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REVIEW 5 major objections 4 minor 47 references

Lesion-Aware Adaptive Fourier Neural Operator for CT-to-PSMA PET Synthesis in Prostate Cancer

T0 review · 5 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper claims that conditioning a Fourier-neural-operator synthesis model on two CT-derived proxy channels and training with lesion-aware losses preserves lesion activity and tumor radiomics in synthetic PSMA-PET, where global…

desk verdict A well-motivated lesion-aware synthesis method whose headline TLA gains are likely optimistic because the loss weights and proxy scales were chosen on the test cohort. read the letter →

arxiv 2608.10429 v1 pith:5DPD7JP4 submitted 2026-08-11 cs.CV physics.med-ph

Rashmi Bhaskara , Waleed M. Almutairi , Matthew Gopaulchan , Maram Musaad Alqurashi , Francis Asamoah , Alex Ocana , Clinton D. Bahler , Oluwaseyi M. Oderinde This is my paper · ORCID
classification cs.CVphysics.med-ph
keywords PSMAPETSyntheticProstatecancerLesion-awarelearningAdaptiveFourierneuraloperatorTumormicroenvironmentRadiomics
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

Whole-body PSMA-PET carries the clinically decisive tumor signal in a tiny fraction of voxels, so models trained to maximize whole-volume similarity can look good while underestimating lesion activity. LAFNO is a CT-to-PET synthesis model that replaces expensive radiomics conditioning with two cheap CT-derived proxy channels—local density contrast and local texture disorder—and trains with lesion-level total-activity, tumor-core contrast, and peritumoral supervision. On a multi-scanner, two-tracer prostate cancer dataset, it reduces mean per-patient total-lesion-activity error to 48.3 percent for 18F-PSMA and 64.0 percent for 68Ga-PSMA, improves tumor-core radiomics reproducibility in every feature class for both tracers, and stays competitive on whole-volume quality. If the result holds, synthetic PET could support lesion quantification and radiomics without administering a tracer or delineating lesions at inference time.

What carries the argument

The central mechanism is the pair of differentiable CT proxy channels plus a lesion-aware loss. The contrast proxy is a Gaussian residual filter that captures the smooth density gradient from tumor core to periphery; the disorder proxy is a sliding-window local variance that captures peritumoral texture heterogeneity. They are computed from CT alone, so at inference no lesion segmentation is needed. They are pooled (average for contrast, max for disorder) and concatenated into the Adaptive Fourier Neural Operator bottleneck, which performs spectral channel mixing so the proxy-conditioned features influence long-range spatial structure. The lesion-wise total-activity loss uses a log-compressed, per-lesion-normalized summed-activity error so small lesions are not dominated by large ones; the tumor-contrast loss supervises the contrast operator on predicted versus ground-truth SUV within the tumor mask; and the peritumoral loss applies an exponential distance-decay weight in the 0–10 mm ring. Together these terms push the model to preserve lesion-level activity and tumor-adjacent structure rather than optimizing global similarity alone.

What would settle it

On an independent cohort of PSMA-PET/CT patients from different scanners, tracers, or institutions, train LAFNO and the CT-only AFNO-L1 baseline with the proxy scales fixed at $\sigma = 5$ mm and $w = 7.5$ mm; if per-patient TLA error and tumor-core radiomics reproducibility no longer improve over the baseline, the proxy conditioning claim is falsified. A cheaper check: replace the two proxy channels with identically shaped channels containing CT intensity or white noise, holding all losses fixed; if TLA error and ICC do not worsen, the proxies' specific encoding carries no weight.

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Extended reading notes

Core claim

The paper's central claim is that a CT-to-PSMA-PET synthesis model conditioned on radiomics-motivated CT proxies and supervised at the lesion level preserves the clinically relevant PET signal that global L1 or MSE training discards. The contrast proxy $C(\mathbf{x}) = \mathrm{CT}(\mathbf{x}) - G_\sigma * \mathrm{CT}(\mathbf{x})$ with $\sigma = 5$ mm encodes the observed core-to-periphery CT attenuation gradient, and the disorder proxy $D(\mathbf{x})$ is local variance over a $7.5$ mm window, encoding tumor-adjacent texture heterogeneity; both are injected into the Adaptive Fourier Neural Operator bottleneck of a 3D U-Net. The loss combines whole-volume L1 with a per-lesion total-activity term, a tumor-core contrast term, and an exponentially distance-weighted peritumoral term. In the reported evaluation LAFNO attains SSIM 0.960 and 0.938 and per-patient TLA errors 48.3 and 64.0 percent for 18F- and 68Ga-PSMA, and the highest tumor-core radiomics ICCs across first-order, GLCM, GLRLM, and GLSZM classes for both tracers, while peritumoral reproducibility remains tracer-dependent. The authors interpret the remaining error as inherent one-to-many CT-to-PET mapping and tracer or SUV heterogeneity rather than a failure that purely architectural changes would fix.

Load-bearing premise

The load-bearing premise is that the two hand-coded CT filters—a 5 mm Gaussian residual and a 7.5 mm local variance—capture CT patterns that actually predict PSMA-PET uptake in and around lesions, and that the chosen scales generalize beyond the dataset where they were selected.

Editorial extensions

If this is right

  • On 18F-PSMA, per-patient TLA error drops to 48.3 percent from 58.7 to 69.0 percent for the four baselines, so a trained model can estimate lesion activity from CT alone at inference.
  • On 68Ga-PSMA, LAFNO reaches 64.0 percent per-patient TLA error and the highest fraction of lesions within 50 and 75 percent error, though cWDM is comparable on absolute lesion-level error.
  • Tumor-core radiomics reproducibility is the highest of all compared models for every feature class on both tracers, indicating the synthetic volumes carry texture-level information rather than only pixel similarity.
  • The ablation shows proxy conditioning alone cuts TLA error from 62.2 to 56.5 percent even without lesion masks or lesion-specific losses, so the CT-derived channels contribute independent information.
  • Whole-volume SSIM (0.960 and 0.938) and PSNR remain competitive with baselines, so the lesion-aware objectives do not trade away global image quality.

Reading between the lines

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

  • If the proxy scales were learned per scanner or tracer rather than fixed on the evaluation dataset, TLA gains might transfer more reliably across institutions; this is a testable extension not performed by the paper.
  • Because the proxies need no lesion segmentation, coupling LAFNO with an automatic lesion detector would give a fully mask-free, CT-only pipeline for PSMA lesion burden.
  • The 68Ga weakness and the peritumoral reproducibility peak at 3–5 mm suggest positron range and partial-volume effects are limiting; partial-volume correction before training or evaluation is a natural next test.
  • The peritumoral term's effect is essentially confined to GLSZM in the 0–3 mm band, implying a single distance-weighted L1 penalty is too weak to shape the whole tumor-adjacent microenvironment; adversarial or multi-scale texture losses are worth trying.
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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

5 major / 4 minor

Summary. The manuscript proposes LAFNO, a 3D U-Net with an Adaptive Fourier Neural Operator bottleneck for synthesizing PSMA-PET from CT in prostate cancer. The main novelties are two handcrafted CT-derived proxy channels (contrast and disorder) injected at the bottleneck, and a training objective that combines whole-volume L1 with lesion-wise total lesion activity (TLA), tumor-core contrast, and distance-weighted peritumoral losses. The authors evaluate on the TCIA PSMA-PET-CT-Lesions dataset with 18F- and 68Ga-PSMA cohorts against four baselines, reporting lesion-level and patient-level TLA error, fractions of lesions within error thresholds, and tumor-core/peritumoral radiomics ICC. They report that LAFNO remains competitive on SSIM/PSNR/MAE while improving TLA error and tumor-core radiomics reproducibility, with a cumulative ablation on the 18F cohort.

Significance. If the results are validated, LAFNO is a useful step toward clinically meaningful CT-to-PET synthesis because it targets lesion-level activity and radiomic structure rather than only global similarity, and the proxy-conditioning idea avoids per-inference radiomics extraction. Strengths include the cumulative ablation isolating each component, the use of lesion-level and radiomics evaluation beyond global metrics, and the explicit discussion of tracer-dependent limitations. However, the absence of a held-out validation set for hyperparameter selection, the lack of statistical inference, and an inconsistency in the TLA loss formulation mean the reported quantitative claims are not yet established. The work is therefore of interest to the medical image synthesis community, but the evidence requires strengthening before publication.

major comments (5)
  1. [§2.2, §5.1, §5.5] The proxy scales σ=5mm and w=7.5mm are described as chosen empirically, and the TLA loss formulation, λ_TLA=0.05, and λ_peri=0.05 are selected from curves and ablations computed on the same 18F test cohort used for the final evaluation (Figure 7, Table 5). With only N=47 test patients and no held-out validation or nested cross-validation, the reported improvements, e.g., patient-level TLA 48.3% vs. 62.2%, may be inflated by selection. Please either introduce a strict validation split for all hyperparameter choices or demonstrate that the conclusions are stable under repeated random splits.
  2. [Table 5] The cumulative ablation shows that adding the peritumoral term changes patient-level TLA error from 47.8% to 48.3%, lowers the ≤25% and ≤50% fractions from 25.2/54.9 to 24.0/50.9, and decreases every tumor-core ICC class (e.g., GLSZM from 0.760 to 0.709). The text states this term leaves the metrics 'essentially unchanged', which is contradicted by the table; it also raises the question of why the term is retained in the final model. This internal inconsistency, combined with the test-set tuning, undermines the ablation-based justification of the final configuration.
  3. [§2.4, Eq. (5); §3.2, Eq. (9)] The TLA loss is defined with ŝ_i and s_i as 'SUV values', but the model is trained on log-normalized PET values from Eq. (9). If the loss is computed on normalized outputs, then A_k and ^A_k are sums of nonlinearly transformed values and are not proportional to physical TLA; the inverse log transform in Eq. (9) is nonlinear, so the proportionality claim does not hold. Please state explicitly whether the inverse transform is applied before computing the TLA loss, or revise the loss definition and the interpretation of the reported TLA improvements accordingly.
  4. [§3.1, Table 3] For 68Ga-PSMA, the patient-level TLA error of LAFNO is 64.0% versus 63.9% for cWDM, so LAFNO does not reduce patient-level TLA error relative to the best baseline on that tracer. Since the 68Ga cohort is less affected by the tuning performed on 18F, this equality weakens the cross-tracer generalization claim and should be reported as a limitation rather than as a reduction.
  5. [§3.2, §3.3] The manuscript does not report confidence intervals, significance tests, or repeated-seed variability for the main TLA and ICC comparisons, and it does not specify the patient-level train/test split (e.g., whether all scans of a patient were confined to one split). These details are essential for assessing whether the reported differences are robust, and the split specification is needed to rule out leakage. Please add this information.
minor comments (4)
  1. [Section 4.3] The text refers to 'Figure 8' for peritumoral reproducibility by distance band, but the figure with that content is labeled Figure 6; the later ablation figure is Figure 8. Please fix the cross-reference.
  2. [Eq. (7)] The sentence 'with this value, the weight decreases to half of its boundary value from the tumor boundary' is inaccurate: with τ=5mm the half-value distance is τ ln 2 ≈ 3.47mm, not 5mm, where the weight is e^{-1} ≈ 0.368 of the boundary value.
  3. [Abstract] The abstract's phrase 'reducing per-patient TLA error to ... 64.0%' for 68Ga is misleading given that cWDM achieves 63.9% on the same metric; please qualify the claim.
  4. [Section 5.1] The paragraph describing the final choice of λ_TLA states that the overestimation rate is below 20% in the final model; the corresponding values (19.98% and 10.47%) appear only in the text and not in Table 3, making the table incomplete for this claim.

Circularity Check

1 steps flagged · score 4.0 of 10

Hyperparameters for the lesion-aware loss and proxy scales are selected on the same 18F-PSMA cohort used for the headline TLA evaluation, so the reported improvement is partly a selected result rather than an independent prediction; the derivation itself is not circular by construction.

  1. fitted input called prediction [Section 5.1 (loss-form and lambda_TLA choice, Figure 7) applied to the final model evaluated in Section 4.2 (Table 3); proxy scale w=7.5mm set in Section 2.2 on the same dataset.]
    "We therefore adopt the lesion-wise L_TLA formulation. Its higher accuracy at large λ comes with an increased overestimation rate, which is why the final model uses a low weight of λTLA=0.05 and relies on the CT proxy channels and the tumor-contrast loss L_c to improve tumor-level performance. This keeps the overestimation rate below 20% in the final model: 19.98% for 18F-PSMA with 48.35% absolute TLA error ... as reported in Table 3."

    The final TLA formulation, its weight, and the proxy window size are chosen by inspecting curves and ablations computed on the same 18F-PSMA cohort (N=47) that later supplies the headline per-patient TLA error of 48.3% in Table 3. lambda_TLA=0.05 was selected specifically to keep the overestimation rate below 20% on that cohort, so the reported 48.35% is not an out-of-sample prediction but a post-selection measurement on the tuning set. The 68Ga cohort (N=30) was not used for this selection, and there LAFNO does not beat cWDM on patient-level TLA (64.0% vs 63.9%), which is consistent with the 18F advantage being partly driven by test-set selection.

full rationale

LAFNO is an empirical deep-learning synthesis method, not a first-principles derivation, and most of its components (CT proxy channels, lesion-aware losses, radiomics evaluation) are independent of one another. I found no equation that is equivalent to its input by construction, and no load-bearing self-citation: the AFNO bottleneck is motivated by the authors' earlier work, but that citation only supports an architectural choice and is not invoked to forbid alternatives. The genuine circularity concern is evaluation-set selection: Section 5.1 tunes the per-lesion loss form and lambda_TLA on the same 18F-PSMA test cohort whose TLA error is then reported as the headline result, and Section 2.2 sets proxy scales empirically on the same dataset; Section 5.5 also retains L_peri after observing on that cohort that it slightly worsens TLA and tumor-core ICC while improving a narrow peritumoral GLSZM band. Thus the 18F improvement is partly a selected optimum rather than an independent prediction. The 68Ga results, which were not used for tuning, are weaker and do not show a patient-level TLA advantage over cWDM, reinforcing the interpretation that the 18F gain is inflated by selection. Because the central architecture and losses still have empirical content and the selection is disclosed in the ablation, the appropriate score is 4 rather than 6 or higher.

Assumptions & free parameters 5 free parameters · 4 assumptions · 2 invented entities

The central claim rests on several ingredients the paper assumes rather than proves: the accuracy of the TCIA lesion masks and SUV values, the learnability of the CT-to-PET mapping, and the transferability of the hand-tuned proxy scales and loss weights. The proxy scales and loss weights are free parameters selected on the same dataset used for evaluation, which is the main in-sample tuning risk. No new physical entities are introduced; the contrast and disorder proxies are computational channels with no external validation.

free parameters (5)
  • contrast proxy scale sigma = 5 mm
    Gaussian residual kernel width in Eq. 1, chosen to match the observed CT firstorder_Mean decay from the tumor core; tuned on the same dataset.
  • disorder proxy window w = 7.5 mm
    Local variance window width in Eq. 2, chosen empirically to capture tumor-peritumoral texture transitions.
  • peritumoral decay tau = 5 mm
    Exponential distance weight in Eq. 7, setting the half-decay distance from the tumor boundary.
  • loss weights lambda_TLA, lambda_c, lambda_peri = 0.05, 0.02, 0.05
    Hand-set in Eq. 4; the ablation in Sec 5.1 shows the TLA weight choice affects the overestimation rate, so values are tuned on the evaluation cohort.
  • SUVmax normalization ceiling = cohort-dependent
    Global SUV ceiling in Eq. 9 used to normalize PET; affects all SUV errors and is computed from the dataset.
assumptions (4)
  • domain assumption Ground-truth PSMA-PET lesion masks and SUV values in the TCIA dataset are accurate enough for training and evaluation.
    The TLA and peritumoral losses require lesion masks, and all evaluation metrics use them; inaccurate delineations would bias results.
  • domain assumption The CT-to-PET mapping is sufficiently learnable from paired CT/PET data despite being one-to-many.
    Acknowledged in the Discussion; if the one-to-many ambiguity dominates, no deterministic model can recover true lesion uptake.
  • ad hoc to paper The two handcrafted proxies preserve the radiomics-observed trends outside the training cohort.
    The paper does not validate proxy fidelity on an independent dataset; Eqs. 1 and 2 assume the observed trends generalize.
  • standard math Standard deep learning training assumptions (batch norm, Adam, ReLU, etc.) work as expected.
    Unproved but conventional; not load-bearing for the clinical claim.
invented entities (2)
  • Contrast proxy channel C(x)
    purpose: Highlight local CT density variation to guide the network toward tumor-like regions.
    Defined by Eq. 1; no external validation that it captures PET-relevant biology beyond the paper's radiomics-motivated assertion.
  • Disorder proxy channel D(x)
    purpose: Highlight local texture heterogeneity in tumor-adjacent tissue.
    Defined by Eq. 2; no independent handle outside this paper.

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Cite this review

Pith. "Pith review of Lesion-Aware Adaptive Fourier Neural Operator for CT-to-PSMA PET Synthesis in Prostate Cancer." pith.science (2026). https://pith.science/paper/5DPD7JP4

@misc{pith2026260810429,
  author       = {Pith},
  title        = {Pith review of: Lesion-Aware Adaptive Fourier Neural Operator for CT-to-PSMA PET Synthesis in Prostate Cancer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5DPD7JP4}},
  note         = {Machine review of arXiv:2608.10429}
}
read the original abstract

Deep learning models that synthesize PET from CT or MRI can reduce patient dose and scanner demand, but are typically optimized with global losses such as L1 or mean squared error (MSE) that treat all voxels similarly. In whole-body PSMA-PET, tumor voxels occupy only a small fraction of the volume, yet carry the clinically relevant activity signal; as a result, models can achieve high structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) while still underestimating lesion activity or failing to preserve tumor-specific structure. Radiomics provides biologically meaningful descriptors of tumor intensity and texture, but direct radiomics conditioning is time-consuming because it requires feature extraction from delineated lesion regions. We propose LAFNO, a Lesion-Aware Adaptive Fourier Neural Operator for CT-to-PSMA-PET synthesis that replaces high-dimensional radiomics conditioning with two efficient CT-derived proxy channels. Motivated by radiomics analysis of PSMA-avid tumor core and peritumoral regions, LAFNO uses a contrast proxy for local density variation and a disorder proxy for local texture heterogeneity, both injected into the model bottleneck. LAFNO combines whole-volume reconstruction with lesion-level total lesion activity (TLA), tumor-core contrast, and peritumoral supervision. We evaluated LAFNO against four baseline architectures on the TCIA PSMA-PET-CT-Lesions dataset. LAFNO remained competitive on whole-volume image quality, achieving SSIM of 0.960 and 0.938 for 18F- and 68Ga-PSMA, respectively, while reducing per-patient TLA error to 48.3% and 64.0% for 18F- and 68Ga-PSMA, respectively, and achieving the highest tumor-core radiomics reproducibility across all feature classes for both tracers. Peritumoral reproducibility remained tracer-dependent, indicating that biological fidelity in synthetic PSMA-PET remains challenging.

Figures

Figures reproduced from arXiv: 2608.10429 by the authors.

Figure 1
Figure 1. CT radiomics profiles from the tumor core to peritumoral shells. (A) firstorder_Mean decreases outward. (B) firstorder_Entropy increases from tumor core to peritumoral tissue and remains relatively stable. features may depend on their spatial distance from the tumor boundary Liu et al. (2025). Therefore, our radiomics analysis explicitly includes the peritumoral region, and motivates the disorder proxy, which approx… view at source ↗
Figure 2
Figure 2. Representative CT-derived proxy maps showing the CT image, contrast proxy, and disorder proxy. Zoomed panels highlight the lesion neighborhood. Zwanenburg et al. (2016). Entropy increased significantly on leaving the tumor core at both lesion and patient levels. At the lesion level, entropy peaked in the 0–5 mm shell, suggesting increased heterogeneity near the tumor boundary. At the patient level, entropy increased… view at source ↗
Figure 3
Figure 3. Overview of the proposed LAFNO architecture with CT proxy conditioning and lesion-aware training supervision. 2.3. LAFNO Architecture LAFNO is a 3D U-Net with an Adaptive Fourier Neural Operator (AFNO) bottleneck Guibas et al. (2021). The encoder applies three stride-2 convolution blocks (Conv3D + BatchNorm + LeakyReLU), mapping a 643 CT patch to an 8 3 representation with 256 channels. The decoder mirrors the encod… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Representative reconstructions from different CT-to-PET synthesis models. supervision. This baseline isolates the effect of the proposed proxy channels and lesion-aware loss while keeping the core architecture fixed. Pix2Pix. Pix2Pix Isola et al. (2017) was used as a 3…
Figure 5
Figure 5. Figure 5: Predicted versus real per-lesion TLA on log–log axes for 18F-PSMA (top) and 68Ga-PSMA (bottom). The dashed line indicates perfect agreement; the annotation gives the mean absolute TLA error across all lesions. All models underestimate high-activity lesions, while LAFNO…
Figure 6
Figure 6. Figure 6: Peritumoral radiomics reproducibility (ICC) by distance band from the tumor boundary, for 18F-PSMA (left) and 68Ga-PSMA (right). The dashed curve shows the training loss weight exp(−𝑑∕5). In the 0–10 mm peritumoral ring, LAFNO achieved the highest ICC across all featur…
Figure 7
Figure 7. Figure 7: Per-lesion loss formulations across 𝜆 ∈ {0.05, 0.1, 0.5, 1.0} on 18F-PSMA. (A) Per-patient overestimate rate. (B) Per-patient absolute TLA error. TumorL1 (TumorL1) saturates after 𝜆 = 0.1; the TLA loss (TLA) continues to respond across the full range. rate flattens n…
Figure 8
Figure 8. Figure 8: Peritumoral radiomics reproducibility (ICC) by distance band, before and after adding peri, for each feature class ( 18F-PSMA). The before/after curves overlap for first-order, GLCM, and GLRLM; the main effect is on GLSZM in the 0–3 mm band. only marginally, and radio…
Figure 9
Figure 9. Figure 9: Whole-volume SUVmax percentage error on the normalized [0, 1] scale and after conversion back to SUV space, for 18F-PSMA (left) and 68Ga-PSMA (right). The inverse log transform amplifies error at the high-uptake end, so SUV-scale error is consistently larger than norma…
Figure 10
Figure 10. Figure 10: CT- and T2-weighted MRI-derived proxy maps in a prostate-region example. The same contrast and disorder operations highlight a stronger local prostate structure on MRI than on CT. density variation and local texture heterogeneity. These proxies do not fully resolve le…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.