D3Recovery · Inter-Crystal Scatter Recovery for Prism-PET with a Diffusion Model

TL;DR

We recover where an inter-crystal scattered photon first interacted, in crystal and depth, with a diffusion-driven and physics-informed pipeline trained on data from one scanner-level experiment and one simulation. On real phantom scans this keeps roughly 70% of coincidences that would otherwise be thrown away, while restoring much of the resolution lost to mispositioning.

Method at a glance

D3Recovery, a diffusion-driven tripartite framework

An observed ICS pattern is a superposition of several interactions, and different combinations can produce nearly the same pattern. A deterministic network tends to average over these possibilities. D3Recovery therefore splits the problem into two stages and three cascaded models.

Stage 1

Scatter diffusion

A conditional DDPM with a U-Net backbone denoises an 8 × 8 Gaussian grid into the SiPM pattern of the first interaction, conditioned on the ICS pattern and block ID embeddings, and returns its deposited energy.

~105M parameters · 100 timesteps

Stage 2a

CrystalAttentionNet

Two ResNet encoders read the recovered and the ICS patterns, exchange information through cross-attention, and output a 16 × 16 probability map over crystals, keeping the neighborhood structure a 256-way classifier ignores.

~20M parameters

Stage 2b

GuidedDepthNet

A dual grid encoder regresses DOI. A crystal classification head is used only during training, as a physics-informed regularizer that keeps depth estimates spatially coherent.

~3M parameters

Scanner experiments

Three reconstructions of the same scan

Ultra-micro Derenzo phantom, ICS events only, reconstructed with D3Recovery — Ultra-micro Derenzo phantom Mean peak-to-valley gain

w/o Recoveryreference

Recovery-Net+13%

D3Recovery+24%

Ultra-micro Derenzo phantom, ICS events only, reconstructed without recovery (CoG positioning) — Ultra-micro Derenzo phantom Mean peak-to-valley gain

w/o Recoveryreference

Recovery-Net+13%

D3Recovery+24%

3D Hoffman brain phantom, ICS events only, reconstructed with D3Recovery — 3D Hoffman brain phantom MAE ↓ · SSIM ↑

w/o Recovery4.208 · 0.376

Recovery-Net3.554 · 0.431

D3Recovery3.457 · 0.435

3D Hoffman brain phantom, ICS events only, reconstructed without recovery (CoG positioning) — 3D Hoffman brain phantom MAE ↓ · SSIM ↑

w/o Recovery4.208 · 0.376

Recovery-Net3.554 · 0.431

D3Recovery3.457 · 0.435

Each image shows one scan from our Prism-PET prototype. Pick two reconstructions to compare, then drag the handle, or swipe sideways on a phone, to move the edge between them. ICS events only uses just the coincidences in which both photons scattered between crystals, the events that conventional positioning handles worst.

Abstract

Background Inter-crystal scattering (ICS) is a fundamental limitation in ultra-high resolution positron emission tomography (PET), particularly in light-sharing detectors with small crystal elements, where frequent Compton scatter across neighboring crystals obscures the initial interaction position and degrades the spatial resolution, image contrast, and quantitative accuracy. In our previous work, a convolutional neural network, Recovery-Net, was proposed and evaluated to recover the crystal location and depth-of-interaction (DOI) of the initial interaction in a light-sharing depth-encoding Prism-PET detector using Monte Carlo (MC) simulations.

Purpose This work aims to develop and experimentally validate a scanner-level ICS recovery framework for a light-sharing depth-encoding Prism-PET prototype scanner using a diffusion model.

Methods We first developed a novel method to prepare the training dataset by combining scanner-level simulations with experimental measurements. The resulting dataset comprises an 8 × 8 array of silicon photomultiplier (SiPM) signals for each ICS event with associated ground-truth information, including crystal location, DOI, and deposited energy of the initial interaction. Using the SiPM signal patterns as input, we proposed a new diffusion-driven and physics-informed tripartite framework, named D3Recovery, to estimate the 3D position and deposited energy of the initial interaction. The previously proposed Recovery-Net was also implemented and evaluated for comparison. An ultra-micro Derenzo phantom and a 3D Hoffman brain phantom from the Prism-PET prototype scanner experiment were used to evaluate the impact of ICS recovery on image quality.

Results Recovery-Net and D3Recovery achieved crystal identification accuracies of 64.1% and 70.1% for ICS events, respectively, with D3Recovery further improving DOI estimation to a full width at half maximum (FWHM) of 3.6 mm compared with 5.1 mm for Recovery-Net. Compared with center-of-gravity (CoG) positioning, D3Recovery reduced the mean crystal localization error from 2.18 mm to 0.99 mm and recovered the deposited energy with an error FWHM of 34.0 keV. For the ultra-micro Derenzo phantom images, Recovery-Net and D3Recovery increased peak-to-valley ratios by 13% and 24% for ICS events and by 14% and 17% for all events, respectively. For the Hoffman brain phantom, Recovery-Net and D3Recovery reduced mean absolute error (MAE) by 15.53% and 17.84% for ICS events and by 16.22% and 18.63% for all events, while increasing structural similarity index measure (SSIM) by 14.59% and 15.60% for ICS events and by 4.60% and 4.75% for all events, respectively. In addition, standard deviation (SD) measured in a uniform region decreased by 12.56% and 20.88% for ICS events, and by 5.26% and 8.48% for all events with Recovery-Net and D3Recovery, respectively.

Conclusions Experimental results demonstrate that D3Recovery significantly improves crystal localization, DOI estimation, and reconstructed image quality in high-resolution PET with small-crystal, light-sharing detectors, while providing a practical scanner-level training dataset acquisition strategy for experimental deployment of AI-based ICS recovery. By retaining a large fraction (~70% in our case) of otherwise discarded coincidences, our results show that we achieve a favorable resolution-sensitivity balance that is most beneficial in count-limited, low-dose imaging.

Full video presentation

Captions appear here as the talk plays

Motivation

Why inter-crystal scatter matters

Each Prism-PET detector module couples a 16 × 16 array of 1.5 × 1.5 × 20 mm³ LYSO crystals to an 8 × 8 SiPM array, with a prismatoid light guide that shares scintillation light between neighboring crystals so that depth of interaction (DOI) can be read out from a single end. At 511 keV, Compton scatter dominates in LYSO, so many photons deposit energy in more than one crystal. In our phantom scans, 71 to 72% of coincidences contained at least one inter-crystal scatter (ICS) event.

Center-of-gravity (CoG) positioning averages the light from all interaction sites, which assigns an ICS event to an averaged or wrong crystal and mispositions its line of response. Rejecting ICS events avoids the blur but discards most of the counts. We instead recover the first interaction, the one that defines the true line of response.

Photoelectric event

Inter-crystal scatter event

Compton scatter
Photoelectric absorption
Scintillation light
Prismatoid light guide

Method · Training data

One experiment plus one simulation

Supervised ICS recovery needs the true first interaction of every training event, which a measurement alone cannot provide. Labeling it experimentally would mean irradiating each of the 10,240 crystals in the scanner with a pencil beam at every depth. We avoid that with a hybrid pipeline.

Measure We scan a uniform cylinder phantom once and keep the photoelectric events, building a repository of at least 100 experimental SiPM patterns for every crystal at each DOI level from 1 to 20 mm.
Simulate A single matching GATE simulation of the scanner records the crystal, DOI and deposited energy of up to four interactions per photon.
Synthesize For each simulated interaction we draw a measured pattern from the same block, crystal and DOI bin, scale it to the simulated energy and sum the patterns channel by channel.

The result is about 136 million ICS events whose inputs carry real detector response while their labels come from simulation.

Pipeline for the training dataset. Top, a cylinder phantom experiment is filtered for photoelectric events to build experimental SiPM patterns for every crystal and DOI bin. Bottom, a GATE simulation provides the interaction sites and energies, and experimental patterns are energy weighted and combined into a synthetic ICS SiPM pattern with first-interaction labels. — (a) Building the repository of experimental photoelectric SiPM patterns for all crystals of the scanner. (b) Generating labeled training events by combining the GATE simulation with that repository.

Three 8 by 8 SiPM patterns. The first interaction deposits 97 keV, the second 418 keV, and their sum forms a synthetic 515 keV ICS pattern. — A synthetic ICS pattern. A 97 keV first interaction and a 418 keV second interaction add up to the observed 515 keV pattern, in which the first interaction is easy to miss. Values are deposited-energy-equivalent keV after calibration.

Method · Model

Inside the diffusion stage

The walkthrough at the top of the page follows one ICS event through all three models. Stage 1 does the hardest part. It has to pull the pattern of the first interaction out of a pattern where several interactions overlap, and a diffusion model can represent that ambiguity where a deterministic network would average it away.

Stage 1 in action

Watch the diffusion model turn Gaussian noise into the first-interaction SiPM pattern for example ICS events. Pick an event and scrub through the denoising steps.

Observed ICS patternmodel condition

Recovered x̂₀Stage 1 output

Ground truthfirst interaction

Each panel uses its own color scale (viridis). Stage 1 is not always right, which is why Stage 2 looks at both the recovered and the original ICS pattern.

Results

Results at a glance

70.1% crystal identification accuracy for ICS events CoG 22.8% · Recovery-Net 64.1%
3.6 mm DOI error FWHM for ICS events Recovery-Net 5.1 mm
0.99 mm mean crystal localization error CoG 2.18 mm · Recovery-Net 1.16 mm
+24% peak-to-valley ratio, Derenzo phantom (ICS events) Recovery-Net +13%

Results · Test events

Locating the first interaction

On held-out ICS events, D3Recovery identifies the correct crystal 70.1% of the time, against 22.8% for CoG and 64.1% for Recovery-Net, and narrows the DOI error distribution from 5.1 mm to 3.6 mm FWHM, about a 29% reduction. The mean crystal localization error falls from 2.18 ± 1.99 mm with CoG and 1.16 ± 2.09 mm with Recovery-Net to 0.99 ± 1.98 mm, and the deposited energy of the first interaction is recovered with an error FWHM of 34.0 keV.

Positioning of the first interaction for ICS events, by location of the primary interaction within the detector block.

Region	Share of events (%)	Crystal ID accuracy (%) ↑			DOI FWHM (mm) ↓
Region	Share of events (%)	CoG	Recovery-Net	D3Recovery	Recovery-Net	D3Recovery
Center	86.1	23.5	65.0	70.8	4.9	3.5
Edge	7.7	18.4	62.9	69.9	6.7	4.6
Corner	6.2	19.4	53.0	60.0	7.2	4.9
All	100.0	22.8	64.1	70.1	5.1	3.6

Event-level results. Ground truth, ICS and recovered SiPM patterns with ground truth, D3Recovery and CoG crystal locations marked, a narrow distribution of energy differences centered at zero, and flood histograms where CoG shows a blurred square and D3Recovery shows well separated crystal clusters. — (a to c) One test event. D3Recovery finds the true crystal while CoG lands elsewhere. (d) Error of the recovered deposited energy. (e, f) Flood histograms built with CoG and with the patterns recovered by D3Recovery, which separate the crystals again.

Histogram of DOI error in millimeters for w/o Recovery, Recovery-Net and D3Recovery. D3Recovery has the tallest and narrowest peak around zero. — Distribution of DOI errors for ICS events. D3Recovery gives the tallest, narrowest peak around zero.

Stage 2 on four representative events

Stage 2 reads both the recovered and the original pattern, so it can still land on the right crystal when Stage 1 is off. We also show the rarer failure cases.

ICS input8 × 8 SiPM signals

Stage 1 recoveredfirst interaction, predicted

Ground truthfirst interaction, true

Stage 2a crystal maptruth prediction

Results · Scanner experiments

Ultra-micro Derenzo phantom

We filled the phantom (rods from 0.80 to 2.50 mm) with 2 mCi of ¹⁸F-FDG and scanned it for 6 hours on the Prism-PET prototype, collecting 171 million coincidences of which 72% contained at least one ICS event. Images were reconstructed with CASToR (30 iterations, 10 subsets, 0.25 mm voxels). Compared with no recovery, Recovery-Net and D3Recovery raise the average peak-to-valley ratio by 13% and 24% for ICS events and by 14% and 17% for all events.

Derenzo phantom. Ground-truth layout of rods from 0.8 to 2.5 mm, the photoelectric-only image, and images from ICS events and from all events without recovery, with Recovery-Net and with D3Recovery. D3Recovery resolves the small rods most clearly. — (a) Phantom layout with the line-profile positions. (b) Reference image from photoelectric events. (c) ICS events and all events, without recovery and with Recovery-Net or D3Recovery.

Line profiles across all rod diameters for ICS events and for all events. D3Recovery has higher peaks and lower valleys than w/o Recovery and Recovery-Net. — Line profiles across each rod group for (a) ICS events and (b) all events.

Peak-to-valley ratios across the ultra-micro Derenzo phantom (higher is better). PE events is the photoelectric-only reference.

Rod diameter (mm)	PE events	ICS events			All events
Rod diameter (mm)	PE events	w/o Recovery	Recovery-Net	D3Recovery	w/o Recovery	Recovery-Net	D3Recovery
2.50	38.90	7.25	7.98	8.30	15.55	16.04	16.76
2.00	6.97	1.73	2.43	2.90	3.20	4.15	4.24
1.50	6.24	1.68	1.76	1.97	3.29	3.46	3.50
1.25	9.96	1.73	2.05	2.17	3.71	4.07	4.28
1.00	1.75	1.12	1.13	1.21	1.54	1.62	1.63
0.80	7.97	1.55	1.57	1.76	2.71	3.57	3.65

3D Hoffman brain phantom

The brain phantom was filled with 1.9 mCi of ¹⁸F-FDG and scanned for 6 hours, giving 425 million coincidences, 71% of them with at least one ICS event (CASToR, 7 iterations, 8 subsets, 0.5 mm voxels). Against a reference reconstructed from photoelectric events only, D3Recovery gives the lowest error, the highest structural similarity and the lowest noise in a uniform region, for ICS events and for all events.

Hoffman brain phantom. Ground truth with a 15 mm uniform region and a zoomed gray matter fold, the photoelectric-only image, and images from ICS events and from all events without recovery, with Recovery-Net and with D3Recovery, each with a zoomed inset. — (a) Ground truth with the 15 mm uniform region and the zoomed gray matter fold. (b) Photoelectric-only reference. (c) ICS events and all events, without recovery and with Recovery-Net or D3Recovery.

Image quality against the photoelectric-only reference. MAE and SD lower is better, SSIM higher is better.

Metric	ICS events			All events
Metric	w/o Recovery	Recovery-Net	D3Recovery	w/o Recovery	Recovery-Net	D3Recovery
MAE ↓	4.208	3.554	3.457	2.143	1.796	1.744
SSIM ↑	0.376	0.431	0.435	0.691	0.723	0.724
SD ↓	6.049	5.288	4.786	3.899	3.693	3.568

Why keep ICS events at all?

With plenty of counts, a photoelectric-only image is the resolution upper bound. But rejecting ICS events throws away about 70% of the data. When we keep only 10% of the Hoffman acquisition, the image built from all events already beats the photoelectric-only image on MAE, SSIM and SD, and adding D3Recovery improves it further. Recovering scattered events is most valuable exactly where counts are scarce, as in low-dose imaging.

Hoffman phantom reconstructed from 10% of the data. Photoelectric events only give MAE 3.942, SSIM 0.417 and SD 11.897. All events without recovery give MAE 3.027, SSIM 0.460 and SD 7.149. All events with D3Recovery give MAE 2.746, SSIM 0.490 and SD 6.545. — Hoffman phantom from 10% of the counts. (a) Photoelectric events only. (b) All events, without recovery and with D3Recovery. The reference image uses all photoelectric events.

Citation

If you find this work useful, please cite the journal article.

.bib

@article{tan2026d3recovery,
  title   = {Inter-crystal scatter recovery of a light-sharing depth-encoding {Prism-PET} prototype scanner using a diffusion model},
  author  = {Tan, Wanbin and Dosi, Saurav and Shabani Sichani, Soroush and Li, Yixin and Wang, Zipai and Petersen, Eric and Zeng, Xinjie and Qi, Jinyi and Goldan, Amir H.},
  journal = {Medical Physics},
  volume  = {53},
  pages   = {e70661},
  year    = {2026},
  doi     = {10.1002/mp.70661}
}

@article{tan2026d3recoverysnmmi,
  title   = {{D3Recovery}: Inter-crystal scatter recovery for {TOF-DOI} {Prism-PET} scanner using diffusion model},
  author  = {Tan, Wanbin and Dosi, Saurav and Shabani Sichani, Soroush and Li, Yixin and Wang, Zipai and Petersen, Eric and Goldan, Amirhossein},
  journal = {Journal of Nuclear Medicine},
  volume  = {67},
  number  = {supplement 1},
  pages   = {261669},
  year    = {2026},
  note    = {SNMMI 2026 Annual Meeting, oral presentation}
}

Tan W, Dosi S, et al. Inter-crystal scatter recovery of a light-sharing depth-encoding Prism-PET prototype scanner using a diffusion model. Med Phys. 2026;53:e70661. doi.org/10.1002/mp.70661

Acknowledgments

This work was supported by the National Institute of Biomedical Imaging and Bioengineering (NIBIB) under grant number R01EB030413. Research reported in this publication was supported by the National Institute on Aging (NIA) of the National Institutes of Health (NIH) under Award Number U01AG082845.