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Abstract

Magnetic particle imaging (MPI) is an emerging medical imaging modality that enables highly sensitive visualization of magnetic nanoparticles with high temporal resolution. However, variations in magnetic particle materials and field-free point trajectories require repeated system matrix recalibration, which is time-consuming and limits the efficiency and flexibility of MPI in practical applications. To address this challenge, we propose a trajectory-aware cross-paradigm transformer (TACPT) for efficient and accurate SM calibration. Leveraging the trajectory-dependent distribution of SM signals relative to FFPs, we introduce a trajectory-based encoding mechanism that embeds physically grounded positional priors derived from FFP trajectories into the transformer backbone. This design guides the network to focus on trajectory-relevant and information-dense regions. To further accommodate the complex structure of SM data, we develop a cross-paradigm feature interaction module that integrates FFT-based inter-channel modeling with spatial structure learning. These complementary representations are adaptively fused through a dynamic sparsity-gated mechanism, suppressing redundant responses and producing compact, discriminative SM representations. Experimental results demonstrate superior SM calibration and MPI reconstruction performance over existing methods, while reducing recalibration overhead without compromising fidelity to improve MPI system efficiency and flexibility. The code is publicly available at https://github.com/learning-TL/TACPTnet.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/1912_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

N/A

Link to the Dataset(s)

N/A

BibTex

@InProceedings{LiJin_TrajectoryAware_MICCAI2026,
        author = { Li, Jintao AND Zhang, Lizhi AND He, Xiaowei AND He, Shuaishuai AND Li, Shuangchen AND Shi, Bo AND Hou, Yuqing AND Guo, Hongbo},
        title = { { Trajectory-Aware Cross-Paradigm Transformers for Efficient System Matrix Calibration in Magnetic Particle Imaging } },
        booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
        year = {2026},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 16888},
        month = {September},
        page = {pending}
}

Reviews

Review #1

Please describe the contribution of the paper

This paper proposes TACPT-Net, a novel deep learning framework for efficient Magnetic Particle Imaging (MPI) system matrix calibration , which uniquely embeds physical priors into the Transformer backbone via a trajectory-aware encoding mechanism based on the Field-Free Point (FFP). It introduces a cross-paradigm feature interaction module to jointly capture FFT-based global channel dependencies and local spatial structural information , and effectively integrates these features using a dynamic sparsity-gated fusion block (via sparsemax) to achieve structured sparsity, preserving critical physical representations while adaptively suppressing redundant noise.
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 core innovation of this paper is its explicit physics-informed modeling, this paper cleverly embeds the physical characteristics of SM signal formation into the Transformer architecture. The Trajectory-Aware Encoding Branch (TAEB) explicitly models the relevance between the Field-Free Point (FFP) trajectory and voxels by assigning spatial distance-based importance weights, which provides a strong theoretical foundation and represents a highly novel approach to solving MPI calibration. Furthermore, the proposed Cross-Paradigm Feature Interaction Module (CP-FIM) effectively unites frequency-domain and spatial-domain analyses. Using Fast Fourier Transform (FFT) to process query and key embeddings to capture global channel correlation is an ingenious design that perfectly aligns with the inherent spectral characteristics of MPI signals. 2.The authors utilize the public OpenMPI dataset and conduct rigorous comparative tests across a wide variety of settings. The evaluation spans different nanoparticle materials (Synomag-D, Perimag), distinct FFP scanning trajectories (3D Lissajous, 2D Lissajous), and various upsampling ratios (2x, 4x), firmly validating the generalizability and robustness of the proposed framework.
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 current experimental evaluation relies entirely on phantom reconstructions and dataset-based quantitative metrics. While these experiments demonstrate the fundamental efficacy of the method, the absence of in vivo data or downstream clinical tasks makes it difficult to assess the model’s robustness against complex, real-world noise distributions and artifacts. This significantly limits the demonstration of the method’s actual clinical impact and translational potential. 2.Although the authors compare their method against several deep learning baselines (e. g. , SMRnet and TranSMS), the overall selection of baselines remains limited. Apart from these methods, the remaining comparisons are primarily with traditional techniques (e. g. , bicubic interpolation) or methods proposed several years ago. Such a setup does not adequately reflect the current state of the art. To provide a more convincing evaluation, it is recommended to include more recent and advanced approaches—both those specifically developed for MPI system matrix super-resolution and those from the broader natural image super-resolution field (e. g. , recent generative or diffusion-based models). This would allow for a more comprehensive and up-to-date assessment of the proposed method’s performance. 3.Marginal quantitative improvements relative to architectural complexity: While the proposed TACPT-Net achieves the best overall scores, the absolute quantitative gains over the best-performing baselines (e. g. , 3dISPAnet) are somewhat limited. For instance, the improvement in SSIM is roughly 1–2%, and the NRMSE reduction is about 10%. The authors should provide further discussion or visual evidence to justify whether these incremental metric gains translate to clinically meaningful differences in visual fidelity or diagnostic accuracy, justifying the added complexity of the cross-paradigm modules.
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 has provided an anonymized link to the source code, dataset, or any other dependencies.
Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?

N/A
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/2026/en/REVIEWER-GUIDELINES.html

1.I have checked the provided code, and there is a mathematical mismatch regarding the Trajectory Aware Encoding Branch (TAEB). Equation (1) in the paper formulates the distance penalty using a fourth-order distance metric ($||. . . ||_2^4 / s^4$), claiming this specific order prioritizes trajectory-related voxels. However, in TrajB. py , the distance is calculated using the standard 1st-order L2 norm (min_dist = torch. sqrt(. . . ) and then torch. exp(-lambda * normalized_dist)). Please clarify which version was actually used to produce the reported results and correct the manuscript/code accordingly to ensure scientific rigor. 2.In LaTeX, you can use the \titlerunning command to provide a shortened title, preventing the “Title Suppressed Due to Excessive Length” warning in the page headers.
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.

(3) Weak Reject — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

1.The integration of physics-informed priors (FFP trajectory) into a Transformer backbone via the Trajectory-Aware Encoding Branch (TAEB) is highly innovative. Moving away from purely data-driven models to a physics-aware architecture is a sensible and effective strategy for MPI calibration. 2.The Cross-Paradigm Feature Interaction Module (CP-FIM) is well-designed, cleverly utilizing FFT to capture global channel correlations while using spatial attention for local structures. 3.Critical Discrepancy Between Manuscript and Code: the mismatch regarding Equation 1.The paper claims a 4th-order distance metric is used to heavily penalize distant voxels, providing a physical justification for this choice. However, the provided source code (TrajB.py) clearly implements a standard 1st-order L2 norm. This raises concerns about the scientific rigor. 4.The absolute gains over existing baselines (e.g., 3dISPAnet) are marginal (e.g., ~1-2% in SSIM). Meanwhile, the manuscript lacks a detailed discussion on computational overhead (FLOPs, inference time). Furthermore, as seen in the code, the broadcasting method in TAEB poses a severe Out-of-Memory (OOM) risk for large FOV scaling. 5.Lack of In Vivo Validation: The evaluation is restricted to phantom data. Without in vivo or clinical downstream task validation, it is difficult to fully assess the model’s robustness against complex, real-world noise.
Reviewer confidence

Very confident (4)
[Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

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

I appreciate the authors’ detailed rebuttal and clarifications. However, the responses do not fully resolve the core concerns raised in the original review. Several important issues, including the claims of methodological novelty, insufficient experimental validation, and the reliance on relatively outdated comparison methods, remain inadequately addressed in the current submission. These concerns are still deferred to future work or discussion rather than being experimentally addressed in the current submission. Therefore, I maintain my original recommendation.

Review #2

Please describe the contribution of the paper

This paper proposes a Trajectory-Aware Cross-Paradigm Transformer (TACPT), a physics-informed deep learning framework designed to significantly enhance the efficiency of System Matrix (SM) calibration in Magnetic Particle Imaging (MPI). To address the time-intensive nature of traditional dense volumetric sampling, the authors developed a Trajectory-Aware Encoding Branch (TAEB) that embeds physically grounded positional priors—derived from the spatial relationship between voxels and the Field-Free Point (FFP) trajectory—directly into the transformer backbone. Furthermore, the model incorporates a Cross-Paradigm Feature Interaction Module (CP-FIM) that synergistically integrates FFT-based inter-channel dependencies with spatial structural modeling. These heterogeneous representations are adaptively fused via a Dynamic Sparsity-Gated Fusion Block (DSGFB) using a sparsemax operator to suppress redundant noise while preserving compact, informative SM responses. Experimental results demonstrate that TACPT-Net achieves superior reconstruction fidelity across diverse nanoparticle materials and scanning trajectories, effectively reducing recalibration overhead and facilitating more scalable and adaptable MPI deployments.
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.

This paper presents a novel Trajectory-Aware Cross-Paradigm Transformer (TACPT) to address the critical bottleneck of time-consuming System Matrix (SM) calibration in Magnetic Particle Imaging (MPI). The primary strength lies in the Trajectory-Aware Encoding Branch (TAEB), which effectively integrates physical priors by embedding voxel-wise distances to the Field-Free Point (FFP) trajectory into the transformer backbone, guiding the model toward information-dense regions. Furthermore, the introduction of a Cross-Paradigm Feature Interaction Module (CP-FIM)—combining FFT-based inter-channel modeling with spatial structural learning—coupled with a Dynamic Sparsity-Gated Fusion Block (DSGFB), allows for the adaptive suppression of redundant noise while preserving compact SM representations. The methodology is rigorously validated on the OpenMPI dataset across diverse nanoparticle materials and scanning trajectories, demonstrating superior reconstruction fidelity with an average relative nRMSE reduction of over 10% compared to existing state-of-the-art methods.
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.

Despite its technical merits, the paper exhibits certain weaknesses, primarily regarding the lack of computational complexity analysis and a limited discussion on clinical translation. While the model maintains a relatively small parameter count, the integration of Fast Fourier Transforms (FFT) within the CP-FIM and the iterative nature of the sparsemax-based gating in DSGFB may introduce significant inference latency compared to simpler CNN-based baselines like SRCNN. Furthermore, the evaluation relies heavily on standard metrics (nRMSE, PSNR, SSIM) without assessing reconstruction robustness against real-world hardware artifacts or patient motion, which are critical for demonstrating the proposed method’s actual clinical feasibility. Lastly, while the trajectory-aware encoding is a strong addition, the paper would benefit from a more rigorous comparison against emerging implicit neural representation (INR) techniques that have recently shown promise in similar medical imaging super-resolution tasks.
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 has provided an anonymized link to the source code, dataset, or any other dependencies.
Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?

N/A
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/2026/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 introduction of the Trajectory-Aware Encoding Branch (TAEB) is a highly original contribution, moving beyond generic super-resolution by embedding voxel-wise distances to the Field-Free Point (FFP) trajectory directly into the transformer’s positional embeddings. This physically grounded approach is complemented by the Cross-Paradigm Feature Interaction Module (CP-FIM), which effectively captures global inter-channel dependencies via FFT while maintaining spatial structural integrity. Furthermore, the use of a Dynamic Sparsity-Gated Fusion Block (DSGFB) with a sparsemax operator ensures compact, noise-resistant SM representations that align with the localized nature of MPI signals. Rigorous evaluation on the OpenMPI dataset demonstrates superior performance across diverse nanoparticle materials and trajectories, yielding a significant nRMSE reduction of over 10% and improved reconstruction fidelity compared to state-of-the-art methods.
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

The paper proposes TACPT - a trajectory-aware, physics-informed transformer architecture for efficient SM calibration in MPI. The central contribution is the explicit integration of FFP trajectory priors into the model via trajectory-aware positional encoding, combined with a feature interaction module that jointly models spectral and spatial dependencies with sparse gated fusion.
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 idea of incorporating trajectory-aware physical priors directly into a transformer architecture for system matrix calibration is interesting, novel and well-motivated. In particular, encoding voxel relevance based on the FFP trajectory and combining it with joint spectral-spatial modeling provides a more physically grounded alternative to existing purely data-driven super-resolution approaches. The framing of the prior is elegant and it proves useful downstream.

The paper is also easy to follow, generally well-framed, and key choices made by the authors are well-motivated.
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.

The claim of novelty in incorporating physical knowledge into SM calibration is overstated. TranSMS already integrates physics into the learning process via a data-consistency module that enforces adherence to the forward MPI signal model between low and high-resolution system matrices. In comparison, the current paper introduces a different form of physical integration (trajectory-aware priors), but the general idea of using a physics prior in SM calibration is not new, and this paper should be positioned as an extension of that idea rather than a fundamentally new direction.

The baseline comparison is incomplete for a strong SOTA claim. While the paper includes several relevant methods, it omits more recent and closely related MPI calibration approaches that explicitly leverage structural or physical priors, such as ProTSM for structured SM learning (https://pubmed.ncbi.nlm.nih.gov/37471193/), MKD-SM (https://ieeexplore.ieee.org/document/11267072) which exploits inter-slice correlations and prior knowledge , and recent position-prior-guided SM super-resolution methods that directly incorporate positional priors into the model (https://arxiv.org/pdf/2511.05795). This weakens the positioning of the paper and makes it unclear whether the reported gains would hold against the strongest prior-/knowledge-driven approaches.

Some claims are not fully supported by the experiments. In particular, the paper emphasizes improved efficiency and reduced recalibration overhead, but does not provide runtime, acquisition-time, or computational cost analysis, and the trajectory-aware prior itself is based on a heuristic formulation without comparison to alternative physically motivated priors.
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 has provided an anonymized link to the source code, dataset, or any other dependencies.
Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?

N/A
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/2026/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.

(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

I believe the paper suffers from some missing baselines and inaccuracies in positioning and framing, however the presented method is sound, reasonably novel, and introduces strong results.
Reviewer confidence

Somewhat confident (2)
[Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.

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

The rebuttal addresses several of my main concerns. In particular, the authors clarify the novelty as trajectory-dependent representation-level physics integration rather than the general use of physics priors, provide useful complexity numbers showing lower parameters/FLOPs/inference time than 3dISPAnet, and commit to discussing recent related methods. These responses strengthen the paper and support my accept recommendation. I strongly encourage the authors to include these additional experiments and sharpened positioning in the final version if accepted. I believe paper still lacks in missing quantitative comparisons to recent prior-/position-guided SM calibration methods, and the reported code/manuscript inconsistency, although explained, still raises some reproducibility concerns. These should be addressed but I do not think they should necessarily inhibit acceptance.

Author Feedback

We sincerely thank the reviewers for thorough and constructive comments. Below are point-by-point responses to key concerns. 1.Quantitative Gains, Model Necessity, Efficiency and OOM Risk(R1/R2/R4) The 1-2% SSIM gain over 3dISPAnet is meaningful. Our method consistently outperforms all baselines across six settings, with 6-17% NRMSE reduction vs. LapSRN, 0.3-0.6 dB PSNR gain vs. 3dISPAnet, and 4-20% SSIM improvement vs. traditional interpolation. Small SM errors propagate severely in trajectory-sensitive MPI regions, so stable multi-metric gains matter clinically. Ablations confirm module necessity: TACPT-Net cuts NRMSE from 0.0318 to 0.0202, raises PSNR to 34.60 dB and SSIM to 0.941, with only 0.92M to 1.21M parameters. TAEB and CP-FIM provide complementary, non-redundant gains. In terms of efficiency, TACPT-Net outperforms 3dISPAnet with fewer parameters (1.21M vs. 1.48M), lower FLOPs (1.25G vs. 1.55G), and faster inference (0.11s vs. 0.14s). The sparsemax gating in DSGFB adds negligible overhead, as it is a single sparse operation rather than iterative refinement. The potential OOM issue from dense voxel-trajectory broadcasting is an implementation concern, not a fundamental limitation: relevance maps can be cached; chunk-wise computation supports large FOVs. 2.In Vivo Validation(R1) We agree that in vivo validation will enhance its clinical relevance, and we will mark it as an important future research direction. Currently, publicly available in vivo MPI datasets with paired LR and HR SMs are scarce. We performed validation using real-world open MRI phantom data that incorporates genuine system responses and measurement noise. Phantom validation is a standard practice in recent studies on MRI scan phantom calibration, including TranSMS, 3dISPAnet, and MKD-SM. Our experimental setup follows mainstream practices and enables us to assess the effectiveness and robustness of the proposed method. 3.Novelty, Baseline Selection and INR(R2, R4) We explicitly clarify the novelty of our work: our contribution is not the general idea of applying physics priors in SM calibration, but the novel design of trajectory-dependent prior and its representation-level integration into deep networks, including the fourth-order TAEB aware encoding, joint frequency-spatial CP‑FIM, and sparse DSGFB gated fusion. This framework provides a valuable complementary improvement to existing physics-guided calibration methods such as TranSMS. We acknowledge the relevance of the suggested baselines: ProTSM, MKD‑SM, and PPGnet. MKD‑SM and PPGnet were published in late 2025, with no public code or pretrained models available at submission time. Although ProTSM was published earlier, it depends on specialized hyperparameter modeling and a separate pre-training–fine-tuning pipeline. Therefore, fair and verifiable quantitative comparisons cannot be completed in a limited time. To ensure fair and reproducibility, we compared with representative reproducible CNN- and Transformer-based baselines under the same setting, including 3dISPAnet, SMRnet, and TranSMS. In the revised edition, we will discuss these latest methods and include full citations. INR is promising, but direct MPI SM SR is non-trivial because SMs are high-dimensional, multi-channel, and trajectory-dependent; We will add a dedicated discussion about INR and list both INR-based SM modeling and the latest 2025 methods as important future benchmarks. 4.Equation and Code Consistency(R1) All reported results used the fourth-order trajectory distance weighting in Eq. (1). The uploaded TrajB.py was an earlier internal exploratory version, an inadvertent code-release error. We have corrected the code in the anonymous repository, re-ran key checks and confirmed consistency with the reported results. 5.Other Minor Revisions(R1, R4) We will add \titlerunning to fix LaTeX warnings, define “reduced recalibration overhead” clearly, and include full complexity analysis to strengthen efficiency claims.

Meta-Review

Meta-review #1

Your recommendation

Invite for Rebuttal
Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.

Please provide justifications and clarifications for the concerns raised by the reviewers.
After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

Reject
Please justify your recommendation.

This paper proposes TACPT-Net, a physics-informed transformer for MPI system matrix calibration that embeds FFP trajectory priors via a trajectory-aware encoding branch and combines spectral and spatial feature modeling.

The core idea of trajectory-aware positional encoding is well-motivated and the ablation study supports the contribution of each component.

However, as R1 summarizes concisely in their post-rebuttal assessment, the novelty claims are insufficiently differentiated from existing physics-informed methods given the missing comparison against recent baselines, the experimental validation relies on phantom data with relatively outdated baselines, and key concerns are deferred to future work rather than addressed in the current submission. The rebuttal does not provide concrete justification for why the proposed approach should be superior to these missing methods, which leaves the novelty question open.

Thus, this paper is not recommended for acceptance in its current form.

Meta-review #2

After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

Accept
Please justify your recommendation.

This paper proposes TACPT-Net, a trajectory-aware cross-paradigm Transformer framework for efficient system matrix calibration in Magnetic Particle Imaging. The method aims to improve sparse SM calibration by incorporating Field-Free Point trajectory priors into the Transformer backbone and jointly modeling frequency-domain and spatial-domain dependencies through cross-paradigm feature interaction.

The reviewers recognized the importance of the MPI calibration problem, the novelty of trajectory-aware physical prior integration, and the generally strong performance across different nanoparticle materials, scanning trajectories, and upsampling ratios. In particular, the idea of using FFP trajectory-dependent positional encoding provides a physically grounded alternative to purely data-driven SM super-resolution methods.

The reviewers raised concerns about incomplete baseline comparisons, limited validation on phantom data, marginal gains over the strongest baselines, and the lack of computational analysis in the original submission. A more serious concern was the reported mismatch between Eq. (1) and the uploaded code for the Trajectory-Aware Encoding Branch. The authors clarified in the rebuttal that the reported results used the fourth-order trajectory distance weighting described in the manuscript, while the uploaded code was an earlier internal exploratory version, and that the code has since been corrected. They also clarified the novelty as trajectory-dependent representation-level physics integration, provided complexity numbers showing fewer parameters, lower FLOPs, and faster inference than 3dISPAnet, and explained the difficulty of fairly comparing with very recent prior-guided SM calibration methods without public code or pretrained models.

Although some limitations remain, especially the lack of in vivo validation and missing quantitative comparisons with the newest prior-/position-guided SM calibration methods, these issues mainly affect the strength of the SOTA and clinical-translation claims rather than invalidating the core contribution. The final version should clearly correct the code/manuscript inconsistency, sharpen the positioning relative to recent physics- and prior-guided MPI calibration methods, and avoid overclaiming clinical impact beyond phantom validation.

Overall, the proposed trajectory-aware physics-informed Transformer is technically sound, reasonably novel, and practically relevant for MPI SM calibration. Therefore, I recommend acceptance.

Meta-review #3

After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

Accept
Please justify your recommendation.

After rebuttal, I recommend Accept. The paper presents a sound and well-motivated trajectory-aware, physics-informed transformer for efficient MPI system matrix calibration. The rebuttal clarifies that the novelty and it addresses complexity concerns with parameter, FLOP, and inference-time comparisons showing better efficiency than 3dISPAnet. While comparisons to very recent prior-/position-guided methods and in vivo validation would strengthen the work, the authors provide reasonable justification for the current scope. The code-manuscript inconsistency was a concern, but the authors stated that the correct formulation was used for reported results and that the repository has been corrected. Overall, the remaining issues are addressable in revision.

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Trajectory-Aware Cross-Paradigm Transformers for Efficient System Matrix Calibration in Magnetic Particle Imaging

Author(s):