompositions

Sørensen, Mads Sølvsten; Eeghem, Frederik Van

doi:10.1109/tsp.2017.2706183

Cited by 24 publications

(26 citation statements)

References 39 publications

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“…in [17], [10], [34]. In particular, an algebraic method for tensors with a block-Toeplitz factor has been introduced in [37], [36]. Here, we will extend this result and consider algebraic methods for tensors with at least two block-Hankel factors.…”

Section: Introductionmentioning

confidence: 94%

Tensor Decompositions With Several Block-Hankel Factors and Application in Blind System Identification

Eeghem

Sørensen

2017

IEEE Trans. Signal Process.

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Several applications in biomedical data processing, telecommunications or chemometrics can be tackled by computing a structured tensor decomposition. In this paper, we focus on tensor decompositions with two or more block-Hankel factors, which arise in blind multiple-input-multipleoutput (MIMO) convolutive system identification. By assuming statistically independent inputs, the blind system identification problem can be reformulated as a Hankel structured tensor decomposition. By capitalizing on the available block-Hankel and tensorial structure, a relaxed uniqueness condition for this structured decomposition is obtained. This condition is easy to check, yet very powerful. The uniqueness condition also forms the basis for two subspace-based algorithms, able to blindly identify linear underdetermined MIMO systems with finite impulse response.

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Section: Introductionmentioning

confidence: 94%

Tensor Decompositions With Several Block-Hankel Factors and Application in Blind System Identification

Eeghem

Sørensen

2017

IEEE Trans. Signal Process.

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“…Shi first applied the inertia weight ω to the PSO algorithm. e inertia weight directly affects the update speed of particles and the convergence performance of the algorithm [12,15]:…”

Section: Adaptive Particle Swarm Algorithm Formentioning

confidence: 99%

Research on the Fault Feature Extraction Method of Rotor Systems Based on GAW-PSO

Miao

Zhao

Wang

2020

Mathematical Problems in Engineering

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In order to solve the problem of blind separation of signals from dynamic hybrid rotor systems, this paper proposed an improved adaptive inertial weight particle swarm optimization method based on genetic mechanism. The method takes the negative entropy of separated signal as the objective function and adaptively adjusts the inertia weight according to the difference of particle fitness, thus reducing the number of invalid iterations. At the same time, genetic hybridization mechanism was introduced to increase population diversity and facilitate the processing of dynamic mixed signals. The orthogonal matrix is expressed as a parameterized form, which can reduce the complexity of the algorithm. The simulation results showed that the performance of the proposed method is better than that of the traditional method for blind separation of dynamic hybrid analog mechanical signals. It can separate the actual dynamic rotor system signals and achieve the purpose of fault feature extraction.

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“…In [68] coupled decompositions yield algebraic uniqueness conditions and linear algebra based algorithms for tensor completion (each of the decompositions takes care of one fully observed subtensor). Noteworthy is also a connection between convolutive extensions of CPD and "instantaneous" coupled CPD [69].…”

Section: Example 16 (Gps)mentioning

confidence: 99%

Numerical Optimization-Based Algorithms for Data Fusion

Vervliet

Lathauwer

2019

Data Handling in Science and Technology

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Combining various sources of information to discover hidden patterns is key in data analysis. These sources can often be represented as matrices and/or multiway arrays, or tensors, which can be factorized jointly, e.g. as sums of simple terms, to gain insight into the data. In this chapter, an overview of (the rationale behind) numerically wellfounded optimization techniques based on a Gauss-Newton framework is given, which has superior convergence properties and allows all multilinear structure to be exploited. Prior knowledge in the form of parametric, box or soft constraints as well as regularization can be incorporated easily. We show how matrices and/or tensors can be coupled through (partially) shared factors or through common underlying variables. The framework is further extended to more general divergences allowing more suitable statistical assumptions. Finally, as tensor problems become large-scale quickly, due to the curse of dimensionality, techniques used to alleviate or overcome this curse are discussed.

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Blind Multichannel Deconvolution and Convolutive Extensions of Canonical Polyadic and Block Term Decompositions

Cited by 24 publications

References 39 publications

Tensor Decompositions With Several Block-Hankel Factors and Application in Blind System Identification

Tensor Decompositions With Several Block-Hankel Factors and Application in Blind System Identification

Research on the Fault Feature Extraction Method of Rotor Systems Based on GAW-PSO

Numerical Optimization-Based Algorithms for Data Fusion

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