On the two-step estimation of the cross-power spectrum for dynamical linear inverse problems

Vallarino, Elisabetta; Sommariva, Sara; Piana, Michele; Sorrentino, Alberto

doi:10.1088/1361-6420/ab67dc

Cited by 9 publications

(22 citation statements)

References 47 publications

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“…In fact, in [26] the authors used numerical simulations to compare the parameter that provides the best estimate of the power spectrum with the one that provides the best estimate of coherence and showed that the latter is in general two orders of magnitude smaller than the former. More recently, Vallarino et al [27] addressed an analogous problem via analytical computations, considering a simplified model. Specifically, under the assumption that the neural time series are realizations of white Gaussian processes, the authors proved that the parameter providing the best neural activity estimate is more than twice as large as the one providing the best estimate of the cross-power spectrum.…”

Section: Introductionmentioning

confidence: 99%

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The Role of Spectral Complexity in Connectivity Estimation

Vallarino

Sorrentino

Piana

et al. 2021

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The study of functional connectivity from magnetoecenphalographic (MEG) data consists of quantifying the statistical dependencies among time series describing the activity of different neural sources from the magnetic field recorded outside the scalp. This problem can be addressed by utilizing connectivity measures whose computation in the frequency domain often relies on the evaluation of the cross-power spectrum of the neural time series estimated by solving the MEG inverse problem. Recent studies have focused on the optimal determination of the cross-power spectrum in the framework of regularization theory for ill-posed inverse problems, providing indications that, rather surprisingly, the regularization process that leads to the optimal estimate of the neural activity does not lead to the optimal estimate of the corresponding functional connectivity. Along these lines, the present paper utilizes synthetic time series simulating the neural activity recorded by an MEG device to show that the regularization of the cross-power spectrum is significantly correlated with the signal-to-noise ratio of the measurements and that, as a consequence, this regularization correspondingly depends on the spectral complexity of the neural activity.

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Section: Introductionmentioning

confidence: 99%

“…, which corresponds to the optimal value of λ x in the case of white Gaussian signals [27]. The blue box in Figure 3 describes the inverse procedure to obtain an estimate of the cross-power spectrum and stresses the role of the regularization parameter in the two-step process.…”

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confidence: 99%

The Role of Spectral Complexity in Connectivity Estimation

Vallarino

Sorrentino

Piana

et al. 2021

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“…It is therefore not advised to use regularization-levels that have been optimized for the estimation of source power instead of source interactions. For [35] have demonstrated that the optimal regularization-level for interactions is lower than that for source-power, at least for the ridge inverse operator (see also [36]). Fig 4 also shows that for all three estimators and for all regularization-levels, suppression levels decrease with increasing interaction lag ϕ.…”

Section: Effectivenessmentioning

confidence: 99%

“…Thus, in [35] it was observed that estimation of brain interactions from MEG data requires less strong regularization than the reconstruction of the activity time-courses. In [36] this observation is formally investigated. Selection of the optimal rank of the projection operators remains an open question that can potentially yield interaction estimators with less bias and more powerful statistical hypothesis tests.…”

Section: Scope and Limitationsmentioning

confidence: 99%

Lag-invariant detection of interactions in spatially-extended systems using linear inverse modeling

Hindriks¹

2020

PLoS ONE

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Measurements on physical systems result from the systems’ activity being converted into sensor measurements by a forward model. In a number of cases, inversion of the forward model is extremely sensitive to perturbations such as sensor noise or numerical errors in the forward model. Regularization is then required, which introduces bias in the reconstruction of the systems’ activity. One domain in which this is particularly problematic is the reconstruction of interactions in spatially-extended complex systems such as the human brain. Brain interactions can be reconstructed from non-invasive measurements such as electroencephalography (EEG) or magnetoencephalography (MEG), whose forward models are linear and instantaneous, but have large null-spaces and high condition numbers. This leads to incomplete unmixing of the forward models and hence to spurious interactions. This motivated the development of interaction measures that are exclusively sensitive to lagged, i.e. delayed interactions. The drawback of such measures is that they only detect interactions that have sufficiently large lags and this introduces bias in reconstructed brain networks. We introduce three estimators for linear interactions in spatially-extended systems that are uniformly sensitive to all lags. We derive some basic properties of and relationships between the estimators and evaluate their performance using numerical simulations from a simple benchmark model.

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“…In order to analyze the distribution of noise energy from the levitation gap sensor across frequency domains, it can use Eq. (17) to get the power spectrum [36] of the gap sensor signal.…”

Section: B Effect Of Signal Noise From the Gap Sensor On The Levitatmentioning

confidence: 99%

Disturbance Rejection Control Using a Novel Velocity Fusion Estimation Method for Levitation Control Systems

Xia

Dou

2020

IEEE Access

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Magnetic levitation has been applied to maglev trains and magnetic suspension wind tunnel. However, there are some problems with the existing levitation control. For example, it is difficult to extract smooth velocity signals from the gap sensor with noise. The classical differentiator is susceptible to noise, which makes the levitation system sometimes vibrate. The accuracy and stability of levitation control need to be improved. The velocity fusion estimation method (VFE) is proposed to extract the velocity signal from the gap and acceleration sensor, which is theoretically derived to prove that it reduced the noise of the velocity signal. Then disturbance rejection control(DRC) is proposed that add VFE into classical levitation control. Because of the high-quality velocity signal and accelerometer's fast responsiveness, it makes DRC have many advantages. The advantages of using the proposed control structure are that it improved the control accuracy of the target gap and resisted disturbance effectively. Air-gap fluctuations in levitation systems can be reduced in transient pulse disturbance test, white noise disturbance test, and external force disturbance test when it applies the proposed control method. The effectiveness and advantages of the proposed control method are verified by the simulation and experiments.

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On the two-step estimation of the cross-power spectrum for dynamical linear inverse problems

Cited by 9 publications

References 47 publications

The Role of Spectral Complexity in Connectivity Estimation

The Role of Spectral Complexity in Connectivity Estimation

Lag-invariant detection of interactions in spatially-extended systems using linear inverse modeling

Disturbance Rejection Control Using a Novel Velocity Fusion Estimation Method for Levitation Control Systems

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