DirectPET: Full Size Neural Network PET Reconstruction from Sinogram Data

Jens Gregor; William Whiteley; Wing K. Luk

REVIEW 3 major objections 5 minor 45 references

DirectPET: Full Size Neural Network PET Reconstruction from Sinogram Data

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read DirectPET reconstructs full-size multi-slice PET volumes directly from sinograms in a single forward pass, producing images quantitatively and qualitatively similar to the clinical OSEM+PSF reference in a fraction of the time.

desk verdict DirectPET is a real architecture contribution that scales direct network PET reconstruction to clinical-size volumes, but its quantitative evaluation is partly circular because the network is trained and scored against the same OSEM+PSF targets using loss metrics. read the letter →

arxiv 1908.07516 v4 pith:FXDAINDT submitted 2019-08-19 eess.IV cs.CVphysics.med-ph

William Whiteley , Wing K. Luk , Jens Gregor This is my paper · ORCID

classification eess.IVcs.CVphysics.med-ph PACS 87.57.uk

keywords PETimagereconstructiondirectneuralnetworkRadoninversionlayersinogramtoOSEM+PSFlow-countdeeplearningmulti-slicevolume

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

This paper argues that direct neural-network PET reconstruction can leave the small-image laboratory setting and handle full-size clinical volumes. The authors introduce DirectPET, a network that takes time-of-flight Fourier-rebinned sinograms plus CT attenuation maps and outputs a 16x400x400 image volume in a single forward pass, by using a memory-efficient Radon inversion layer instead of the fully connected layers that limited earlier direct methods. On 10 held-out patient studies, they report that DirectPET reconstructions are quantitatively and qualitatively similar to the OSEM+PSF reference images, with an average network pass of about 1.3 seconds versus 31 seconds for OSEM+PSF. They also show that a version trained on half-count sinograms with full-count targets still matches the full-count network, suggesting that direct reconstruction can preserve image quality in low-dose settings. The stated goal is to establish that this class of method is clinically viable, while acknowledging that performance boundaries on unseen data are not yet proven.

What carries the argument

The load-bearing component is the Radon inversion layer, a sparse domain-transformation layer that replaces the dense fully connected mapping from sinogram to image. It partitions the output image into patches, learns a sinogram mask per patch from the activation maps of a small fully connected reconstruction experiment, refines the masks by smoothing, morphological operations, and thresholding, and then connects only the surviving sinogram bins to the neurons of each patch's independent fully connected network. This cuts the transformation parameters from billions to hundreds of millions, making full-size volumes feasible. A convolutional encoder compresses the sinogram before the transform, and a refinement-and-scaling segment with residual blocks and pixel-shuffle upsampling restores full resolution while also ingesting the CT attenuation maps. The training procedure uses a dynamically balanced loss of mean absolute error, multi-scale structural similarity, and a perceptual feature loss computed from a pretrained image-classification network.

What would settle it

Run DirectPET on a NEMA image-quality phantom or on a multi-center patient cohort acquired with a different scanner geometry and radiopharmaceutical, and compare against OSEM+PSF with lesion-level and region-of-interest metrics. If the per-patient MAE, bias, or lesion full-width half-maximum differences exceed the small ranges reported here, or if the network produces artifacts on anatomy outside its training distribution, the claim that DirectPET produces OSEM-equivalent images would be refuted.

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Extended reading notes

Core claim

DirectPET is an Encoding–Transformation–Refinement-and-Scaling (ETRS) network that reconstructs full-size multi-slice PET volumes directly from measurement data. Its central claim is that a single trained forward pass can produce 16x400x400 images whose quantitative metrics—mean absolute error, bias, signal-to-noise ratio, and multi-scale structural similarity—match the clinically used OSEM+PSF reconstruction closely enough to be considered equivalent in quality: average MAE 33.07 Bq/ml, average absolute bias 1.82%, MS-SSIM at or above 0.99, and lesion full-width half-maximum within about 1% of the reference. The paper further claims that this equivalence holds when the network is trained on half-count sinograms against full-count targets, producing images nearly identical to the full-count DirectPET and far superior to OSEM+PSF applied to the same half-count data. The authors conclude that image quality in this paradigm depends more on the quality of the training targets than on the raw count level, and that the speed of the method opens the door to clinical use if the remaining distributional and safety questions are resolved.

Load-bearing premise

The argument rests on treating OSEM+PSF reconstructions as both the training targets and the reference standard for image quality; if those images are not faithful to true tracer uptake, or if the ten held-out patients do not represent the wider clinical population, the reported similarities do not establish that DirectPET reconstructs correctly on unseen data.

Editorial extensions

If this is right

If DirectPET's results hold, an entire 400x400x400 whole-body PET study can be reconstructed in a little more than one second on a GPU, versus tens of seconds for OSEM+PSF; dynamic and gated studies with many frames would shrink from minutes to seconds.
Because DirectPET-50 matches DirectPET, low-dose acquisitions could be reconstructed at normal-dose quality, potentially reducing patient radiation exposure without changing scanner hardware.
The dependence of output quality on training targets means improvements in the reference reconstruction, for example maximum a posteriori or non-local-means filtered images, should transfer directly into better network outputs.
Clinicians could rerun a reconstruction quickly with different settings, provided a small library of networks is trained, replacing the iteration, subset, and filter choices of iterative reconstruction.
Scatter and attenuation correction are learned rather than explicitly modeled, so the network implicitly encodes scanner physics; this is a direct corollary the paper uses to explain its speed.

Reading between the lines

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

The masked-domain-transformation trick should transfer to other tomographic modalities, such as SPECT, CT, or limited-angle imaging, since the masks encode Radon geometry rather than PET-specific physics.
Because the masks are learned from activation maps, the approach could extend to non-Radon acquisition geometries, such as curved detectors or non-uniform angular sampling, where analytic inversion is hard, potentially by learning masks directly from forward projections.
A test the paper leaves implicit: train DirectPET on images from a superior reconstruction, such as MAP or a denoised target, and run an observer or lesion-detectability study; the paper's own logic predicts the network will inherit the target's advantages.
The speed comparison mixes hardware, with OSEM and FBP on a dual-CPU workstation and DirectPET on a GPU workstation, so a controlled same-hardware benchmark would sharpen the factor-of-7 speed claim.

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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

DirectPET is worth a real look: it scales direct network PET reconstruction to clinical-size volumes (16x400x400) from sinograms, using a patch-based Radon inversion layer that sidesteps the memory wall that kept AUTOMAP and DeepPET at 1x128x128. It is also trained and tested on real patient data with attenuation maps as input, which is a step beyond synthetic demonstrations. The speed gain is concrete: 1.3 seconds forward pass versus 31 seconds for OSEM+PSF for a field of view. If you work on PET reconstruction, the ETRS design and the mask-based transform are the contributions to remember.

The paper is honest about its own limits. Section 4.5 says plainly there is no guarantee for unseen data and defers detectability and observer work. It does not oversell the lesion analysis, calling it preliminary and anecdotal. Good.

The soft spot is real and load-bearing: the evaluation is partly circular. The training targets are OSEM+PSF images; the loss includes MAE and MS-SSIM; then the test metrics are MAE and MS-SSIM against OSEM+PSF. So MS-SSIM at or above 0.99 and MAE around 33 Bq/ml largely show the network matched its target distribution, not that it recovers true activity independent of that reconstruction protocol. That is a useful generalization check within one scanner and reconstruction pipeline, not an independent accuracy claim. The low-dose result has the same structure: DirectPET-50 is trained to map half-count data to full-count OSEM+PSF targets, and it beats OSEM+PSF-50 at matching those targets. The roughly 50% negative bias of OSEM+PSF-50 is surprising and not really explained; because there is no ground truth, "superior image quality" is not established. Also, the whole-body single-pass statement is extrapolated from a 16-slice model with batching.

The authors acknowledge most of these limitations, which raises my confidence in their judgment even while it lowers my confidence in the headline. No code or data are released, so the numbers cannot be independently checked. I would still send it to a serious referee: the architecture contribution is new and likely reproducible in spirit, and the evaluation gap is discussable rather than fatal. The useful review would push for an independent reference, whether phantom measurements, lesion detectability, or at least evaluation metrics not included in the loss.

Referee Report

3 major / 5 minor

Summary. The paper presents DirectPET, a convolutional neural network that reconstructs 16x400x400 PET image volumes directly from Fourier-rebinned, time-of-flight sinograms together with CT-based attenuation maps. The architecture consists of an encoding segment, a novel patch-wise Radon inversion layer that masks the compressed sinogram and applies small fully connected networks, and a refinement/scaling segment with ResNet blocks. The network is trained on OSEM+PSF reconstructions from 40 whole-body studies and evaluated on 10 held-out patients. The reported results include a reconstruction time of about 4.3 s per field-of-view versus 31 s for OSEM+PSF, a mean absolute error of 33 Bq/ml, MS-SSIM values around 0.99, low bias, and similar lesion line profiles. A half-count variant, DirectPET-50, is trained on thinned raw data with full-count targets and compared against OSEM+PSF-50. The authors acknowledge in Section 4.5 that there is no mathematical or statistical guarantee for unseen data and defer lesion-detectability and observer studies to future work.

Significance. The architectural contribution is significant: direct neural network reconstruction at clinical volume sizes has previously been limited by memory, and the Radon inversion layer with learned masks is a plausible and interesting solution to that bottleneck. The speed advantage is potentially important for dynamic, gated, or interventional PET applications. If the results hold, this would be a substantial step toward practical direct reconstruction. However, the quantitative image-quality evidence is weakened by the fact that the main evaluation metrics, MAE and MS-SSIM, are the same terms that appear in the training loss of Eq. (2), and all image-quality comparisons are made against the training target. The paper therefore demonstrates generalization to held-out patients from the same scanner and reconstruction protocol, but it does not yet establish independent reconstruction accuracy or clinical superiority. The absence of released code or trained models also limits reproducibility. The significance is real but conditional on further validation.

major comments (3)

[§4.3, Eq. (2) and Fig. 6] The central quantitative evidence for similarity to OSEM+PSF uses MAE and MS-SSIM, both of which are explicit components of the training loss in Eq. (2). The high test-set values (MAE of 33 Bq/ml and MS-SSIM around 0.99) are therefore partly by construction and do not constitute an independent measure of reconstruction accuracy. The authors themselves note in Section 4.3 that the high MAE and MS-SSIM values are driven by these quantities being in the loss function. This is load-bearing for the paper's claim that DirectPET produces images "quantitatively and qualitatively similar" to OSEM+PSF, so the evaluation should be supplemented with at least one independent measure, such as NEMA phantom measurements, lesion contrast or detectability, or image-quality metrics not used in training.
[§4.3, Fig. 6(b) and §5] The claim that DirectPET-50 provides "superior image quality" in the low-count setting is not supported by the presented comparison. OSEM+PSF-50 is reported to have a negative bias of roughly 50%, which is an unexpectedly large and unexplained systematic effect. It is not shown whether this baseline was tuned for half-count data, for example by adjusting the number of iterations, subsets, regularization, or post-reconstruction filtering. Without a fair and well-optimized low-count baseline, the comparison to OSEM+PSF-50 does not establish that the network maintains image quality under reduced dose. Please explain the observed bias or repeat the comparison with a more appropriate baseline.
[§4.3, Fig. 7] The spatial-resolution analysis is based on line profiles and full-width half-maximum measurements of only two lesions, which the authors themselves describe as preliminary and somewhat anecdotal. Consequently, the statement that DirectPET preserves spatial resolution is not supported at the level needed for a clinical-viability claim. A quantitative lesion study or a phantom-based resolution measurement would be required to substantiate that claim.

minor comments (5)

[§4.2] The sentence containing "Is is noteworthy" should read "It is noteworthy."
[§4.4] The section title "Qualitative Image Image Analysis" contains a duplicated word and should be "Qualitative Image Analysis."
[§3.1.1] The natural-image data set used to learn the activation maps for mask creation is not identified; please provide a reference or a brief description of that data set.
[§4.1] The fixed scaling factors for input sinograms and target images (division by 5 and 400, respectively) are stated but not justified; a sentence explaining how these values were chosen would improve reproducibility.
[§1 and §5] The phrase "path to superior image quality" overstates what is demonstrated; the full-count results show parity with the OSEM+PSF target, and the low-count comparison relies on an apparently unoptimized OSEM+PSF-50 baseline.

Circularity Check

2 steps flagged · score 6.0 of 10

Reported OSEM+PSF similarity and low-dose superiority are partly circular: the network is trained to minimize MAE/MS-SSIM against OSEM+PSF targets and is then scored with those same targets and metrics; the low-dose comparison also uses the full-count training target as the reference.

fitted input called prediction [Section 3.2, Eq. (2); Section 4.3, Fig. 6 (MAE/MS-SSIM evaluation)]
"The loss between reconstructed image ˆx and target image x was thus made to consist of three terms, namely: L(ˆx,x ) =β VGG(ˆx,x ) + (1−α) MAE(ˆx,x ) +α MS-SSIM(ˆx,x ) (2) ... The nearly identical performance of the two neural networks is driven by MAE being a component of their loss function causing them to specifically optimize this measurement in the same way."

The headline test-set numbers (MAE about 33 Bq/ml, MS-SSIM at or above 0.99) are computed against the OSEM+PSF reconstructions that define the network's training targets, using two of the three terms that Eq. (2) explicitly minimizes. The paper itself states that the high MAE and MS-SSIM scores are driven by those terms being in the loss. A held-out split shows the mapping generalizes across patients, but the metric is not independent: it measures how well the trained network reproduces the mean-absolute-error and structural-similarity objective on new inputs from the same scanner and reconstruction protocol, not the accuracy of either DirectPET or OSEM+PSF against true tracer uptake. Consequently the quantitative 'similar to OSEM+PSF' claim is partly forced by construction.
fitted input called prediction [Section 4.1 and Section 4.3, DirectPET-50 low-dose experiment; Section 5 conclusion]
"The second version, which will be referred to as DirectPET-50, was trained with half of the raw counts removed using list-mode thinning while retaining the full count images as training targets. ... This capability was demonstrated by removing half the counts in the raw data through list-mode thinning, training the DirectPET network to reconstruct full count images from half count sinogram data, and comparing the results to OSEM+PSF reconstructions on the decimated data."

DirectPET-50's training targets are the full-count OSEM+PSF images, and the low-dose evaluation compares DirectPET-50 and OSEM+PSF-50 against those same full-count OSEM+PSF images. Since DirectPET-50 is optimized to minimize MAE/MS-SSIM to that reference while OSEM+PSF-50 is an independent reconstruction from decimated data, the reported 'superior' quality of DirectPET-50 (SNR, bias around 2%, MS-SSIM at or above 0.99 versus 0.88) is structurally favored by the choice of reference: the network was trained to land on the reference, and the conventional low-count reconstruction was not. This demonstrates that a fitted mapping can mimic the full-count target, not an independent advantage in clinical accuracy.

full rationale

The central quantitative evidence is not independent of the training objective. The OSEM+PSF reconstructions described in Section 4.1 are both the training targets and the reference standard in Section 4.3, and the loss in Eq. (2) is a weighted sum of VGG, MAE, and MS-SSIM. Therefore test-set MAE around 33 Bq/ml and MS-SSIM at or above 0.99 quantify how well the network generalizes the exact objective it was trained for, not whether either DirectPET or OSEM+PSF matches true tracer uptake. The paper's own text makes this explicit: 'The nearly identical performance of the two neural networks is driven by MAE being a component of their loss function causing them to specifically optimize this measurement in the same way' and 'The fact that MS-SSIM is included in the loss function is what once again leads to similar high performance.' Similarly, the low-dose claim that DirectPET-50 outperforms OSEM+PSF-50 is a consequence of training DirectPET-50 to reproduce full-count OSEM+PSF and then measuring both against that same reference. This is partial circularity, not fabrication: the held-out 10-patient split and the use of an external OSEM+PSF implementation give some independent content, especially for reconstruction speed and cross-patient generalization within the same acquisition protocol. No load-bearing self-citation chain is present; the ETRS and Radon-inversion citations are architectural precedents, not uniqueness theorems. The limitations section further weakens the clinical-reconstruction claim by conceding 'there is no mathematical or statistical guarantee that some unknown new data will be reconstructed with the same image quality' and by deferring lesion-detectability and observer studies to future work. Score 6 reflects that the central similarity claim reduces in part to the training objective while retaining real, but limited, test-set generalization content.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central contribution is an empirical network design with several hand-chosen hyperparameters; there are no new physical entities. The main free parameters are architectural and training choices that affect the reported efficiency and quality trade-off, and the network itself is a fitted model. The axioms are the domain assumptions about transferability of the learned masks, validity of OSEM+PSF as reference, and generalization beyond the training cohort.

free parameters (7)

Image patch size = 40 x 40 pixels
Chosen empirically as a balance between speed and memory; Table 1 shows the parameter count varies from 209M to 1.055B with patch size.
Mask Gaussian smoothing sigma = 4
Used to smooth summed activation maps before thresholding (Section 3.1.1); affects mask size and thus parameter count.
Mask morphological structuring element radius = 8 (disk)
Used in opening/closing during mask refinement; affects mask shape and memory.
Input and target scaling factors = sinogram scaled by 1/5, image scaled by 1/400
Fixed scaling to bring average values near 1 for training stability (Section 4.1).
Learning rate bounds = eta_min = 0.5e-5, eta_max = 9.0e-5
Determined by a learning-rate range test (Section 3.2).
Number of input slices = 16
Settled on 16 after experimenting with 1 to 32 slices (Section 3.1.2).
VGG loss weight beta = 0.5
Fixed weighting of perceptual loss in Eq. 2; alpha is dynamic.

assumptions (5)

domain assumption The PET reconstruction mapping from preprocessed sinograms to images is a continuous function with bounded input, so the Universal Approximation Theorem applies.
Invoked in the Introduction to justify using a neural network for direct reconstruction; continuity and boundedness are not proven for the actual PET mapping.
domain assumption Sinogram masks learned from a fully-connected layer trained on natural images transfer to PET sinogram geometry.
Section 3.1.1 uses activation maps from a natural-image experiment to generate masks for the Radon inversion layer; no PET-specific validation of the masks is given.
domain assumption OSEM+PSF reconstructions are valid as both training targets and reference for image quality.
Section 4.1 defines the manufacturer's OSEM+PSF output as the training target; Section 4.3 uses the same OSEM+PSF images as reference for all metrics. If those images contain systematic bias, the network inherits it.
domain assumption The held-out test patients are representative of the broader clinical population.
Section 4.1 sets aside 10 patients from the same 54-patient cohort; no external dataset or scanner variation is tested.
domain assumption Scatter and attenuation correction can be learned implicitly from training data.
Section 3.1 and Fig. 1 state that scatter and attenuation correction are not performed in the sinogram domain but are accounted for by learned network parameters; this assumes the training data contains enough variation for the network to learn these corrections.

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Cite this review

Pith. "Pith review of DirectPET: Full Size Neural Network PET Reconstruction from Sinogram Data." pith.science (2026). https://pith.science/paper/FXDAINDT

@misc{pith2026190807516,
  author       = {Pith},
  title        = {Pith review of: DirectPET: Full Size Neural Network PET Reconstruction from Sinogram Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FXDAINDT}},
  note         = {Machine review of arXiv:1908.07516}
}

read the original abstract

Purpose: Neural network image reconstruction directly from measurement data is a relatively new field of research, that until now has been limited to producing small single-slice images (e.g., 1x128x128). This paper proposes a novel and more efficient network design for Positron Emission Tomography called DirectPET which is capable of reconstructing multi-slice image volumes (i.e., 16x400x400) from sinograms. Approach: Large-scale direct neural network reconstruction is accomplished by addressing the associated memory space challenge through the introduction of a specially designed Radon inversion layer. Using patient data, we compare the proposed method to the benchmark Ordered Subsets Expectation Maximization (OSEM) algorithm using signal-to-noise ratio, bias, mean absolute error and structural similarity measures. In addition, line profiles and full-width half-maximum measurements are provided for a sample of lesions. Results: DirectPET is shown capable of producing images that are quantitatively and qualitatively similar to the OSEM target images in a fraction of the time. We also report on an experiment where DirectPET is trained to map low count raw data to normal count target images demonstrating the method's ability to maintain image quality under a low dose scenario. Conclusion: The ability of DirectPET to quickly reconstruct high-quality, multi-slice image volumes suggests potential clinical viability of the method. However, design parameters and performance boundaries need to be fully established before adoption can be considered.

Figures

Figures reproduced from arXiv: 1908.07516 by the authors.

**Figure 2.** The DirectPET reconstruction neural network consists of three distinct segments each with [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** A single, fully-connected layer can be trained to learn the distinctive sinusoidal pattern [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: The mask creation process begins with summing the raw pixel activation maps for an im [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: The histograms in (a) and (b) show the relative distribution of slice counts in the Fourier [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]

**Figure 6.** Figure 6: Quantitative measurements of the reference OSEM+PSF reconstructions, DirectPET, Di [PITH_FULL_IMAGE:figures/full_fig_p021_6.png]

**Figure 7.** Figure 7: Quantitative analysis of two lesions showing a line profile and full-width half-maximum [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]

**Figure 8.** Figure 8: Full resolution test set reconstructions using OSEM+PSF, DirectPET and DirectPET-50 [PITH_FULL_IMAGE:figures/full_fig_p024_8.png]

**Figure 1.** Figure 1: The DirectPET imaging pipeline uses TOF Fourier rebinned PET data and X-ray CT based attenuation maps to generate PET image volumes [PITH_FULL_IMAGE:figures/full_fig_p035_1.png]

**Figure 3.** Figure 3: A single, fully-connected layer can be trained to learn the distinctive sinusoidal pattern associated with the Radon transform [PITH_FULL_IMAGE:figures/full_fig_p035_3.png]

**Figure 5.** Figure 5: The histograms in (a) and (b) show the relative distribution of slice counts in the Fourier rebinned sinograms for the training and test sets. (c) Shows the reconstruction time of a single FOV for both conventional methods and DirectPET demonstrating 7.2x and 4.9x impr…

**Figure 7.** Figure 7: Quantitative analysis of two lesions showing a line profile and full-width half-maximum (FWHM) for each reconstruction method [PITH_FULL_IMAGE:figures/full_fig_p036_7.png]

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write newline

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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