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End-to-end Triple-domain PET Enhancement: A Hybrid Denoising-and-reconstruction Framework for Reconstructing Standard-dose PET Images from Low-dose PET Sinograms

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that TriPLET, a hybrid denoising-and-reconstruction framework operating on sinograms, wavelet frequency maps, and images, reconstructs standard-dose PET images from low-dose PET sinograms with higher similarity and…

desk verdict Solid incremental extension of the authors' TriDoRNet with a clear, honest statement of its main limitation: all sinograms are synthesized from reconstructed images, so the raw-data claim is untested. read the letter →

arxiv 2412.03617 v1 pith:RXUM56WH submitted 2024-12-04 eess.IV cs.CV

Caiwen Jiang , Mianxin Liu , Kaicong Sun , Dinggang Shen This is my paper · ORCID
classification eess.IVcs.CV
keywords low-dosePETstandard-dosereconstructionsinogramdenoisingtriple-domainframeworkdiscretewavelettransformTransformergenerativeadversarialnetworkRadon
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

TriPLET is an end-to-end framework for converting low-dose PET sinograms into standard-dose PET images. The paper's thesis is that this conversion is best done as a hybrid denoising-and-reconstruction process that works in three coupled domains: a denoising network cleans the LPET sinogram in the projection domain before any reconstruction happens; a wavelet-domain reconstruction network then builds the image with explicit frequency sub-band supervision; and an adversarial network judges the result in the image domain. The authors argue that a significant part of the LPET-to-SPET gap lives in projection-domain noise, so removing noise before reconstruction matches the physics of PET and stops noise from being amplified later. On their chest-abdomen dataset they report the highest similarity and signal-to-noise ratio against six comparison methods, with PSNR of 25.932 ± 0.671 dB, SSIM of 0.992 ± 0.004, and rRMSE of 0.296 ± 0.213 on the internal test set, and top results on an external dataset. If the claim holds, the practical consequence is that patients could receive one-tenth of the usual radiotracer dose while reconstructed images stay close to standard-dose quality.

What carries the argument

The machinery is the triple-domain pipeline itself, coupled end to end: DenNet turns an LPET sinogram into a denoised sinogram via residual CNN and windowed-transformer blocks; RecNet receives the denoised sinogram, passes it through an inverse Radon transform, and reconstructs the image in the wavelet domain using discrete wavelet and inverse wavelet transforms in place of pooling and upsampling; AdvNet evaluates the predicted SPET image against the real one in the image domain. The Radon transform and its inverse provide a lossless bridge between sinogram and image, and the discrete wavelet transform provides a lossless decomposition into eight sub-band frequency maps, so high-frequency details can be supervised separately. Three losses are aligned to the domains: projection-domain MSE ($\mathcal{L}_P$), focal frequency loss over wavelet sub-bands ($\mathcal{L}_F$), and image-domain MSE plus paired adversarial loss ($\mathcal{L}_I$), combined with GradNorm. The design choice the whole argument rests on is that noise in low-dose PET is most visible in the sinogram and best removed there, before reconstruction.

What would settle it

Train TriPLET on true list-mode low-dose raw sinograms paired with standard-dose reconstructions from a clinical scanner, then test on held-out raw data and compare PSNR, SSIM, and rRMSE with the reported 25.932 dB, 0.992, and 0.296; a substantial drop would show that the simulated-sinogram assumption, not the triple-domain design, drove the reported gains.

Watch

Extended reading notes

Core claim

The central discovery this paper advances is that a three-network cascade—DenNet, RecNet, and AdvNet—can reconstruct SPET images from LPET sinograms at the state of the art when each network is matched to the domain where its effect is strongest. DenNet uses alternating CNN and windowed-transformer blocks with residual learning to suppress sinogram noise; RecNet replaces the usual pooling and upsampling of a 3D U-Net with discrete wavelet and inverse wavelet transforms, decomposing the image into eight sub-band frequency maps and reconstructing it from them; AdvNet discriminates real from predicted image pairs, conditioning on the LPET image. The authors show by ablations that each added component—wavelet reconstruction, sinogram denoising, frequency loss, and adversarial evaluation—improves PSNR, SSIM, or rRMSE, and that the complete framework beats all six comparison methods with p < 0.05.

Load-bearing premise

The load-bearing premise is that sinogram patches obtained by applying the inverse Radon transform to reconstructed PET image patches faithfully represent real low-dose PET raw sinograms; the authors explicitly acknowledge in Section 4.1 that their indirectly obtained sinograms may differ from real raw data, so the projection-domain gain could shrink on clinical raw data.

Editorial extensions

If this is right

  • If TriPLET holds, clinical low-dose PET protocols could reduce injected radiotracer activity to one-tenth of the standard dose while images remain quantitatively close to standard-dose reconstructions.
  • Denoising the sinogram before reconstruction should suppress projection-noise amplification, so the hybrid ordering should matter most at very low doses where raw-data noise dominates.
  • Wavelet-domain supervision should preserve high-frequency boundaries and small structures better than pure image-domain GANs, reducing over-smoothing and edge blur.
  • The end-to-end design means a trained network produces a reconstructed SPET image in a single forward pass, without iterative OSEM-style reconstruction at inference time.
  • External validation on a different scanner suggests the benefit transfers across PET scanners, though with a measurable performance drop.

Reading between the lines

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

  • An implication the paper leaves implicit is that the simulated-sinogram-to-real-raw-data gap could be small enough that the same architecture would train directly on list-mode raw data, potentially extending to dynamic or total-body PET where noise statistics change across frames.
  • Because the sinogram patches are generated through the inverse Radon transform, the same three-domain recipe could transfer to other tomographic modalities whose raw data are sinogram-like, such as SPECT.
  • A direct testable extension is to train TriPLET on real raw sinograms paired with standard-dose reconstructions and compare against the reported 25.932 dB PSNR; the authors acknowledge performance may vary without quantifying how much.
  • The reported gains over the earlier TriDoRNet are small, so a reader should treat the transformer-based denoiser and adversarial network as refinements whose marginal value is measured mainly by the ablation study rather than by large leaps in absolute metrics.
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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

3 major / 6 minor

Summary. This paper proposes TriPLET, an end-to-end framework for reconstructing standard-dose PET (SPET) images from low-dose PET (LPET) sinograms. The method couples three subnetworks: a CNN-Transformer denoising network operating on sinograms, a wavelet-transform-based reconstruction network, and a paired adversarial network in the image domain, with losses in the projection, wavelet, and image domains. The authors evaluate TriPLET on 70 paired chest-abdomen uEXPLORER scans (converted to sinogram patches via inverse Radon transforms of reconstructed images) and on an external Ultra Low Dose PET challenge dataset, reporting the highest PSNR/SSIM and lowest rRMSE among six baselines, including their own prior TriDoRNet. The paper includes an ablation study of each component and acknowledges that the sinograms are not real raw data.

Significance. If the projection-domain results transfer to real raw sinograms, the hybrid denoising-and-reconstruction design is a sensible way to reduce noise propagation in low-dose PET, and the triple-domain supervision is a useful methodological contribution. The paper is transparent about its main limitation, ships a clear ablation chain, uses five-fold cross-validation, and provides an external dataset evaluation. However, the central quantitative claim is only as strong as the fidelity of the synthetic sinograms; the reported gain over TriDoRNet is small (PSNR +0.04 dB, SSIM +0.001, rRMSE -0.029), and the external validation reuses the same synthetic-sinogram pipeline, so it does not independently confirm that the projection-domain denoising generalizes to real raw data.

major comments (3)
  1. [Section 4.1, Fig. 4] The LPET sinograms used for training and testing are obtained by applying the inverse Radon transform to reconstructed image patches, not by acquiring raw list-mode or sinogram data. As the authors explicitly note, "sinograms indirectly obtained from reconstructed PET images may indeed differ from the real PET raw data." Reconstructed OSEM images already incorporate attenuation/scatter/random corrections, TOF modeling, and iterative regularization, so their inverse Radon transforms do not reproduce the Poisson counting statistics, detector-response correlation, or truncation characteristics of true low-dose raw sinograms. Because the projection-domain denoising loss L_P is the mechanism that distinguishes TriPLET from image-domain-only methods, the reported improvements in Table 3 over TriDoRNet may not transfer. The external validation in Section 5.1 also uses the same inverse-Radon conversion, so it does not close this gap. The central claim therefore needs either validation on real raw sinogram data or a more realistic forward simulation (e.g., re-projection with Poisson noise) to be convincing.
  2. [Section 4.4, "Quantitative Comparison"] The claim that TriPLET is "significantly better" than all baselines with p < 0.05 is not adequately documented. It is unclear whether the paired t-test was computed on the five fold-level means, per-subject metrics, or per-patch metrics; no p-values, test statistics, or degrees of freedom are reported. Since the gain over TriDoRNet is small relative to the reported standard deviations (Table 3: 25.932 ± 0.671 vs 25.892 ± 0.784 for PSNR), the significance claim is load-bearing and must be supported with exact details of the test procedure.
  3. [Section 4.1, Fig. 4] The statement that "the sinogram and image can be losslessly converted ... hence this method of obtaining sinogram patches does not introduce additional errors" is misleading for patch-based data. Applying the inverse Radon transform to a zero-padded 96×96×96 image patch produces the global sinogram of that patch (with zero attenuation outside the patch), not a local patch of the true scanner sinogram; the two are not equivalent because the integration paths and detector geometry differ. This affects both the denoising network's input distribution and the projection-domain loss. The authors should clarify the relationship to the full-field sinogram or extract patches directly in the sinogram domain for a true correspondence.
minor comments (6)
  1. [Section 4.1] The phrase "normalized to [0, 1] using Z-score normalization" is contradictory because Z-score normalization does not bound values to [0, 1]; please describe the actual preprocessing (e.g., Z-score followed by min-max scaling).
  2. [Section 4.1] The description "filter each PET image's values (i.e., only retaining values within the 5% to 95% range)" is actually a clipping or truncation operation, not a filter; the terminology should be corrected for clarity.
  3. [Section 3.1] The number of CNN and Transformer blocks is stated inconsistently: the text first describes seven blocks with {1st, 3rd, 5th, 7th} as CNN and {2nd, 4th, 6th} as Transformer (four CNN, three Transformer), then says "an alternating combination of 3 CNN blocks and 3 Transformer blocks." Please reconcile these counts.
  4. [Figure 5 caption] The caption refers to "Table 1" when describing the methods shown, but the ablation results are presented in Table 2; this cross-reference should be corrected.
  5. [Section 4.2, Eq. (5)] The notation for rRMSE uses a symbol in the denominator that is described only in words as "the all-voxel-averaged value of the ground-truth image." Define the symbol explicitly and confirm whether the same ground-truth maximum is used for PSNR in Eq. (6).
  6. [Section 5.1] The external validation describes 40 pairs but gives no details about whether the same value clipping, normalization, and patch-extraction protocol were applied to the external data; a brief description would help assess the fairness of the cross-dataset comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the method is supervised by real SPET targets, and the synthetic-sinogram caveat is an external-validity limitation rather than a circular step.

full rationale

The paper's derivation chain is self-contained rather than circular. The paired LPET/SPET targets are real reconstructed images from a uEXPLORER scanner, and all three losses (L_P, L_F, and L_I) are supervised by the real SPET ground truth; no fitted parameter is renamed as a prediction. The main caveat is explicitly stated in Section 4.1: 'we did not collect PET raw data (i.e., sinograms). The sinograms indirectly obtained from reconstructed PET images may indeed differ from the real PET raw data.' This is a genuine external-validity limitation, because the sinogram patches are produced by a Radon transform of image patches rather than acquired raw counts, but it is not circular: the transform is a fixed invertible preprocessing, and the network still learns a nontrivial LPET-to-SPET mapping that is evaluated against real SPET images. The comparison includes the authors' own TriDoRNet as a baseline, but TriDoRNet is fully described in the present paper and the comparison is empirical, not a citation used to justify the central claim. No uniqueness theorem, ansatz, or known result is smuggled in via self-citation. The claimed statistical significance (p<0.05) would benefit from per-fold reporting, but that is a reporting issue, not circularity.

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

The paper introduces no new physical entities or new mathematical axioms. The free parameters are standard architectural hyperparameters. The main assumptions are the losslessness of Radon conversion on discretized patches, the noise-dominance assumption for the LPET-to-SPET difference, and the transferability of the denoising-first decomposition across scanners.

free parameters (4)
  • alpha (focal frequency loss scaling) = 1
    Set by hand in Section 3.4; affects the weighting of hard-to-reconstruct frequency elements.
  • patch size and number of patches per subject = 96x96x96, 40 patches per subject
    Chosen to fit GPU memory and increase training samples; affects what the network learns but not a parameter of the final model per se.
  • window size in W-MSA = 4x4x4
    Chosen by hand in Section 3.1; affects the receptive field of the transformer blocks.
  • learning rates for the three training stages = 0.001, 0.001, 0.0001
    Hand-set hyperparameters; no sensitivity analysis is provided.
assumptions (4)
  • standard math Radon transform and inverse Radon transform are lossless conversions between image domain and sinogram domain.
    Invoked in Section 4.1 to justify generating sinogram patches from reconstructed image patches. Holds for ideal continuous data but not exactly for discretized, truncated, or attenuated PET data.
  • domain assumption The paired low-dose and standard-dose images differ mainly by sinogram noise level, so denoising the sinogram before reconstruction is the right decomposition.
    Stated in the introduction and Section 3.1. If the difference also involves systematic biases, motion, or reconstruction differences, the denoising-first decomposition may be suboptimal.
  • domain assumption Discrete wavelet transform decompositions can be treated as concatenated channels for the CNN blocks.
    Used in the RecNet design in Section 3.2. This is a design choice, not a mathematical necessity, and its benefit is demonstrated only empirically on this dataset.
  • domain assumption The external validation dataset (Ultra Low Dose PET Challenge) is sufficiently similar to the internal dataset to test generalization.
    Invoked in Section 5.1. The two datasets come from different scanners and possibly different reconstruction protocols; the paper does not report the exact preprocessing applied to the external data.

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Cite this review

Pith. "Pith review of End-to-end Triple-domain PET Enhancement: A Hybrid Denoising-and-reconstruction Framework for Reconstructing Standard-dose PET Images from Low-dose PET Sinograms." pith.science (2026). https://pith.science/paper/RXUM56WH

@misc{pith2026241203617,
  author       = {Pith},
  title        = {Pith review of: End-to-end Triple-domain PET Enhancement: A Hybrid Denoising-and-reconstruction Framework for Reconstructing Standard-dose PET Images from Low-dose PET Sinograms},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RXUM56WH}},
  note         = {Machine review of arXiv:2412.03617}
}
read the original abstract

As a sensitive functional imaging technique, positron emission tomography (PET) plays a critical role in early disease diagnosis. However, obtaining a high-quality PET image requires injecting a sufficient dose (standard dose) of radionuclides into the body, which inevitably poses radiation hazards to patients. To mitigate radiation hazards, the reconstruction of standard-dose PET (SPET) from low-dose PET (LPET) is desired. According to imaging theory, PET reconstruction process involves multiple domains (e.g., projection domain and image domain), and a significant portion of the difference between SPET and LPET arises from variations in the noise levels introduced during the sampling of raw data as sinograms. In light of these two facts, we propose an end-to-end TriPle-domain LPET EnhancemenT (TriPLET) framework, by leveraging the advantages of a hybrid denoising-and-reconstruction process and a triple-domain representation (i.e., sinograms, frequency spectrum maps, and images) to reconstruct SPET images from LPET sinograms. Specifically, TriPLET consists of three sequentially coupled components including 1) a Transformer-assisted denoising network that denoises the inputted LPET sinograms in the projection domain, 2) a discrete-wavelet-transform-based reconstruction network that further reconstructs SPET from LPET in the wavelet domain, and 3) a pair-based adversarial network that evaluates the reconstructed SPET images in the image domain. Extensive experiments on the real PET dataset demonstrate that our proposed TriPLET can reconstruct SPET images with the highest similarity and signal-to-noise ratio to real data, compared with state-of-the-art methods.

Figures

Figures reproduced from arXiv: 2412.03617 by the authors.

Figure 1
Figure 1. Representation of PET data in three domains: (a) projection domain, (b) image domain, and (c) wavelet domain, with the SPET and LPET shown on the left and right of each subfigure, respectively. Radon transform and discrete wavelet transform can convert PET data between images and sinograms, and also between images and frequency spectrum maps, respectively. After applying discrete wavelet transform, a 3D PET image ca… view at source ↗
Figure 2
Figure 2. Our proposed TriPLET involves three domains, i.e., the projection, wavelet, and image domains. PET data have different representations in each domain, such as the LPET sinogram 𝑆𝐿𝑜𝑤 and the denoised sinogram 𝑆𝐷𝑒𝑛 in the projection domain, the denoised frequency spectrum map 𝐹𝐷𝑒𝑛 and the predicted SPET map 𝐹̂ 𝑆𝑡𝑑 in the wavelet domain, and the LPET image 𝐼𝐿𝑜𝑤, the predicted SPET image 𝐼̂ 𝑆𝑡𝑑 , and the actual SPET ima… view at source ↗
Figure 3
Figure 3. Architectural detail of the Transformer block in the DenNet (denoising network). (such as max-pooling). Specifically, ℝ includes an encoder and a decoder. First, the denoised image is passed through the encoder to generate 4096 sub-band frequency spectrum maps. Then, these frequency spectrum maps are utilized as the input of the decoder to reconstruct the SPET image 𝐼̂ 𝑆𝑡𝑑. In the encoder, WT, instead of the pooling… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Process of extracting image patches and sinogram patches from the whole PET image [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Visual comparison of SPET images produced using five different combinations of loss functions and network components shown in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Visual comparison of SPET images generated by six different methods. The arrangement from left to right includes the LPET images, results obtained from five alternative comparison methods (2nd to 6th columns), our TriPLET (7th column), and the GT (SPET image). Addition…

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.