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arxiv: 2601.05717 · v2 · submitted 2026-01-09 · ⚛️ physics.med-ph

Inclusion of Inter-crystal Scattering in PET: Analytical Models and Dedicated Reconstruction

Jorge Roser , Hong Phuc Vo , Rebecca Kantorek , Steven Seeger , Magdalena Rafecas This is my paper

Pith reviewed 2026-05-16 16:10 UTC · model grok-4.3

classification ⚛️ physics.med-ph
keywords inter-crystal scatteringPET reconstructionanalytical modelssystem matrixsensitivity imagelist-mode MLEMsmall animal PETCompton scattering
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The pith

Inter-crystal scattering can be modeled analytically to improve PET image uniformity and reduce noise.

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

The paper develops physics-based analytical expressions for the contribution of inter-crystal scattering events to the PET system matrix and sensitivity image. These expressions allow ICS events to be included directly in list-mode maximum likelihood expectation maximization reconstruction alongside conventional coincidence events. Validation using both Monte Carlo simulations and experimental data from the MERMAID small-animal PET scanner shows that this inclusion reduces statistical noise and improves image uniformity, though recovery coefficients decrease slightly. This approach is particularly relevant for applications where scanner sensitivity is limited, such as imaging small animals.

Core claim

Analytical models derived from Compton scattering physics provide expressions for the sensitivity image and system matrix that incorporate inter-crystal scattering without requiring identification of the first interaction point. When used in a joint reconstruction algorithm with conventional PET events, these models yield images with lower noise and better uniformity on both simulated and real data from the MERMAID scanner.

What carries the argument

Analytical expressions for the ICS contribution to the system matrix and sensitivity image, based on Compton-scattering physics.

If this is right

  • Reconstruction algorithms can now account for ICS events to increase effective sensitivity.
  • Image uniformity improves and noise decreases in small-animal PET.
  • No need for data-driven or machine-learning methods to locate scattering sites.
  • Applicable to list-mode MLEM for joint processing of ICS and standard events.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method might generalize to other PET scanner geometries with similar modifications to the models.
  • It could enable lower dose imaging protocols by leveraging more events.
  • Similar analytical approaches might apply to other imaging modalities affected by scattering.

Load-bearing premise

The derived analytical expressions accurately capture the ICS events for the specific geometry and energy window of the MERMAID scanner without introducing bias.

What would settle it

Reconstructing the same phantom data with and without the ICS model and measuring if the noise reduction and uniformity improvement persist or if new artifacts emerge.

Figures

Figures reproduced from arXiv: 2601.05717 by Hong Phuc Vo, Jorge Roser, Magdalena Rafecas, Rebecca Kantorek, Steven Seeger.

Figure 1
Figure 1. Figure 1: Scheme of an ICS event with relevant quantities of the proposed [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Transversal (XY ) and sagittal (Y Z) projections over the analytical ICS sensitivity image, computed for the MERMAID geometry with 3 rotation steps and 10 bed positions, using (9) and assuming an energy threshold of 180 keV over the ICS events. The scale represent the probability of an annihilation emitted in a given group of voxels (e.g. a Z-row of voxels for the transversal projection) to be detected as … view at source ↗
Figure 3
Figure 3. Figure 3: Transversal (XY ) projections over two different analytical ICS system matrix rows, computed for the MERMAID geometry using (13). The scale represents the probability of annihilation emitted in a Z-row of voxels to be detected in terms of the particular measurement element considered. was subsequently used to obtain images of the downscaled IQ phantom, both with experimental and MC-simulated data. Likewise… view at source ↗
Figure 4
Figure 4. Figure 4: Validation of the ICS analytical sensitivity image model with no [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Results with the 1 MBq MC-simulated cylinder source: (a) Transversal (XY ) projection at iteration 10 for golden and ICS events, with the color scale representing the activity in MBq recovered in the sum of voxels involved in the projection; (b) evolution of the total activity recovered in the golden and ICS, only golden and only ICS images by summing all the voxel values in the three cases. and 16 058 ICS… view at source ↗
Figure 6
Figure 6. Figure 6: Transversal (XY ) projections over the IQ-phantom uniformity region at iteration 5 (first column), 10 (second column) and 20 (third column) for golden and ICS (first row), only golden (second row) and only ICS (third row) events, obtained with simulations. The scale represents the activity in MBq recovered in the sum of voxels involved in each projection (e.g. a Z-row of voxels for the transversal projecti… view at source ↗
Figure 7
Figure 7. Figure 7: Transversal (XY ) projections over the NEMA rods region at iteration 5 (first column), 10 (second column) and 20 (third column) for golden and ICS (first row), only golden (second row) and only ICS (third row) events, obtained with MC simulations. The scale represents the activity in MBq recovered in the sum of voxels involved in each projection (e.g. a Z-row of voxels for the transversal projection). (a) … view at source ↗
Figure 8
Figure 8. Figure 8: IQ metrics obtained with MC simulated data. (a) Evolution of [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Transversal (XY ) projections over the NEMA rods region at iteration 5 (first column), 10 (second column) and 20 (third column) for golden and ICS (first row), only golden (second row) and only ICS (third row) events, obtained with MERMAID. The scale represents the activity in MBq recovered in the sum of voxels involved in each projection (e.g. a Z-row of voxels for the transversal projection). (a) (b) [… view at source ↗
Figure 11
Figure 11. Figure 11: Image quality metrics obtained with experimental data. (a) Evolution [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Validation of the golden analytical sensitivity image model with [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Transversal (XY ) projections over the NEMA inserts region at iteration 5 (first column), 10 (second column) and 20 (third column) for golden and ICS (first row), only golden (second row) and only ICS (third row) events, obtained with MC-simulated data. The scale represents the activity in MBq recovered in the sum of voxels involved in each projection (e.g. a Z-row of voxels for the transversal projection… view at source ↗
Figure 15
Figure 15. Figure 15: SOR metrics obtained in one of the IQ-phantom inserts with (a) [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
read the original abstract

Inter-crystal scattering (ICS) in Positron Emission Tomography (PET) is commonly regarded as a degradation effect that might compromise the image spatial resolution. In parallel, the inclusion of ICS events has also been recognized as a potential approach to increase PET sensitivity, which could be especially beneficial in scenarios where the latter is a limiting factor, such as very small animal imaging. Several methods for the recovery of ICS events have been proposed, many of which aim to locate the first interaction, i.e., the Compton scattering site, usually limited by their success rate, computational burden or data and training dependency. Conversely, this work proposes a physics-based model for ICS events, leading to analytical expressions of the sensitivity image and the system matrix (required by statistical reconstruction algorithms), without the need to identify the original line of response. After validating the model, the work shows how ICS events can be integrated into a joint image reconstruction algorithm (based on list-mode MLEM) together with conventional PET events, for which dedicated analytical models are also developed. To assess the performance of the proposed approach, Monte-Carlo simulated and experimental data of an image quality phantom were obtained with the MERMAID small-fish PET scanner prototype. Both simulation and experimental results indicate that, while slightly decreasing the recovery coefficient values, the inclusion of ICS clearly reduces statistical noise and improves uniformity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript develops physics-based analytical models for inter-crystal scattering (ICS) events in PET, deriving closed-form expressions for the sensitivity image and system matrix from Compton kinematics and scanner geometry. These models enable joint list-mode MLEM reconstruction of ICS events together with conventional coincidences without explicit first-interaction localization. Validation uses Monte Carlo simulations and experimental data from the MERMAID small-animal PET scanner on an image-quality phantom, reporting reduced statistical noise and improved uniformity with a modest decrease in recovery coefficients.

Significance. If the analytical ICS contributions are unbiased for the MERMAID geometry and energy window, the work supplies a parameter-free route to recover sensitivity lost to inter-crystal scattering. This is especially relevant for small-animal PET where sensitivity is limiting, and the reported noise and uniformity gains are obtained within a standard statistical reconstruction framework.

minor comments (2)
  1. The derivation steps leading from Compton differential cross-section to the explicit system-matrix element for ICS events are only summarized; expanding one representative calculation (e.g., the integral over scattering angle for a given crystal pair) would improve reproducibility.
  2. Quantitative noise and uniformity metrics (e.g., coefficient of variation or standard deviation within ROIs) are mentioned qualitatively; reporting numerical values alongside the recovery-coefficient tables would strengthen the experimental claims.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our work on physics-based analytical models for inter-crystal scattering in PET and for recommending minor revision. The assessment correctly captures the derivation of closed-form expressions for the sensitivity image and system matrix, the joint list-mode MLEM approach, and the observed gains in noise and uniformity on MERMAID data. No specific major comments appear in the report, so we provide no point-by-point rebuttals.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper derives analytical expressions for the ICS contribution to the system matrix and sensitivity image directly from Compton-scattering kinematics and the known MERMAID scanner geometry. These expressions are not fitted to the target image-quality metrics (recovery coefficients, noise, uniformity) but are instead validated against independent Monte-Carlo simulations and experimental phantom data. No load-bearing self-citation, self-definitional step, or renaming of a fitted result appears in the reported workflow; the central claim therefore rests on external physics and separate validation datasets rather than on its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard Compton-scattering kinematics and PET detector geometry; no new free parameters, ad-hoc constants, or postulated entities are introduced in the abstract description.

axioms (2)
  • standard math Compton scattering kinematics govern the probability and energy deposition of inter-crystal scattering events in PET detectors
    Invoked to derive the analytical sensitivity and system-matrix expressions.
  • domain assumption The system response for both ICS and non-ICS events can be expressed analytically for the given scanner geometry and energy window
    Core premise enabling closed-form models without first-interaction identification.

pith-pipeline@v0.9.0 · 5549 in / 1334 out tokens · 88016 ms · 2026-05-16T16:10:51.985644+00:00 · methodology

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