Personalized MR-Informed Diffusion Models for 3D PET Image Reconstruction

Alexander Hammers; Andrew J. Reader; Andrew P. King; George Webber

REVIEW 4 major objections 5 minor 40 references

Personalized MR-Informed Diffusion Models for 3D PET Image Reconstruction

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Warping other patients' PET scans into a target's MR space yields a personalized diffusion prior that reconstructs low-count PET better than generic priors

desk verdict The pseudo-PET registration idea is a genuine, useful contribution; the evaluation is honest but has enough selection bias and weak-reference issues that the headline claim is supported rather than proven. read the letter →

arxiv 2506.03804 v2 pith:M45OFRY7 submitted 2025-06-04 physics.med-ph cs.CV

George Webber , Alexander Hammers , Andrew P. King , Andrew J. Reader This is my paper

classification physics.med-phcs.CV

keywords PETreconstructiondiffusionmodelsMR-guidedpseudo-PETsynthesisimageregistrationlow-countscore-basedgenerativepersonalizedpriors

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Positron emission tomography at low dose is noisy, and using MR to guide reconstruction can silently impose anatomy that the tracer signal does not support. The paper proposes a softer form of MR guidance: warp other subjects' PET images into the target subject's MR-defined space using MR-to-MR registration, and train a diffusion model on these synthetic 'pseudo-PET' volumes as a personalized prior. Reconstructing with the PET-DDS algorithm, the paper reports that this prior improves accuracy from 2.5%-count FDG data, with lower error where PET and MR disagree, retained accuracy where they agree, better lesion contrast recovery relative to background noise, and a better bias-variance frontier on real data. The method needs no generative network for synthesis and works with fewer than about fifty paired PET-MR scans. If correct, it provides a practical route to personalized MR-guided PET reconstruction that preserves PET-only features such as lesions.

What carries the argument

The central object is the pseudo-PET image: another subject's measured PET volume deformed into the target brain's coordinate frame by an affine alignment followed by a deep-learning deformable registration field learned from MR-to-MR alignment [24]. A random weighted sum of one or more such deformed images forms each training sample, so a small library of paired PET-MR scans yields a large, diverse, subject-specific training set without any generative model. The diffusion model is trained on these volumes with slice conditioning, since all volumes already share the target's slice geometry. Reconstruction then runs PET-DDS (Decomposed Diffusion Sampling), which alternates the diffusion denoiser with Poisson log-likelihood gradient steps on sinogram subsets, and the personalized prior is what anchors the iterate. The registration step is the load-bearing mechanism: it transfers anatomical context from MR into the PET training distribution while leaving the PET intensities measured, not hallucinated.

What would settle it

On a cohort whose FDG-avid lesions are partly invisible or misaligned on T1 MR, generate pseudo-PET by MR-to-MR registration and reconstruct 2.5% count data; if lesion contrast recovery falls below that of PET-DDS trained on unregistered PET, the MR-transfer assumption is the cause.

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Extended reading notes

Core claim

The central claim is that a diffusion prior personalized to one subject's anatomy can be built by registering other subjects' measured PET images into that subject's MR space, and that this prior beats both a generic PET prior and an MR-conditioned prior for low-count 3D PET reconstruction. The pseudo-PET images mix real tracer measurements with MR-visible anatomy, so the learned score function becomes a joint anatomical-functional prior rather than an MR-imposing one. Using PET-DDS, the paper reports lower normalized root-mean-square error in mismatch regions, unchanged or better accuracy in agreement regions, and better lesion contrast versus background noise on simulated data with out-of-distribution lesions. On real FDG brain scans at 2.5% of full counts, it reports the best bias-variance trade-off among diffusion-based methods and improved agreement with full-count OSEM. The paper also reports that direct MR conditioning, either as an extra channel or through classifier-free guidance, does not consistently deliver these gains on small real datasets.

Load-bearing premise

The load-bearing premise is that warping another subject's brain into the target's MR space also carries that subject's PET tracer distribution into a plausible PET image for the target; if PET uptake does not track MR anatomy, the personalized prior is biased rather than helpful.

Editorial extensions

If this is right

If the central claim holds, low-count brain PET can be reconstructed with a prior built from tens of paired scans instead of large corpora of high-quality images.
Out-of-distribution lesions should remain detectable: lesion contrast recovery per unit background noise improves without sacrificing accuracy in MR-PET agreement regions.
MR guidance becomes softer: the reconstruction can use anatomical information without requiring the tracer to match every MR boundary, reducing the blending artifacts seen with stronger MR priors.
The improvement should transfer across tracers and dose levels, because the registration uses MR anatomy and is therefore tracer- and dose-invariant.
On real data, the approach should dominate classifier-free MR conditioning when only limited paired training data are available, since the registration-based prior was the only diffusion variant that improved the bias-variance frontier.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

We infer that the random weighted summing step is itself a lightweight generative mechanism: it can synthesize an unbounded supply of plausible pseudo-PET volumes from a few registered scans, an idea the paper notes but leaves for future work.
We infer a boundary condition: any tracer distribution that is invisible on MR, such as early amyloid deposition or tumors without structural correlate, will stress the MR-transfer assumption, and mixing in unregistered native PET training images may hedge against that failure.
We infer that the shared target coordinate frame makes slice conditioning meaningful, so a patch-based or slab-wise training variant could cut the per-subject training cost while preserving the personalization benefit.
We infer that the deformation fields, being MR-driven, are tracer-independent; a library of precomputed fields could be reused for new tracers without retraining the registration network.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The core idea here is real: instead of training a diffusion prior on generic multi-subject PET, warp other subjects' PET into the target subject's MR space via MR-to-MR registration, and train a personalized prior on those pseudo-PET images. That is a simple, sensible way to inject MR information without a large training set or a black-box generator, and it appears to help. The paper also deserves credit for what it does not do: it does not oversell PET-DDS+MR, it reports that classifier-free MR guidance failed to help on real data, and it includes ablations (PET-PET registration, MR side-channel) that mostly strengthen the case for the proposed method.

The main soft spot is the evaluation. The simulated data are built from MR segmentations, so PET-MR correspondence is perfect by construction; the simulated experiments therefore cannot test the load-bearing assumption that MR-derived deformation fields are valid for PET tracer distributions. The real-data experiment is the only test of that assumption, and there the reference is a 100%-count OSEM image, not ground truth, with hyperparameters selected on the test data (min NRMSE/max SSIM). The simulated figures also lack error bars. The paper openly states that the test data are used for registration training, which is legitimate for this task, but the overall evaluation still carries a selection-bias smell. None of this is fatal; the real-data results do show the method winning on bias-variance against the other diffusion baselines, and the paper is transparent about its choices. But the reader should not walk away thinking the deformation assumption is independently validated—it is not, on the evidence here.

If I were refereeing this, I would ask for repeated-realization error bars on the simulated metrics, a predefined hyperparameter selection protocol (e.g., validation-set selection), and ideally a real-data comparison against an independent high-quality reconstruction method instead of OSEM alone. The central claim is plausible and the method is simple enough to reproduce, but the evidence is currently conditional rather than conclusive.

This paper is worth engaging with: it gives a practical alternative to MR-conditioned diffusion training, and the pseudo-PET synthesis idea could have legs beyond PET. A serious referee should get it, though with the expectation of revision.

Referee Report

4 major / 5 minor

Summary. The paper proposes a method for generating subject-specific 'pseudo-PET' training images by registering other subjects' paired PET-MR images into the target subject's MR space using VoxelMorph MR-to-MR deformation fields, optionally summing several warped PET images. A diffusion model is trained on these pseudo-PET images and used as the prior within the PET-DDS reconstruction algorithm, which is then applied to low-count (2.5%) simulated and real [18F]FDG PET sinograms. The authors evaluate the method against OSEM, Bowsher, PET-DDS, and PET-DDS+MR, reporting improved NRMSE/SSIM in PET-MR mismatch regions, better lesion CRC versus background noise in simulations, and improved bias-variance and NRMSE on real data. The central claim is that personalizing the diffusion prior with MR-registered pseudo-PET images improves low-count PET reconstruction accuracy and the trade-off between PET-specific and MR-shared features.

Significance. If the quantitative claims hold, the method is a simple and practical way to inject MR information into diffusion-based PET reconstruction without training a conditional model, and it addresses the PET-MR mismatch problem by learning a softer MR-guided prior. The approach is original in its use of registration-based pseudo-PET synthesis rather than deep generative synthesis, and the authors show that it can be useful in low-training-data regimes. The scope of the experiments is commendable: both simulated and real FDG data, multiple baseline algorithms, and a bias-variance analysis. However, the evaluation has several methodological weaknesses—test-set hyperparameter selection, missing error bars in the simulated lesion experiments, and the use of full-count OSEM as the real-data reference—that currently prevent the quantitative claims from being fully established. The paper does not provide code, but the method is described in sufficient detail to be reproduced.

major comments (4)

[V-D, Fig. 9 and Fig. 10] The real-data comparison in Fig. 9 reports the 'best NRMSE' for each method across hyperparameter choices, and Fig. 10 selects hyperparameters to maximize SSIM on the test reconstruction. Because the regularization strength lambda_DDS and the number of iterations were chosen after seeing the test data, the reported improvements may reflect post-hoc selection rather than a reproducible operating point. Please report hyperparameters chosen by a validation set or a pre-specified rule, and show the full trade-off curves with the selected operating point marked.
[IV-D5 and V-D] The bias-variance analysis and the real-data NRMSE in Figs. 9 and 11 use the 100%-count OSEM reconstruction as the ground truth. This is not an independent ground truth, and because all diffusion models are trained on OSEM images, the metric may favor reconstructions that are close to OSEM rather than accurate to the true tracer distribution. An independent reference (for example, a phantom with a known activity distribution, or a high-count reconstruction with a different algorithm) is needed to support the real-data claims.
[IV-A1 and IV-B1] The central premise that an MR-derived deformation field is a valid transformation for PET tracer distributions is not directly tested. In the simulated data the ground-truth PET is analytically derived from MR segmentations, so the premise holds by construction; in the real data there is no independent ground truth and the subject population is not described with respect to pathology. The lesion experiments in Section V-B insert lesions only at test time, so the learned training distribution never contains PET-only structures. Please add a direct validation of the deformation assumption, for example by comparing warped PET images to native PET images of the same subject when available, or by reporting quantitative agreement between MR-registered and PET-registered pseudo-PET.
[V-B, Figs. 5-7] Figures 5-7 report trade-off curves for the simulated lesion study without error bars or significance tests. It is not stated whether the metrics are averaged over multiple Poisson noise realizations, and several of the curves are close. Please provide means and standard deviations over at least 10 independent noise realizations (or an equivalent statistical summary) and a significance test for the claimed differences.

minor comments (5)

[IV-D3] The sentence 'Over-fitting is not a concern for this task, as the test data is available during training' is confusing and, taken literally, describes a circular evaluation of the registration network. Please rephrase to clarify what is being personalized and why using the target MR for registration training is valid despite using that same MR for evaluation.
[IV-A1] The heuristic for summing pseudo-PET images (P(N=n) proportional to 1/n and weights w_i ~ U[0,1]) is not justified, and since MR-reg & sum + PET-DDS 'performed similarly to MR-reg + PET-DDS' in Section V-B, the benefit of the summing step is not demonstrated empirically. Please provide supporting evidence or present the summing as an optional variant with limited effect.
[IV-C3] The hyperparameters for PET-DDS+MR are not fully specified: lambda_MR is introduced as the guidance strength, but the text does not state which values were used or how it was varied. Please report the values or state explicitly that it was fixed.
[II-E and IV-A1] There are typographical and formatting issues, including 'V oxelMorph' with extra spaces, 'bourne out' in Section V-C1, and the caption of Fig. 2 using 'blues' instead of a consistent term. These should be corrected.
[V-D] The real-data evaluation omits MR-reg & sum + PET-DDS, even though random summing is part of the proposed method as described in Section IV-A1. The omission should be noted in the main text or the method should be evaluated on real data as well.

Circularity Check

1 steps flagged · score 6.0 of 10

Simulated validation of the MR-to-PET deformation assumption is self-fulfilling; real [18F]FDG results are the only non-circular support.

self definitional [Section IV-A1 (pseudo-PET generation) and Section IV-B1 (simulated data generation)]
"we simulated ground truth [18F]FDG PET scans (and corresponding attenuation maps) from 39 real T1 MR images (following [26]) using representative activity values for segmented tissues. ... we compute the VoxelMorph registration map for image i as phi_i := phi(B_target xMR_target, B_i xMR_i), and use it to transform PET image xPET_i to the target reference space."

In the simulation, ground-truth PET is generated from MR tissue segmentations, and pseudo-PET is generated by warping other subjects' PET with MR-to-MR deformation fields. Because each simulated PET is a deterministic function of its own MR segmentation, aligning source MR to target MR also aligns the simulated source PET to the target's simulated PET (up to discretization). The pseudo-PET training set is therefore drawn from the target's true distribution by construction, so the simulated finding that personalized pseudo-PET pre-training improves reconstruction is an artifact of the experiment design: it asserts the MR-to-PET deformation assumption rather than testing it.

full rationale

The core reconstruction pipeline is not circular: the target low-count sinogram is never used to create pseudo-PET training images, and the target MR is legitimately available at test time for registration and guidance. PET-DDS data consistency enforces the measured sinogram, so the method does not simply return its training inputs. The one significant circularity is confined to the simulated validation: because the simulated ground-truth PET is derived from the same T1 MR segmentations used for MR-to-MR registration, the pseudo-PET training images are near copies of the target ground truth by construction, making the simulated improvement in NRMSE/CRC and bias-variance partly self-fulfilling. The real-data study provides non-circular support, though its force is tempered by using a 100%-count OSEM reference of the same kind used to create training images, and by reporting the minimum NRMSE over hyperparameters chosen on the test set. No load-bearing self-citation or imported uniqueness claim was found; the central method rests on external tools (VoxelMorph, PET-DDS) and its own real-data evaluation.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

No fundamentally new physical entity is introduced. The method's non-standard assumptions are about image registration validity, reference standards, and generalization from lesion-free training data. These are empirical assumptions, not mathematical axioms.

free parameters (5)

lambda_DDS (diffusion anchoring strength) = varied per method, best chosen on test data
Controls how strongly the reconstruction is anchored to the diffusion output; the paper sweeps it to produce bias-variance curves.
lambda_RDP (axial RDP penalty strength) = 5e-4
Fixed regularization strength on axial slices, taken from previous work; central to PET-DDS stability.
delta (gradient descent step size) = 0.2
Step size for data-consistency gradient updates; fixed by the authors.
number of diffusion steps and data-consistency steps = 100 and 10
Computational schedule for reconstruction; chosen without sensitivity analysis.
pseudo-PET summing distribution = P(N=n) proportional to 1/n; weights w_i ~ U[0,1]
Heuristic introduced to balance noise reduction and diversity; its influence on the main result is not ablated.

assumptions (5)

domain assumption MR-to-MR deformation fields are valid for warping PET images
Pseudo-PET images are generated by applying VoxelMorph MR registration maps to other subjects' PET (Section IV-A1). If PET uptake does not follow MR anatomy, the synthetic training data is biased.
domain assumption OSEM reconstruction from 100% counts is a valid reference for real data
NRMSE and bias-variance are computed against full-count OSEM (Sections IV-D5 and V-D). If OSEM is biased or noisy, the ranking of methods may change.
domain assumption Training on lesion-free pseudo-PET generalizes to out-of-distribution lesions
All diffusion models were trained with lesion-free data to test robustness to PET-MR mismatch (Section IV-A2). The prior must not suppress lesions during reconstruction.
domain assumption Poisson thinning of prompt sinograms simulates low-count data
Real low-count data were generated by sampling counts without replacement to reach 2.5% expected counts (Section IV-B2), assuming count-lowering preserves the noise model.
standard math Standard score-matching diffusion training is valid for 3D medical images
The paper relies on denoising score matching and PET-DDS theory from Singh et al. without re-deriving them (Sections II-C, II-D).

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Cite this review

Pith. "Pith review of Personalized MR-Informed Diffusion Models for 3D PET Image Reconstruction." pith.science (2026). https://pith.science/paper/M45OFRY7

@misc{pith2026250603804,
  author       = {Pith},
  title        = {Pith review of: Personalized MR-Informed Diffusion Models for 3D PET Image Reconstruction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M45OFRY7}},
  note         = {Machine review of arXiv:2506.03804}
}

abstract

Recent work has shown improved lesion detectability and flexibility to reconstruction hyperparameters (e.g. scanner geometry or dose level) when PET images are reconstructed by leveraging pre-trained diffusion models. Such methods train a diffusion model (without sinogram data) on high-quality, but still noisy, PET images. In this work, we propose a simple method for generating subject-specific PET images from a dataset of multi-subject PET-MR scans, synthesizing "pseudo-PET" images by transforming between different patients' anatomy using image registration. The images we synthesize retain information from the subject's MR scan, leading to higher resolution and the retention of anatomical features compared to the original set of PET images. With simulated and real [$^{18}$F]FDG datasets, we show that pre-training a personalized diffusion model with subject-specific "pseudo-PET" images improves reconstruction accuracy with low-count data. In particular, the method shows promise in combining information from a guidance MR scan without overly imposing anatomical features, demonstrating an improved trade-off between reconstructing PET-unique image features versus features present in both PET and MR. We believe this approach for generating and utilizing synthetic data has further applications to medical imaging tasks, particularly because patient-specific PET images can be generated without resorting to generative deep learning or large training datasets.

Figures

Figures reproduced from arXiv: 2506.03804 by the authors.

**Figure 1.** Outline of our reconstruction methodology to reconstruct the target’s PET image: generating pseudo-PET images in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Simulated data: example sagittal slices from 3D [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Real [18F]FDG data: example transverse slices from 3D pseudo-PET images that have been transformed via deeplearned MR-to-MR registration maps, with the clinical PET and MR images for comparison. The PET and MR images in columns 1 and 2 are shown after the initial affine registration stage. Red = image in target space; blues = rigid transformations of images from their original spaces; dashed line = non-linearly re… view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Reconstructed transverse image slices for each of six PET reconstruction algorithms (each shown with 3 different [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Error trade-off between areas of PET-MR agreement [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: Structural similarity trade-off between areas of PET [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 8.** Figure 8: Results (on simulated data at 2.5% count) for variants of the proposed method. PET-reg + PET-DDS is a variant of [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: Comparison of best NRMSE for each reconstruc [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

**Figure 10.** Figure 10: Example reconstructed transverse slices from real 2.5% [ [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

**Figure 11.** Figure 11: Bias-variance trade-off comparison between different [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

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