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Abstract
Magnetic Particle Imaging (MPI) enables highly sensitive and rapid mapping of magnetic nanoparticle distributions, yet its image quality critically depends on accurate system matrix (SM) calibration. Conventional SM acquisition requires exhaustive full-volume measurements and is time-consuming, while purely physics-based SM simulators often deviate from real measurements due to simplifying assumptions and imperfect system characterization. To overcome these limitations, we propose P2R-Net, a Physics-to-Reality SM Calibration Network for High-Precision MPI Reconstruction. It is realized as a dual-branch encoder–decoder architecture, which integrates sparse measurement guidance with dense, idealized SMs generated from anisotropic magnetization model. The Multi-scale cross-attention aligns physics-domain representations with measurement-domain characteristics, preserving physical plausibility while adapting to real acquisition conditions. In addition, It incorporates Spatial shift convolution Block (SC-Block) to model SM spatial coupling and an Attention-Enhanced Feature Distillation (AFD) module to stabilize physics-derived features. Extensive experiments show that P2R-Net yields higher-fidelity SMs and improves downstream MPI reconstruction quality over state-of-the-art baselines, providing an efficient and practical alternative to time-consuming full-volume calibration. Code is available at https://anonymous.4open.science/r/P2Rnet.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/1881_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/lzclz/P2Rnet.git
Link to the Dataset(s)
N/A
BibTex
@InProceedings{ZhaLiz_P2RNet_MICCAI2026,
author = { Zhang, Lizhi AND Li, Jintao AND Guo, Hongbo AND Tang, Zijian AND Cui, Yinong AND Pan, Haoyu AND He, Xiaowei},
title = { { P2R-Net: Physics-to-Reality SM Calibration Network with Sparse Measurement Guidance for High-Precision MPI Reconstruction } },
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 addresses the bottleneck of system matrix (SM) calibration in Magnetic Particle Imaging (MPI), where exhaustive full-volume measurement is expensive and physics-only simulation often deviates from real scanner responses. The proposed P2R-Net takes as input a dense physics-derived SM prior and a sparse measured SM, and learns a physics-to-reality mapping to generate a higher-fidelity calibrated SM for downstream MPI reconstruction. The method is implemented as a dual-branch encoder-decoder with multi-scale cross-branch fusion, complemented by an SC-Block for spatial coupling modeling and an AFD/FMA-style refinement module for stabilizing physics-derived features. The paper also evaluates whether the calibrated SM improves downstream phantom reconstruction quality.
- 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 paper targets a real bottleneck in MPI, namely the cost of repeated system matrix calibration. This is a meaningful problem, and the motivation is clear. The core idea is sensible. Using a dense physics-derived prior together with sparse real measurements is a natural way to combine physical plausibility with system-specific correction. The method design is mostly coherent with the stated goal. The dual-branch architecture and the fusion strategy are at least conceptually aligned with the physics-to-reality calibration setting. The reported results are strong within the tested setup. The method improves both SM recovery and downstream reconstruction over the included baselines, and the ablation study is reasonably supportive.
- 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.
Some implementation-critical details are still not sufficiently clear for reproducibility. The paper does not fully specify the sparse sampling construction, sampling pattern/mask generation, tensor organization, normalization/preprocessing, or the exact formulation of the measurement-consistency term in the unsupervised setting. Similarly, the physics-derived prior is described at a conceptual level through the Adaptive Truncation Anisotropic Equilibrium model, but the experimental parameterization and generation pipeline are not fully spelled out. These may be partly standard choices, but the current description still leaves non-trivial ambiguity. There are some discrepancies between the paper and the code; for instance, the code employs an eight-directional Shift8 operator, whereas the paper describes a four-directional shift.
- Please rate the clarity and organization of this paper
Satisfactory
- 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.
(2) Reject — should be rejected, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
My overall recommendation is Weak Accept. The paper addresses a relevant MPI calibration problem and proposes a technically sensible solution that combines a physics-derived SM prior with sparse measurement guidance. This formulation is well motivated, and the reported gains on both SM recovery and downstream reconstruction are convincing within the tested setting. My concerns are mainly about scope and completeness rather than a fatal flaw. The novelty is moderate, the validation is still somewhat limited, and some implementation details could be described more clearly. That said, I think the paper contains enough technical value to merit acceptance, especially if the authors clarify the sparse sampling setup, the unsupervised loss, and the physics-prior generation more explicitly in the final version.
- Reviewer confidence
Confident but not absolutely certain (3)
- [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 authors have responsed my comments.
Review #2
- Please describe the contribution of the paper
The paper proposes a method for system matrix (SM) estimation in magnetic particle imaging (MPI) reconstruction. The method uses a deep neural network (U-Net) to merge a physics-based SM prior with a sparsely measured SM map to obtain a more accurate and higher-resolution SM prediction. The network includes two branches for two input sources respectively, and contains several specialized designs, for modeling spatial coupling and frequency features in SM. The method is evaluated on phantom data and shows competitive results with existing approaches.
- 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 paper studies MPI, a promising imaging approach that can provide complementary clinical information to conventional MRI. The proposed method may facilitate MPI’s application by reducing the time for acquisition.
- 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 major technical novelties can be better motivated. 1.1.In SC-block, it is unclear how shifting the feature maps by one pixel and aggregating can help model the spatial coupling, and why this specific design is used. Why did the authors choose shifting by one pixel, rather than more pixels, or applying a Gaussian smoothing kernel on the feature maps? Is it related to the properties of SM maps? Does the coupling occur only between neighboring pixels through uniform averaging? The authors may want to provide more information on this. 1.2.In AFD, how does the Frequency Modulation layer “enforce tracer-dependent harmonic consistency”? It is unclear what “harmonic consistency” means here and how the 1x1 convolution in frequency space enforces this.
2.The writing is relatively unclear and can be hard to follow. 2.1.In Section 2.2, many symbols in Eq. (2) are undefined: \mu_0, m_0, \beta, H(r,t), etc. 2.2.Details on training are largely lacking. What is the data split and how many phantoms are used for training and testing, respectively? How is the unspervised training loss defined? Are all compared methods trained on the same dataset using the same loss? 2.3.In Section 3, no references or explanations are provided for the competing methods. 2.4.Many terms used to describe the method, as well as the method’s naming, appear vague, insufficiently defined, and unnecessarily grandiose, e.g., “Reality” in “Physics-to-Reality”, “structure-aware” refinement, “stabilized” fusion, “reality-aware”, etc. Many of these words are do not rigorously convey the technical contributions and may confuse readers.
- Please rate the clarity and organization of this paper
Satisfactory
- 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?
Lack of clarity overall and insufficient justification of the logic behind the proposed technical innovations.
- 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.
The authors’ feedback on the SC-Block is contradictory with their original paper. In the original paper, they wrote “the shift-based fusion enlarges the effective receptive field with zero extra parameters.” In the rebuttal, they said “shifted features are fused by learnable convolutions”, which means that extra parameters are needed for fusion. This, along with the large number of undefined notations that calls for significant rewriting, prompts me to recommend rejection.
Review #3
- Please describe the contribution of the paper
This paper directly derives the system function encompassing the easy magnetization axis and anisotropy intensity from the underlying physical mechanisms of MPI. This approach preserves the physical consistency of non-linear responses (e.g., high-order harmonic features), making the generated system matrix more physically reasonable and robust. The proposed methodology of fusing physical simulation with sparse real measurements provides a valuable reference idea for addressing the gap between MPI signal models and hardware systems. Although this study makes a valuable attempt to combine physical priors with data-driven methods to enhance MPI reconstruction quality and achieves good quantitative metrics on a public dataset, there is still significant room for improvement regarding experimental details, method validation, and manuscript readability.
- 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 addresses the highly time-consuming system matrix (SM) calibration in Magnetic Particle Imaging (MPI) and the discrepancy between purely physical models and actual measurements by proposing the P2R-Net framework. The network employs a dual-branch encoder-decoder architecture, utilizing sparse measurement data to guide a dense physical system matrix generated based on an anisotropic magnetization model. Although this study makes a valuable attempt to combine physical priors with data-driven methods to improve MPI reconstruction quality and achieves good quantitative metrics on a public dataset, there remains significant room for improvement regarding experimental details, method validation, and the readability of the manuscript.
- 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 paper only utilizes a single public dataset (SM13), which originates from a single Bruker preclinical scanner with a field of view (FOV) of only 34 × 30 mm². To demonstrate the broad applicability of this “Physics-to-Reality” mapping network, it is essential to conduct multi-center cross-validation across different hardware configurations, magnetic field gradients, or tracers. (2)The authors propose the use of an “Adaptive Truncation Anisotropic Equilibrium Model” ` to reduce the computational cost of constructing the frequency-domain system matrix, and mention the retention of high-order Chebyshev terms by setting a cumulative energy threshold γ. However, the paper does not provide quantitative analysis on the selection criteria and rationale for this threshold γ, nor its sensitivity to the final reconstruction accuracy. (3)The essence of this paper is similar to system matrix super-resolution. To the best of our knowledge, there are other super-resolution works in MPI beyond the baseline methods presented in the paper; therefore, the authors should conduct a more comprehensive comparison to demonstrate the superiority of their proposed work. (4)The paper mentions two training paradigms (supervised and unsupervised learning), yet fails to disclose the specific sample sizes and the splitting ratio between the training and testing sets. (5)One of the paper’s motivations is to solve the excessively time-consuming issue of full measurement calibration, claiming that the proposed method offers an “efficient and practical” alternative. Nevertheless, the manuscript lacks specific quantitative comparisons of model parameter counts, training time, inference time, and computational complexity (FLOPs). (6)The manuscript contains several typographical, formulaic, and formatting errors, which do not meet publication standards. For instance, “Sparse” is misspelled as “Spase” in Figure 1, and the typo “form u=Sc” appears in Section 2.1.
- Please rate the clarity and organization of this paper
Satisfactory
- 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 authors claimed to release the source code and/or dataset upon acceptance of the submission.
- 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?
This study combine physical priors with data-driven methods to improve reconstruction quality in MPI.
- Reviewer confidence
Very confident (4)
- [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 authors clarify my concerns. No more comments.
Author Feedback
We sincerely thank the reviewers for their comments. Before addressing the technical concerns, we respectfully note a possible discrepancy in Reviewer #1’s evaluation: the selected rating is “Reject,” while the written recommendation states “Weak Accept” and recognizes sufficient technical value. We focus below on the major concerns.
1.Reproducibility/training (R1,R2,R3) (1)Our setup follows common MPI SM calibration practice and is reproducible. Sparse sampling uses a fixed deterministic downsampling mask on a unified spatial-frequency grid. Complex SMs use real/imaginary channels with zero-padding and normalization. Only SNR >4 measurements are used; 1517 SMs are padded to 1717, and the sparse branch is downsampled to 9*9.Data are split 80%/20% before augmentation, giving 1600 augmented training samples and 40 independent raw test samples. Supervised loss is MSE to fully measured SMs. Unsupervised loss is L=L_phys+L_meas: L_phys uses MSE+VGG loss to the dense physics prior, while L_meas applies MSE between downsampled generated SMs and real sparse measurements. All methods use the same split/settings.
(2)We apologize for this manuscript-implementation inconsistency. The 4-directional description was a writing error and does not affect the conclusions: both Shift4 and Shift8 are parameter-free local shifts, while Shift8 additionally includes diagonal neighbors for 8-neighborhood aggregation in MPI SMs.
2.Technical Novelty/Design(R1,R2,R3) P2R-Net’s novelty is mapping a dense physics-derived SM and sparse real measurements to a calibrated, physically plausible, scanner-specific SM, which is not a simple SM super-resolution. (1) The SC-block is motivated by local spatial continuity: neighboring voxels have correlated but non-identical frequency responses from continuous encoding/receive sensitivity. 1-pixel shifting captures nearest-neighbor coupling without excessive smoothing. Unlike Gaussian smoothing, it imposes no fixed isotropic averaging; shifted features are fused by learnable convolutions for adaptive directional weights. (2) For AFD frequency modulation, it is not a hard physical constraint, but learned frequency-channel modulation that models harmonic correlations and reweights frequency features guided by the physics prior, refining the physics-derived SM when aligned with sparse real measurements. (3) The physics prior is from the Adaptive Truncation Anisotropic Equilibrium model. Since Chebyshev expansion energy decays rapidly with order, we retain the minimal term set reaching cumulative energy gamma=0.95, preserving dominant harmonics while discarding negligible high-order terms; smaller gamma may lose useful harmonics, while larger gamma increases cost with diminishing gain.
3.Experimental scope/generalizability/baselines(R2,R3) (1)multi-center cross-validation would strengthen generality. However, public MPI datasets with complete metadata for constructing matched physics-derived SMs remain limited, including scanner settings, anisotropy-related parameters, and field configurations. This matters because our key novelty is introducing physics-derived dense SMs, not using measured data alone. Thus, our claim is not universal scanner-independent generalization, but a proof of feasibility. (2)We selected 3D-ISPAnet as a recent and strong MPI SM generation baseline, since it was published in 2025 and already includes extensive comparisons with existing SM super-resolution methods. We are aware of the newer VRF-Net, but its code and implementation details were not publicly available, making faithful reproduction difficult. (3)P2R-Net has approximately 2.99M trainable parameters and requires about 1.06 GFLOPs per SM generation. We did not emphasize computational-complexity comparisons because the main efficiency gain comes from reducing dense SM calibration measurements, rather than reducing offline training cost or network FLOPs.
4.Minor issues will be corrected in the subsequent revised manuscript.
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 that address the concerns raised by all reviewers, regardless of any potential discrepancies between ratings and written justifications in the reviews.
- 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 P2R-Net, a dual-branch encoder-decoder network that combines a dense physics-derived system matrix prior with sparse real measurements for efficient MPI system matrix calibration.
Reviewers broadly agree that the problem is meaningful and well-motivated: reducing MPI calibration overhead while bridging the simulation-to-reality gap is a practically important direction. The combination of physics-derived priors with sparse measurements is sensible, and the downstream reconstruction results are convincing within the tested setup.
The shared concerns include unclear method description with undefined symbols, missing training details, vague terminology, and insufficient description of key components including the SC-block and the unsupervised loss. The evaluation is also limited to a single dataset from one scanner, efficiency analysis is missing despite efficiency being a stated motivation, and the comparison with other SM super-resolution methods is incomplete. The rebuttal provides useful clarifications on the training setup, sparse sampling construction, and SC-block design, but the writing issues cannot be resolved through rebuttal alone.
Overall the paper addresses a relevant problem with a sensible approach and convincing results, but needs revision before publication. The strength modestly outweighs the weaknesses and I recommend acceptance, with the expectation that the authors improve the method description and address the clarity concerns in the final version.
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 P2R-Net, a physics-to-reality system matrix calibration network for Magnetic Particle Imaging, aiming to reduce the cost of full SM calibration by combining a dense physics-derived SM prior with sparse real measurements. The reviewers recognized the importance of the MPI calibration problem, the sensible formulation of using sparse measurement guidance to correct physics-based SM simulation, and the reported improvements in both SM recovery and downstream MPI reconstruction. The reviewers raised concerns about methodological clarity, reproducibility, and implementation consistency. In particular, several key details were insufficiently specified in the original manuscript, including sparse sampling construction, data splitting, normalization, the unsupervised loss, and the generation of the physics-derived prior. R2 also noted a potential inconsistency between the manuscript and rebuttal regarding the SC-Block, where the paper described shift-based fusion as having zero extra parameters, while the rebuttal mentioned learnable convolution-based fusion. This issue should be clearly corrected in the final version by distinguishing the parameter-free shift operation from the subsequent learnable fusion module. However, these concerns mainly relate to presentation, implementation clarity, and manuscript-code consistency, rather than a fundamental flaw in the proposed idea or experimental conclusions. In the rebuttal, the authors clarified the sparse sampling setup, data split, loss formulation, Shift4/Shift8 discrepancy, physics-prior truncation strategy, and computational complexity. R1 and R3 were satisfied with the response and supported acceptance. Although R2 maintained a reject recommendation due to the remaining ambiguity and writing issues, the central contribution of combining physics-derived dense SM priors with sparse real measurements for scanner-specific SM calibration remains technically meaningful and practically relevant. Therefore, I recommend acceptance, with the expectation that the final manuscript will substantially improve the method description, correct the SC-Block and Shift4/Shift8 inconsistencies, define all key notations, and present the implementation details more rigorously.
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.
The rebuttal clarified several important reproducibility concerns, including sparse sampling, data organization, normalization, train/test split, supervised and unsupervised losses, and physics-prior generation. The authors reasonably reframed the single-dataset evaluation as a proof-of-feasibility study rather than a claim of broad scanner-independent generalization.
One reviewer noted remaining limitations, stating that the authors’ explanation of the SC-Block should be clarified, as the rebuttal appears inconsistent with the original manuscript. The paper states that shift-based fusion enlarges the effective receptive field with zero extra parameters, whereas the rebuttal states that shifted features are fused by learnable convolutions, which could imply additional parameters required for fusion. The manuscript also contains some undefined notations and would benefit from improved clarity. Overall, given the relevant problem, technically sensible approach, clarified methodology, and positive support from two reviewers after rebuttal, I recommend acceptance, with final revisions to resolve the remaining issues noted.