Optimization of Signal Space Separation for Optically Pumped Magnetometer in Magnetoencephalography

Wang, Ruonan; Wu, Huanqi; Liang, Xiaoyu; Cao, Fuzhi; Xiang, Min; Gao, Yang; Ning, Xiaolin

doi:10.1007/s10548-023-00957-w

Cited by 6 publications

(13 citation statements)

References 27 publications

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“…Nor is the purpose of this work to describe how one may optimize SSS for a particular OPM system. That is now described elsewhere (Holmes et al, 2023; Nurminen et al, 2023; Wang et al, 2023; Zhdanov et al, 2023). As such, we did not explore the many ways in which the SSS method could have been stabilized.…”

Section: Discussionmentioning

confidence: 86%

“…The formulation presented above can be equivalently represented in a single matrix multiplication with an oblique projection matrix by utilising the fact that the parameter estimates ( β in ) of column wise partitioned matrices can be computed compactly (Baksalary & Baksalary, 2007) Where R out defines the projection orthogonal to the external space Now we can define the modelled data in a single oblique projection This projection is not guaranteed to be stable for all types of MEG systems (as it is an oblique projection) and can be very sensitive to white noise if the condition number (ratio of largest to smallest singular values) of the harmonic matrix ( H ) is high. Typically, in SSS this is addressed by optimising the harmonics in the basis set (Wang et al, 2023) or by optimising the system so that the resulting basis set will always be well conditioned (Zhdanov et al, 2023).…”

Section: Theorymentioning

confidence: 99%

“…Software based correction of motion artefacts and environmental interference is a key (and currently unresolved) issue in the development of wearable OPM systems (Brookes et al, 2021; Ding et al, 2023; Hill et al, 2022; Holmes et al, 2023; Mellor et al, 2021; Nardelli et al, 2020; Rea et al, 2021; Seymour et al, 2021, 2022; Tierney et al, 2021; Wang et al, 2023). Thankfully, multipole models of magnetic field are uniquely suited for suppressing the interference encountered in this scenario (Tierney et al, 2022).…”

Section: Introductionmentioning

confidence: 99%

“…For instance, purely radial or purely tangential sensor arrays will not result in a stable multipole model (Nurminen et al, 2010; Tierney et al, 2022). As such, careful optimisation of the model’s harmonic order or substantial numerical regularisation may be required (Wang et al, 2023).…”

Section: Introductionmentioning

confidence: 99%

“…This projection is not guaranteed to be stable for all types of MEG systems (as it is an oblique projection) and can be very sensitive to white noise if the condition number (ratio of largest to smallest singular values) of the harmonic matrix (𝑯) is high. Typically, in SSS this is addressed by optimising the harmonics in the basis set (Wang et al, 2023) or by optimising the system so that the resulting basis set will always be well conditioned (Zhdanov et al, 2023).…”

mentioning

confidence: 99%

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Adaptive multipole models of OPM data

Tierney,

Seedat,

Pier

et al. 2023

Preprint

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Multipole expansions have been used extensively in the Magnetoencephalography (MEG) literature for mitigating environmental interference and modelling brain signal. However, their application to Optically Pumped Magnetometer (OPM) data is challenging due to the wide variety of existing OPM sensor and array designs. We therefore explore how such multipole models can be adapted to provide stable models of brain signal and interference across OPM systems. Firstly, we demonstrate how prolate spheroidal (rather than spherical) harmonics can provide a compact representation of brain signal when sampling on the scalp surface with as few as 100 channels. We then introduce a type of orthogonal projection incorporating this basis set, the Adaptive Multipole Models (AMM), which provides robust interference rejection across systems, even in the presence of spatially structured nonlinearity errors. This projection is always stable, as it is an orthogonal projection, and will only ever decrease the white noise in the data. However, for array designs that are suboptimal for spatially separating brain signal and interference, this method can remove brain signal components. We contrast these properties with the more typically used multipole expansion, Signal Space Separation (SSS), which never reduces brain signal amplitude but is less robust to the effect of sensor nonlinearity errors on interference rejection and can increase noise in the data if the system is sub-optimally designed (as it is an oblique projection). We conclude with an empirical example utilizing AMM to maximize signal to noise ratio (SNR) for the stimulus locked neuronal response to a flickering visual checkerboard in a 128-channel OPM system and demonstrate up to 40dB software shielding in real data.

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Section: Discussionmentioning

confidence: 86%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Adaptive multipole models of OPM data

Tierney,

Seedat,

Pier

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

Adaptive multipole models of optically pumped magnetometer data

Tierney,

Seedat,

St Pier

et al. 2024

Human Brain Mapping

View full text Add to dashboard Cite

Multipole expansions have been used extensively in the Magnetoencephalography (MEG) literature for mitigating environmental interference and modelling brain signal. However, their application to Optically Pumped Magnetometer (OPM) data is challenging due to the wide variety of existing OPM sensor and array designs. We therefore explore how such multipole models can be adapted to provide stable models of brain signal and interference across OPM systems. Firstly, we demonstrate how prolate spheroidal (rather than spherical) harmonics can provide a compact representation of brain signal when sampling on the scalp surface with as few as 100 channels. We then introduce a type of orthogonal projection incorporating this basis set. The Adaptive Multipole Models (AMM), which provides robust interference rejection across systems, even in the presence of spatially structured nonlinearity errors (shielding factor is the reciprocal of the maximum fractional nonlinearity error). Furthermore, this projection is always stable, as it is an orthogonal projection, and will only ever decrease the white noise in the data. However, for array designs that are suboptimal for spatially separating brain signal and interference, this method can remove brain signal components. We contrast these properties with the more typically used multipole expansion, Signal Space Separation (SSS), which never reduces brain signal amplitude but is less robust to the effect of sensor nonlinearity errors on interference rejection and can increase noise in the data if the system is sub‐optimally designed (as it is an oblique projection). We conclude with an empirical example utilizing AMM to maximize signal to noise ratio (SNR) for the stimulus locked neuronal response to a flickering visual checkerboard in a 128‐channel OPM system and demonstrate up to 40 dB software shielding in real data.

show abstract