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REVIEW 4 major objections 6 minor 25 references

Joint estimation of activity, attenuation and motion in respiratory-self-gated time-of-flight PET

T0 review · 4 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Respiratory self-gated TOF PET data contain enough information to jointly estimate activity, gate-matched attenuation, and motion, yielding a single motion- and attenuation-artifact-free image without external hardware.

desk verdict Useful methods paper: the phantom benchmark shows the joint MLACF+motion approach recovers static-reference lesion contrast, but the end-to-end 'no hardware' claim is only partially tested. read the letter →

arxiv 2412.15018 v2 pith:7K3CYB2E submitted 2024-12-19 physics.med-ph

Masoud Elhamiasl , Frederic Jolivet , Ahmadreza Rezaei , Michael Fieseler , Klaus Schäfers , Johan Nuyts , Georg Schramm , Fernando Boada This is my paper · ORCID
classification physics.med-ph
keywords respiratorymotioncorrectiontime-of-flightPETjointactivityandattenuationestimationMLACFADMMdata-drivengatingartifactsmotion-compensatedreconstruction
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

The paper proposes two fully data-driven reconstruction algorithms for respiratory self-gated time-of-flight (TOF) PET: a simple Hybrid JRMA and a more complex ADMM-based JRMA. Both jointly estimate a single activity image, gate-matched attenuation sinograms, and respiratory motion vector fields, so that a single motion-corrected, attenuation-artifact-free image can be reconstructed without external gating hardware. In the Wilhelm thorax phantom, both methods raised a liver-dome lesion's contrast from 2.0 to 5.2, matching the static acquisition reference, while motion correction with static CT-based attenuation reached only 3.5. The methods also reduced motion blur and the liver-dome 'banana' attenuation artifact in three patient datasets acquired on a second scanner. The authors recommend the hybrid method for practical use because the ADMM variant is sensitive to its penalty parameter.

What carries the argument

The central objects are the forward model $\bar{y}^k_{it}(\lambda) = a^k_i \big(P(S^k\lambda)\big)_{it} + r^k_{it}$ for each respiratory gate $k$, the factorization $a^k = g^k \tilde{a}$ of gate-matched attenuation sinograms into the static CT-based sinogram $\tilde{a}$ and gate-specific multiplicative correction factors $g^k$, and the MLACF update that estimates $g^k$ under an intensity prior favoring values close to 1. The factorization converts the ill-posed joint estimation of activity and attenuation into a well-scaled multiplicative correction problem, and the MLACF estimates are used both to define non-rigid image warps (via diffeomorphic demons registration of gate-by-gate reconstructions) and to provide gate-matched attenuation for the final joint reconstruction.

What would settle it

Acquire a moving phantom whose true attenuation is known at each respiratory gate (for example, by fast CT at each phase) alongside the PET list-mode data. If the jointly estimated gate-matched attenuation sinograms do not match the true phase-matched CT sinograms up to the known scaling ambiguity, or if the final activity image does not match a reconstruction that used the true gated attenuation, the central claim that the data-driven estimates are free of attenuation bias is contradicted.

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Extended reading notes

Core claim

The central claim is that respiratory self-gated TOF PET data contain enough information to estimate, purely from the emission data, the respiratory phase-matched attenuation sinograms and the non-rigid motion between respiratory gates, and to combine all gates into a single high-quality activity image. The load-bearing idea is to write each gate's attenuation sinogram as a product of a breath-hold CT-based static attenuation sinogram and nonnegative gate-specific correction factors, estimated with MLACF updates and an intensity prior that keeps the correction factors close to unity; this resolves the scale ambiguity inherent in joint activity/attenuation estimation. Attenuation and motion estimates obtained either separately (Hybrid) or jointly (ADMM) are then used in a final joint-reconstruction OS-MLEM that uses all acquired counts. The paper reports that this restores phantom lesion contrast to the static-scan value and visibly removes motion and attenuation artifacts in patients.

Load-bearing premise

The whole pipeline presumes that the breath-hold CT-based static attenuation sinogram is a valid baseline and that every respiratory attenuation change can be represented by nonnegative multiplicative correction factors pulled toward 1 by a hand-tuned intensity prior, with a static scatter estimate treated as adequate.

Editorial extensions

If this is right

  • A single activity image can be reconstructed from all respiratory gates, using all counts without discarding data, which minimizes noise while removing motion blur.
  • The data-driven PCA-based respiratory signal correlates strongly with the true motion signal (Pearson correlation 0.91 in the phantom), so external gating hardware can be omitted.
  • Correcting attenuation per gate removes the liver-dome banana artifact and improves lesion-to-background contrast beyond motion correction with static attenuation alone.
  • The comparable performance of both methods across two scanner types (Siemens mCT and GE DMI) suggests the approach generalizes to different TOF PET/CT systems.
  • The authors recommend Hybrid JRMA for clinical translation over ADMM JRMA because the latter is sensitive to the Lagrangian penalty parameter.

Reading between the lines

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

  • If the multiplicative correction model and the intensity prior hold for other attenuation mismatches (for instance, patient positioning differences in PET/MRI), the same factorization could be applied as long as a reliable baseline attenuation image is available.
  • The motion vector fields were underestimated (12.2 mm vs. the true 20 mm in the phantom), so residual bias in small moving-structure quantification is likely; clinical use would need to tolerate or compensate for that bias.
  • The method's reliance on a static scatter estimate may limit accuracy at high scatter fractions; replacing it with gated scatter estimates is a testable extension.
  • The hybrid pipeline's dependence on non-rigid registration of MLACF reconstructions means that registration errors propagate into the final image; learning-based motion priors could reduce that error.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The manuscript proposes two data-driven algorithms for jointly estimating activity, gate-dependent attenuation, and respiratory motion in respiratory self-gated TOF PET, with the goal of producing a single motion- and attenuation-corrected activity image without external respiratory hardware. The hybrid JRMA method estimates gate-by-gate MLACF attenuation sinograms and motion warping operators from gate-by-gate MLACF reconstructions, then performs a final JR OS-MLEM reconstruction; the ADMM JRMA method couples these estimates inside a modified ADMM framework. The methods are evaluated on a moving Wilhelm thorax phantom with a matching static reference acquisition and on three clinical FDG PET/CT datasets. The phantom experiment shows lesion-to-background contrast improving from 2.0 (no motion correction) to 5.2/5.3 with the proposed methods, matching the 5.2 contrast of the static reference, while patient datasets show reduced banana artifacts and improved lesion contrast on visual inspection.

Significance. If fully validated, this work would make respiratory motion and attenuation correction more practical by removing the need for external respiratory hardware and by estimating gate-matched attenuation without reconstructing attenuation images. The phantom experiment with an independent static reference is the strongest element, and the evaluation on two different scanner platforms supports generalizability. The appendix derivations are coherent, the MLACF-based updates are transparent, and the authors honestly recommend the simpler hybrid method over the more complex ADMM variant. The principal quantitative result, contrast recovery matching the static phantom, is compelling. However, the headline claims are not yet directly supported: the only ground-truth phantom experiment used the actor-based gating signal rather than the data-driven signal, and the attenuation model is a regularized multiplicative correction to a breath-hold CT sinogram, so the 'free from attenuation artifacts' claim is conditional on the CT prior and on the manually tuned regularization strength. The paper is a solid proof-of-concept but needs additional validation before the stated guarantees can be accepted.

major comments (4)
  1. [Section 4, Fig. 2] The quantitative Wilhelm phantom experiment uses the actor-based ground-truth gating signal for gate definition rather than the PCA data-driven signal, as stated in Section 4: 'we decided to use actor-based ground-truth signal for the gate definition in the Wilhelm acquisition.' Because the headline claim is operation without external hardware, the only ground-truth experiment does not test that claim. Please repeat the phantom evaluation with data-driven gating, or quantitatively assess the sensitivity of lesion contrast and artifact reduction to the choice of gating signal.
  2. [Section A.2, Eqs. (21)-(24); Table 2] The gate-dependent attenuation is modeled exclusively as nonnegative multiplicative correction factors g_k applied to the breath-hold CT attenuation sinogram, regularized toward unity with gamma = 0.2 mean(emission sinogram). The claim that the reconstructed images are 'free from attenuation artifacts' is therefore conditional on the CT-derived baseline being accurate and on gamma being appropriately tuned. No experiment perturbs the CT prior (e.g., misregistration, truncation, or bias) or varies gamma. Because a biased CT prior cannot be fully corrected by g_k under the strong regularization, please add robustness tests over both the CT prior and gamma, or explicitly reformulate the claim to reflect this dependence.
  3. [Section 4, Fig. 4] The estimated peak displacement between gate 1 and gate 6 is 12.2 mm against the true 20 mm, a 39% underestimation, and the corresponding JR MLEM estimate is 9.3 mm. The paper offers plausible explanations (intra-gate motion, 5 mm slices, regularization) but provides no quantitative evidence that this residual motion error does not affect the final activity image or the reported contrast recovery. Please quantify residual motion after correction in the static-reference phantom, or provide a motion-error sensitivity analysis, to support the claim that the methods produce a motion-corrected image.
  4. [Section 5.2; Eq. (23)] The MLACF attenuation update in Eq. (23) uses the expected scattered and random coincidences r_k in the numerator, but the scatter estimate is static and not gate-matched, as acknowledged in Section 5.2. Since the attenuation correction factors g_k are estimated jointly with the emission data, a gate-dependent scatter mismatch could bias the estimated attenuation sinograms. Please add a sensitivity analysis or a brief quantitative argument showing that smooth, static scatter does not materially bias g_k in the tested count statistics.
minor comments (6)
  1. [Abstract and Fig. 1] The acronym is used inconsistently: 'JMRA' appears in Figure 1 and in some text passages, while the title and most of the manuscript use 'JRMA.' Please standardize the acronym throughout.
  2. [Fig. 5 caption] The caption contains a typo: 'reconstructon' should be 'reconstruction.'
  3. [Section 3.2.2] The injected activity is written as '4.25 ˙MBq/kg' with an unusual dot before 'MBq'; this should be '4.25 MBq/kg.'
  4. [Section 2.4] The text says the algorithm is divided into 'four simpler subproblems' but then lists five subproblems (subproblems 1 through 5). Please renumber or reword the introduction to this subsection.
  5. [Appendix A.3, Eqs. (25)-(27)] The replacement of the exact ADMM subproblem (25) with the denoising problem (26)-(27) using the average of inverse-warped gate images is an approximation that is not covered by standard ADMM convergence theory. Because this is a heuristic modification, it should be flagged as such in the main text rather than only in the appendix.
  6. [Section 3.3] The paper does not state whether the reconstruction code or phantom data will be made available. A data/code availability statement would improve reproducibility, especially given the complexity of the proposed pipelines.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the reported contrasts are measured against an independent static acquisition, and the MLACF/TOF attenuation machinery is external, not fitted to the claimed endpoints.

full rationale

The derivation chain is self-contained rather than circular. The forward model (Eq. 1) and the joint optimization (Eq. 3) are standard Poisson-model formulations; the attenuation sinograms are estimated from the gated emission data via MLACF updates (Eq. 23), not by fitting the lesion contrast or any reported endpoint. The phantom validation compares against a separate 10-minute static acquisition with phase-matched CT attenuation, which is an independent external benchmark: the lesion-to-background contrast of 5.2 is measured, not enforced by construction. The paper does rely on prior work by overlapping authors for the MLACF algorithm [5] and for the TOF attenuation-identification theory [3], [4], but those are published, externally established results and are not invoked as a substitute for the current experiment. The passages that weaken the claims are limitations, not circular steps: Section 4 states that the Wilhelm gate definition used the actor-based 'ground-truth' signal rather than the data-driven signal, and Section 5.2 concedes a static scatter estimate and hand-tuned parameters (γ and ρ). These affect generalizability and robustness, but no equation reduces to its own input and no fitted parameter is renamed as a prediction. Therefore the circularity score is 0.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the CT-based attenuation prior, the Poisson gating model, two analytic approximations in the ADMM solver, and hand-tuned regularizer weights; no new physical entities are introduced. The phantom static acquisition is the main external anchor.

free parameters (4)
  • Intensity prior weight gamma = gamma = 0.2 x mean(emission sinogram)
    Controls how strongly MLACF correction factors are pulled toward 1; it must resolve the activity and attenuation scale ambiguity without suppressing motion-related attenuation changes (Section 5.1, Table 2).
  • ADMM penalty parameter rho = rho = 1e-6 after rescaling forward operators to unit norm
    Sets the quadratic penalty in the augmented Lagrangian; the authors report improper tuning can cause poor performance or divergence (Section 5, Table 2).
  • Total variation weight beta = beta = 7e-5
    Controls edge-preserving smoothing of the activity image in ADMM subproblem 3 and affects motion estimation; no ablation study is provided (Table 2).
  • Number of respiratory gates = 6
    Defined by amplitude-based gating of the PCA signal; more gates would reduce intra-gate motion but lower counts per gate, and the chosen value contributes to the measured 12.2 mm versus 20 mm motion underestimation (Section 5).
assumptions (6)
  • domain assumption A breath-hold CT/MR attenuation image is available and all respiratory attenuation changes can be represented as nonnegative multiplicative correction factors on its sinogram.
    Used in Eq. (21)-(24) and in both methods; if the CT baseline is wrong or the multiplicative factor model cannot express true attenuation changes, the gate-matched attenuation and the final activity image inherit errors.
  • domain assumption TOF-PET emission data determine the attenuation sinogram up to a global constant, as established in the cited literature.
    This identifiability result is the theoretical basis for MLACF and for the JRMA attenuation updates; if it failed, attenuation could not be estimated from emission data alone.
  • domain assumption Each respiratory gate is an independent Poisson realization with known expected scatter and random coincidences.
    Defines the likelihood in Eqs. (1)-(3); the paper uses a static, non-gated scatter estimate, so this assumption is only approximately met (Section 5.2).
  • domain assumption Respiratory motion is modeled by invertible diffeomorphic warps that can be recovered by demons registration of gated reconstructions.
    Needed for the inverse-warp averaging in Eq. (27) and for the motion subproblem in Eq. (29); the measured displacement of 12.2 mm versus the true 20 mm shows the assumption is only partially accurate (Section 5).
  • ad hoc to paper The Poisson likelihood in the attenuation update can be replaced by a non-TOF weighted Gaussian likelihood to obtain an analytic MLACF update.
    Introduced in Appendix A.2 before Eq. (23) to make the update analytic; this approximation is not exact and is not validated against the original Poisson likelihood.
  • ad hoc to paper ADMM subproblem 3 can be approximated by a single-denoising problem using the average of inverse-warped gate images.
    Made for computational efficiency in Eqs. (26)-(27); it replaces the exact lambda-update with a heuristic average, so the ADMM algorithm has no convergence guarantee (Section 2.4, A.3).

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Pith. "Pith review of Joint estimation of activity, attenuation and motion in respiratory-self-gated time-of-flight PET." pith.science (2026). https://pith.science/paper/7K3CYB2E

@misc{pith2026241215018,
  author       = {Pith},
  title        = {Pith review of: Joint estimation of activity, attenuation and motion in respiratory-self-gated time-of-flight PET},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7K3CYB2E}},
  note         = {Machine review of arXiv:2412.15018}
}
read the original abstract

Whole-body PET imaging is often hindered by respiratory motion during acquisition, causing significant degradation in the quality of reconstructed activity images. An additional challenge in PET/CT imaging arises from the respiratory phase mismatch between CT-based attenuation correction and PET acquisition, leading to attenuation artifacts. To address these issues, we propose two new, purely data-driven methods for the joint estimation of activity, attenuation, and motion in respiratory self-gated TOF PET. These methods enable the reconstruction of a single activity image free from motion and attenuation artifacts. The proposed methods were evaluated using data from the anthropomorphic Wilhelm phantom acquired on a Siemens mCT PET/CT system, as well as 3 clinical FDG PET/CT datasets acquired on a GE DMI PET/CT system. Image quality was assessed visually to identify motion and attenuation artifacts. Lesion uptake values were quantitatively compared across reconstructions without motion modeling, with motion modeling but static attenuation correction, and with our proposed methods. For the Wilhelm phantom, the proposed methods delivered image quality closely matching the reference reconstruction from a static acquisition. The lesion-to-background contrast for a liver dome lesion improved from 2.0 (no motion correction) to 5.2 (proposed methods), matching the contrast from the static acquisition (5.2). In contrast, motion modeling with static attenuation correction yielded a lower contrast of 3.5. In patient datasets, the proposed methods successfully reduced motion artifacts in lung and liver lesions and mitigated attenuation artifacts, demonstrating superior lesion to background separation. Our proposed methods enable the reconstruction of a single, high-quality activity image that is motion-corrected and free from attenuation artifacts, without the need for external hardware.

Figures

Figures reproduced from arXiv: 2412.15018 by the authors.

Figure 1
Figure 1. Overview of the workflow for data-driven gating and different image reconstruction algorithms [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. PCA derived respiratory gating signal (orange) in comparison to actor signal (blue) for (a) the [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Same coronal slices of gate-by-gate MLEM reconstructions using a single static attenuation [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: (top row) sagittal slice of reconstructions of the estimated gate-by-gate attenuation sinograms [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: (left) coronal lesion slice, (2nd from left) sagittal lesion slice, (3rd from left) sagittal slice of [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: (left) coronal lesion slice, (2nd from left) sagittal lesion slice, (3rd from left) coronal slice of [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

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