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Abstract

Magnetoencephalogram (MEG) with high spatio-temporal resolution plays a crucial role in the field of functional imaging. Incorporating vector source modeling enables explicit estimation of triaxial current components, thereby mitigating reconstruction errors caused by orientation bias in scalar leadfield approximations. This directional precision enables accurate identification of epileptogenic zones and oscillatory network hubs, providing neurosurgeons with electrophysiologically validated targets. Vector beamformers, grounded in spatial filtering theory, provide computationally efficient solutions for large-scale sensor data and dynamic high-resolution analyses. However, a vector source requires a vector beamformer whose performance degrades under high noise, limited time samples, or strongly correlated sources due to sample covariance matrix singularity. In this study, we propose a vector Bayesian learning framework to enhance beamformer robustness by addressing covariance matrix singularity. Specifically, we model the vector source linear system with full positive-definite noise covariance structures and employ data-driven Bayesian learning to refine the sample covariance matrix. By leveraging sparsity priors on source distributions and data-driven, our method improves spatial focusing and temporal reconstruction accuracy. We validated the approach using simulated data across varying signal-to-noise ratios (SNR) and real 64-channel optically pumped magnetometer (OPM)-MEG datasets under diverse stimulus-evoked paradigms. Comparative evaluations demonstrate that our Bayesian learning-based framework achieves 18. 03% higher AUC compared to conventional beamformers while preserving millimeter-level spatial precision, outperforming existing benchmarks in both spatial localization accuracy and dynamic reconstruction fidelity for neuroscience and clinical applications. Our codes are publicly accessible at: https://github.com/gao815/VBNLBF.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/2924_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

https://github.com/gao815/VBNLBF

Link to the Dataset(s)

N/A

BibTex

@InProceedings{GaoTia_HighRes_MICCAI2025,
        author = { Gao, Tianyu and Liu, Kunye and Ma, Weikai and Gao, Yang and Ning, Xiaolin},
        title = { { High-Res Brain Source Imaging of MEG using a Vector Bayesian Beamformer with Noise learning } },
        booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
        year = {2025},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 15972},
        month = {September},
        page = {265 -- 274}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    This paper introduces a novel hierarchical Bayesian beamforming model for vector source inference in MEG data, specifically the method introduces a positive semi-definite structured covariance in the source term, which in combination with sparsity priors and noise covariance modelling, is shown to demonstrate accurate spatial and temporal reconstructions on simulated data and plausible results on real data.

  • Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

    The primary novelty comes from the combination of positive-definite noise modelling and introducing a block diagonal structure for the source covariance, with a voxelwise 3x3 positive semi-definite matrix, which is solved for by a convex updating strategy. These seem to effectively address the issues caused by singularity in the sample covariance matrix. The approach seems elegant, does not require learning and there is no mention of hyperparameter tuning required.

    The experimental results on simulated data seem very promising, it seems to be capable of robust inference on data with a variety of different signal to noise ratios and in both white and mixed white and correlated noise.

  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.

    Although the paper is generally well presented, it is still quite dense and there are some parts that are a little tricky to follow (partly given the condensed format of the conference and the level of mathematics). I don’t feel that Fig 1 c adds a lot to the explanation of the paper, and perhaps this can be dropped to make space for a derivation of the NLL (eq 1) and the source covariance updates (which in Fig 1 use Q which is not defined in the text). Moreover, I’m not familiar with the term “Grounded” in this case, and I can’t find it clearly defined here or in reference 14. I suggest the authors clearly define their terminology to help the reader follow the argument of the mathematics.

    How computationally expensive is inference? What are the memory requirements? Are there hyperparameters that are required to be tuned, and if so, how is this done?

    It would have been instructive to show the results of any of the other methods on the real dataset for comparison.

  • Please rate the clarity and organization of this paper

    Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not mention open access to source code or data but provides a clear and detailed description of the algorithm to ensure reproducibility.

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html

    The sentence “The trace tr(Σsi) regulates source strength, providing a differentiable foundation for optimization.” is a bit nebulous.

    Why is the “mixed” noise not just called “correlated” - are the noise components not additive?

    I’d highly recommend the authors to release their implementation.

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (5) Accept — should be accepted, independent of rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    The work is novel, principled and is demonstrated to be effective.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    N/A

  • [Post rebuttal] Please justify your final decision from above.

    N/A



Review #2

  • Please describe the contribution of the paper

    The paper proposes a serialized Bayesian-learning and beamforming approach for solving inverse problem in MEG recordings. The contribution of the paper is significant in the field as the method can effectively learn both noise and neural sources as the same time.

  • Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
    1. The performance is strongly compared with the existing SOTA.
    2. The method itself seems solid.
  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
    1. There are typos and editorial errors in the paper (such as abstract [invesgiates instead of investigated], Page 5 [vectorization instead of Vectorization).
    2. Before equation (1), the authors mentioned \mathbf{B} and \mathbf{S} are temporally independent, while during the process of estimation such condition is violated. Please elaborate more.
    3. The paper in its current form is hard to follow. There are a lot of equations in the middle of the text. For example, in the last line of Page 3 and first line of Page 4, “The former enforces sparsity; the latter ensures fidelity.” which is not clear. There are similar misconceptions in other sentences. I would highly recommend authors to describe methods using algorithm environments (\alg in LaTeX). Also, you may use the appendix to support the conclusions (using mathematical equations).
    4. Clinical importance of the method if largely missing in the results/discussion section.
    5. Regarding the simulated data, it is not clear why the proposed method is not consistently performing better by increasing SNR (the SNR curve is somehow sinusoidal). Please elaborate and discuss more in the paper.
    6. As a minor suggestion, you may seek a more accurate title to reflect the significance of the proposed method.
  • Please rate the clarity and organization of this paper

    Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not provide sufficient information for reproducibility.

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html

    N/A

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (5) Accept — should be accepted, independent of rebuttal

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    The paper seems solid and holds clinical potentials. Also, the results are supported using fair comparisons with SOTA benchmarks.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    N/A

  • [Post rebuttal] Please justify your final decision from above.

    N/A



Review #3

  • Please describe the contribution of the paper

    This paper proposes a Bayesian framework for MEG source localization, specifically using sparse priors on source distributions. This is a timely contribution with the emergence of OPM-MEG as it presents new challenges not easily solved by existing source localization methods.

  • Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

    Overall, this paper is comprehensive and really well-written. This is a novel approach that shows clear advantages over current approaches, especially for low SNR settings. Given the emergence and popularity of OPM-MEG, this is both methodologically and clinically impactful. I can imagine this work being applied is several clinical and research settings to improve and/or corroborate previous findings.

  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
    1. The introduction is really well-written overall. But I think a little more info needs to be added to the intro and abstract about the performance. Specifically, what is being used to calculate the AUC and temporal correlation? What is the ground truth?
    2. In the results, I think LCMV source reconstruction should be added since it had the second lowest DLE. The simulation shows a clear advantage of the proposed framework, so it seems a visual in the empirical data would strengthen and solidify this.
    3. I do not see a mention of limitations for the proposed method.
  • Please rate the clarity and organization of this paper

    Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not mention open access to source code or data but provides a clear and detailed description of the algorithm to ensure reproducibility.

  • Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2025/en/REVIEWER-GUIDELINES.html

    While not necessary, it would be nice to provide a link to the code repository once this work is presented.

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.

    (6) Strong Accept — must be accepted due to excellence

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    This is a really comprehensive paper that justifies every decision and shows a clear, strong advantage of the proposed method compared to other current methods for MEG source localization. To me, there is nothing missing and the weaknesses I mentioned are minor.

  • Reviewer confidence

    Very confident (4)

  • [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

    N/A

  • [Post rebuttal] Please justify your final decision from above.

    N/A



Author Feedback

I would like to thank all the reviewers for their valuable comments and affirmations on this paper. Reviewer #1 We use an improved AUC calculation method proposed in this paper [1] to overcome the distortion of the classical AUC metric when the activations are small. Ground truth refers to the activation strength and location of the simulation source setting under noise-free conditions. The calculation details for each evaluation index can be found in the supplementary file. It should be emphasized that the classical beamformer method to calculate the covariance matrix only needs to use the sample covariance matrix which can be calculated immediately. The proposed method involves a large number of matrix inversion operations in the iterative update process, which sacrifices the computational efficiency to a certain extent, and is not a real-time imaging scheme. Reviewer #2 “The trace tr（Σsi） …” means that in the vector source condition, the magnitude of the activation intensity of the reaction ith source is characterized by the trace of the 3×3 matrix, which is different from the scalar source which only uses diagonal elements to characterize the activation intensity. Regarding the covariance matrix corresponding to the ith source of 3×3 is an differentiable foundation, the detailed derivation of the article can be found in the supplementary file. The noise components are indeed additive. Correlation refers to the noise of the correlated part of the sensor, and the two are not contradictory. Actually, Meg noise can be divided into environmental noise and brain background signal noise. Environmental noise includes colored noise of sensors and electromagnetic noise of external equipment. Brain background signal noise usually refers to the brain activity signal in the resting state, which is not our focus. But usually these physiological background signals are also related signals generated by a large number of neurons firing synchronously. Reviewer #3 We are sorry for our spelling mistakes. For Q2, sorry we didn’t make it clear, there are ways to talk about the temporal non-independence assumption [2]. May I ask where the article specifically refers to the violation of the assumption of time independence? Further discussion is welcome. “The former …” means the first term is a logarithmic constraint on the modulus of the covariance matrix, reflecting the expectation that the data covariance matrix elements are as sparse as possible, and the second term reflects the approximation of Σb to Cb. For example, when Cb is the identity matrix, the sparser Σb is, the value of the first term is smaller, but the likelihood term is larger. Therefore, the two terms of Eq. 1 need to adjust Σb to ensure the balance of sparsity and likelihood constraints, which is automatically achieved by data-driven. Why the SNR improved and why the AUC did not change much deserves further discussion. At present, we believe that by Eq. (6), the beamforming filter still involves the inverse operation of the data covariance matrix. This feature is present in all beamforming methods. As MNE and SLORETA methods belong to the norm constraint class, SNR has a significant impact on the performance of the two methods. When the SNR is high, the matrix is approximately singular. This is despite the fact that we achieve high accuracy data covariance matrix reduction via the Bayesian estimator. However, the approximate singular matrix inversion operation in (6) will cause an increase in error. However, the SNR of Meg system is usually <20dB in practice. For the confirmation of this point, it may be necessary to set the covariance matrix of the simulation source to full rank and explore whether the AUC index changes with the SNR under this simulation condition. [1] Evaluation of EEG localization methods using realistic simulations of interictal spikes. [2] Electromagnetic Source Imaging via Bayesian Modeling With Smoothness in Spatial and Temporal Domains.



Meta-Review

Meta-review #1

  • Your recommendation

    Provisional Accept

  • If your recommendation is “Provisional Reject”, then summarize the factors that went into this decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. You do not need to provide a justification for a recommendation of “Provisional Accept” or “Invite for Rebuttal”.

    N/A



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