A review of second‐order blind identification methods

Pan, Yan; Matilainen, Markus; Taskinen, Sara; Nordhausen, Klaus

doi:10.1002/wics.1550

Cited by 26 publications

(11 citation statements)

References 92 publications

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“…Therefore, we suggest another approach which combines the three nonstationarity measures (3), ( 4) and (5). Denote from now on M m = M 1 , M v = M 2 and M τ = M 3 .…”

Section: Combination Of Methodsmentioning

confidence: 99%

“…The stationary components are identifiable when the components follow a second-order source separation (SOS) model or a stationary independent time series model. For details see for example [5]. In that case methods such as AMUSE [28,29], SOBI [30,1], gSOBI [31] or gJADE [32] can be applied to the identified stationary subspace.…”

Section: Practical Issues and Identifiability Of Componentsmentioning

confidence: 99%

“…In nonstationary source separation (NSS), as defined in [2], the variances of uncorrelated sources are allowed to change over time. For a recent review of these and other variants of BSS, see [3,4,5].…”

Section: Introductionmentioning

confidence: 99%

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Stationary subspace analysis based on second-order statistics

Flumian¹,

Matilainen²,

Nordhausen³

et al. 2021

Preprint

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In stationary subspace analysis (SSA) one assumes that the observable p-variate time series is a linear mixture of a k-variate nonstationary time series and a (p − k)-variate stationary time series. The aim is then to estimate the unmixing matrix which transforms the observed multivariate time series onto stationary and nonstationary components. In the classical approach multivariate data are projected onto stationary and nonstationary subspaces by minimizing a Kullback-Leibler divergence between Gaussian distributions, and the method only detects nonstationarities in the first two moments. In this paper we consider SSA in a more general multivariate time series setting and propose SSA methods which are able to detect nonstationarities in mean, variance and autocorrelation, or in all of them. Simulation studies illustrate the performances of proposed methods, and it is shown that especially the method that detects all three types of nonstationarities performs well in various time series settings. The paper is concluded with an illustrative example.

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“…Therefore, we suggest another approach which combines the three nonstationarity measures (3), ( 4) and (5). Denote from now on M m = M 1 , M v = M 2 and M τ = M 3 .…”

Section: Combination Of Methodsmentioning

confidence: 99%

Section: Practical Issues and Identifiability Of Componentsmentioning

confidence: 99%

See 1 more Smart Citation

Stationary subspace analysis based on second-order statistics

Flumian¹,

Matilainen²,

Nordhausen³

et al. 2021

Preprint

Self Cite

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show abstract

“…Blind source separation (BSS) consists of the extraction of source signals from their observed mixtures without prior knowledge of the mixing matrix or its inputs. BSS is widely used in many signal processing applications, and a plethora of works have been devoted to develop solutions in different contexts and under different mixing models, e.g., [1][2][3][4][5][6][7]. In particular, second order statistics based methods are highly regarded due to their low computation load and efficiency to separate temporally coherent (colored) sources.…”

Section: Introductionmentioning

confidence: 99%

“…However, in many applications the measurements are affected by impulsive noise or outliers, e.g., [21][22][23], in which context standard methods fail to achieve the BSS. To deal with impulsive noise, some authors have proposed robust batch BSS algorithms, e.g., [7,[14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A New Robust Adaptive Algorithm for Second Order Blind Source Separation

Bekhtaoui

Abed-Meraim

Meche

et al. 2022

ENPESJ

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This paper deals with the adaptive blind source separation problem in presence of impulsive noise. New algorithms extending the well known SOBI method from batch to adaptive scheme are introduced. At first, the standard Gaussian noise case is considered, leading to our first algorithm referred to as Adaptive SOBI (A-SOBI). Later on, a robust version of A-SOBI, referred to as RA-SOBI is derived to handle the impulsive noise case. RA-SOBI relies on robust subspace tracking for the whitening stage together with robust correlation estimation for the separation stage. All proposed algorithms are of relatively low complexity and allow to achieve good separation quality as illustrated by our simulation results.

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Self‐gated free‐running 5D whole‐heart MRI using blind source separation for automated cardiac motion extraction

Montón Quesada,

Ogier,

Ishida

et al. 2024

Magnetic Resonance in Med

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PurposeTo compare two blind source separation (BSS) techniques to principal component analysis and the electrocardiogram for the identification of cardiac triggers in self‐gated free‐running 5D whole‐heart MRI. To ascertain the precision and robustness of the techniques, they were compared in three different noise and contrast regimes.MethodsThe repeated superior–inferior (SI) projections of a 3D radial trajectory were used to extract the physiological signals in three cardiac MRI cohorts: (1) 9 healthy volunteers without contrast agent injection at 1.5T, (2) 30 ferumoxytol‐injected congenital heart disease patients at 1.5T, and (3) 12 gadobutrol‐injected patients with suspected coronary artery disease at 3T. Self‐gated cardiac triggers were extracted with the three algorithms (principal component analysis [PCA], second‐order blind identification [SOBI], and independent component analysis [ICA]) and the difference with the electrocardiogram triggers was calculated. PCA and SOBI triggers were retained for image reconstruction. The image sharpness was ascertained on whole‐heart 5D images obtained with PCA and SOBI and compared among the three cohorts.ResultsSOBI resulted in smaller trigger differences in Cohorts 1 and 3 compared to PCA (p < 0.01) and in all cohorts compared to ICA (p < 0.04). In Cohorts 1 and 3, the sharpness increased significantly in the reconstructed images when using SOBI instead of PCA (p < 0.03), but not in Cohort 2 (p = 0.4).ConclusionWe have shown that SOBI results in more precisely extracted self‐gated triggers than PCA and ICA. The validation across three diverse cohorts demonstrates the robustness of the method against acquisition variability.

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A review of second‐order blind identification methods

Cited by 26 publications

References 92 publications

Stationary subspace analysis based on second-order statistics

Stationary subspace analysis based on second-order statistics

A New Robust Adaptive Algorithm for Second Order Blind Source Separation

Self‐gated free‐running 5D whole‐heart MRI using blind source separation for automated cardiac motion extraction

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