To understand why the team’s approach matters, it helps to know what a PET scanner actually records. When a radiotracer decays inside a patient, the scanner detects pairs of gamma photons and tallies them into a sinogram, a projection-domain representation in which every point in the body traces out a characteristic sinusoidal curve. Reconstructing the image from this sinogram is an ill-posed inverse problem, and at low count levels the Poisson noise in the measurements can swamp the signal entirely. Classical maximum likelihood expectation maximization, or MLEM, remains the workhorse solution, but the new study confirmed that MLEM produces the blurriest and least faithful reconstructions under noisy conditions, falling well behind every learned method tested.

The research builds on the Learned Primal-Dual, or LPD, framework, an unrolled iterative algorithm originally devised for computed tomography. In LPD, each iteration alternates between updates in the dual domain, which is the sinogram, and the primal domain, which is the image, using the physical forward and backward projection operators to shuttle information between them. Residual connections let information from earlier iterations flow forward unchanged, creating a kind of memory across the reconstruction process. Previous adaptations of LPD to PET relied on convolutional neural networks as the learned update operators, and those CNNs worked well but carried a hidden assumption: that the features that matter are local. That assumption holds reasonably well for images, but it breaks down in sinograms, where pixels that are adjacent in the body scatter their contributions across wide stretches of the projection data.

The Swedish-Italian-American team attacked that locality problem with three different transformer-based designs. The first, the Dual-Domain Stacked Transformer-based LPD, replaces the CNN in the sinogram channel entirely with attention. Rather than slicing the sinogram into conventional square patches, the method exploits the known scanner geometry: it forward-projects small rectangular patches from the image space to identify which sinogram pixels belong to the same sinusoidal curve, then treats each curve as a token. A learnable positional encoding and a transformer block refine these curve tokens before they are weighted by activation level and added back onto the sinogram. The result is a pure transformer formulation that captures global dependencies across the dual domain while respecting the physics of the acquisition.

The second architecture, the Dual-Domain Restormer-based LPD, takes a hybrid route. The Restormer design keeps convolutional layers for extracting fine-grained local features but uses depth-wise convolutions to compute the query, key, and value matrices, then applies multi-head attention along the channel dimension rather than the flattened spatial dimension. This channel-wise attention makes the approach computationally feasible for high-resolution data, and a gated depth-wise convolution feed-forward network replaces the standard MLP inside each transformer block. The third variant, the Dual-Domain UNet-based LPD with Cross-Attention, keeps the familiar U-Net backbone but inserts cross-attention blocks between the primal and dual channels, allowing the network to directly compare how well a candidate image patch matches its forward-projected counterpart in the sinogram. In an idealized sense, this lets the model score the fit between image and measurement, exchanging complementary information across the two domains without waiting for the projection operators alone to mediate the dialogue.

Training such models normally demands vast amounts of real scanner data, which is expensive and ethically fraught. The researchers sidestepped the problem with a system-aligned synthetic data generator that faithfully replicates the MiniPET-3, an in-house preclinical PET scanner dedicated to small-animal imaging. The generator built random three-dimensional ellipsoid phantoms, applied Gaussian blur calibrated to the positron range of fludeoxyglucose, which averages 0.6 millimeters with a maximum of 2.4 millimeters in this system, and simulated the exact acquisition geometry of the scanner’s twelve detector modules, each holding 35 by 35 crystals, using the parallelproj projection library. Poisson noise was then added at randomly sampled levels spanning low-count to high-count conditions, so that every network learned across a realistic spectrum of noise severity rather than a single fixed setting.

Evaluated on synthetic Shepp-Logan phantom test data at noise levels of 0.3, 0.7, 1.0, and even an out-of-distribution 1.5, the transformer-equipped models delivered consistent gains. Both the Stacked Transformer-based LPD and the Restormer-based LPD beat the UNet-based LPD baseline in mean squared error and peak signal-to-noise ratio at every noise level, with the Restormer achieving the strongest results at low noise, reaching a PSNR of about 24.66 decibels at the cleanest setting. The cross-attention UNet variant also improved MSE and PSNR over the baseline and proved the most robust performer at moderate to high noise levels. Structural similarity, however, told a more nuanced story, since some attention models traded a small amount of SSIM for their pixel-wise accuracy, a reminder that the two families of metrics do not always move together. Wilcoxon signed-rank tests confirmed that the improvements were statistically significant, with p-values below 0.0001.

Perhaps the most striking and humbling finding emerged when the networks, trained exclusively on synthetic data, were confronted with real experimental measurements from a 3D-printed mouse-like phantom scanned on the MiniPET-3. The models generalized well, producing high-quality reconstructions without ever having seen real sinograms during training, which validates the synthetic data strategy as a route to robust transfer learning. Yet the ranking of the architectures shifted. On experimental data, the Stacked Transformer-based LPD delivered the most homogeneous and visually plausible reconstructions, while the Restormer-based model, despite its synthetic-domain dominance, produced brighter images marred by beam-like artifacts. The authors attribute this to domain shift: the Restormer’s greater representational power appears to come with heightened sensitivity to the messy physical realities, scatter, attenuation inaccuracies, and noise mismatches, that the simplified simulation did not fully capture. The researchers also ran a capacity-controlled experiment, expanding the baseline UNet-LPD from three to four unrolled iterations, and found that although extra parameters helped, they did not explain away the advantage of attention-based designs, confirming that architecture, not just model size, drives the gains.

The study carries clear implications for the future of low-count PET, from reduced radiotracer doses in pediatric and longitudinal oncology imaging to faster preclinical scans in small-animal research. Visualizations of the unrolled iterations revealed distinct reconstruction personalities: the Restormer began over-smoothed and progressively sharpened anatomical boundaries, while the cross-attention UNet produced noisier intermediates that converged to a cleaner final image than its CNN-only counterpart. The authors are candid about limitations, noting that the experimental validation rests on a single phantom without voxel-wise ground truth, and they outline future directions including iteration-aware attention mechanisms that exploit the progressive refinement of the LPD loop and spatio-temporal attention for dynamic imaging. For now, the message is that attention helps, but the specific way attention is wired into the reconstruction determines whether the reward is sharper images in simulation or sturdier ones in the real world. In the ongoing contest between representational power and robustness, transformer-based learned primal-dual reconstruction has staked a serious claim as the next chapter in PET image reconstruction.

Subject of Research: Transformer-based deep learning architectures for PET image reconstruction

Article Title: Dual-domain transformer-based learned primal-dual reconstruction for PET imaging

Article References: Adelöw, A., Rashidykanan, H., Guazzo, A., & Colarieti-Tosti, M. (2026). Dual-domain transformer-based learned primal-dual reconstruction for PET imaging. Frontiers in Nuclear Medicine, 6, Article 1885873. https://doi.org/10.3389/fnume.2026.1885873

Image Credits: AI Generated

DOI: 10.3389/fnume.2026.1885873

Keywords: PET imaging, image reconstruction, transformers, attention mechanism, learned primal-dual, deep learning, sinogram, low-count imaging, cross-attention, preclinical PET, MiniPET-3, medical imaging