Radon Mask Augmentation Strategy for PET

• RMAS is a physics-aware data augmentation strategy that projects image masks into sinogram space to preserve PET acquisition geometry.
• It dynamically generates multiple non-overlapping masks with positive/negative constraints to create over 200,000 diversified training examples from limited PET data.
• Its integration within a latent diffusion model enables competitive sinogram synthesis and reconstruction quality under low-resource, low-shot conditions.

Searching arXiv for the cited paper and closely related PET projection-domain foundation modeling context. Radon Mask Augmentation Strategy (RMAS) is a physics-aware data augmentation strategy introduced in "ALL-PET: A Low-resource and Low-shot PET Foundation Model in the Projection Domain" for low-resource, low-shot PET foundation modeling directly in the projection, or sinogram, domain (Huang et al., 11 Sep 2025). It was designed to address the mismatch between typical foundation-model requirements—large, diverse image-domain datasets and heavy compute—and the practical constraints of PET, where raw projections are scarce, privacy-restricted, and their physics-informed structure is easily degraded by post-reconstruction processing. RMAS shifts the burden of generalization from parameter-heavy networks to intelligent, physics-aware data design by projecting randomized image-domain masks into Radon space, pairing those masks with strict positive/negative geometric constraints, and using the resulting composites within a latent diffusion model (LDM). In the ALL-PET framework, RMAS is coupled with a Dynamic Multi-Mask (DMM) mechanism and positive/negative mask constraints, enabling high-quality sinogram synthesis and downstream task performance under low-shot, low-resource conditions (Huang et al., 11 Sep 2025).

1. Conceptual role within projection-domain PET modeling

RMAS was introduced to make low-resource, low-shot PET foundation modeling feasible directly in the projection domain (Huang et al., 11 Sep 2025). The core premise is that PET raw data should be modeled in measurement space rather than only after reconstruction, because sinograms retain angle and radial geometry that can be obscured by image-domain post-processing. RMAS therefore operates on masks that are first defined in image space and then forward projected into sinogram space, so that augmentation remains aligned with PET acquisition physics.

Within ALL-PET, RMAS is not an isolated preprocessing heuristic but part of a broader design principle: data efficiency is obtained by embedding structure into the training examples rather than by enlarging the network. The method turns a small collection of real sinograms—500 per tracer or anatomical region—into over 200,000 structurally diverse, physically consistent training examples (Huang et al., 11 Sep 2025). This supports a latent diffusion workflow while preserving measurement-space priors and maintaining memory use under 24 GB on a single RTX 3090 (Huang et al., 11 Sep 2025).

A plausible implication is that RMAS repositions augmentation from a generic regularization device to a geometry-preserving component of the generative model’s conditioning pipeline. In that formulation, diversity is introduced through controlled perturbations of physically interpretable support rather than through unconstrained image-domain transformations.

2. Mathematical formulation in Radon space

RMAS builds on the Radon transform to map image-domain masks into the sinogram domain and to construct complementary masked targets that enforce geometric consistency (Huang et al., 11 Sep 2025). The continuous Radon transform for a 2D image $f(x, y)$ is defined as

$$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$

where the projection is taken along lines parameterized by angle $0$ and signed distance $s$ from the origin (Huang et al., 11 Sep 2025). In discrete implementation, with detector bins and angle indices, the Dirac delta is approximated by a smooth interpolation kernel $K(\cdot)$.

For randomly sampled image masks $M(x, y)$, projection to sinogram space is expressed as

$$M_s(s, 0) \sim \sum M_i(x_i, y_i)\cdot K(s - x, \cos 0 - y, \sin 0)$$

and the individual sinogram masks are summed to form a multi-mask aggregate,

$M_s(s, 0) = \sum_k M_s^k(s, 0).$

To keep values bounded and comparable across samples, the paper specifies two normalization schemes:

$$\hat{M}_s(s, 0) = \frac{M_s(s, 0)}{\max_{s,0} M_s(s, 0)}$$

and

$$\hat{M}_s(s, 0) = \operatorname{clip}(M_s(s, 0), 0, 1).$$

A central property is the linearity of the Radon operator:

$$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$0

This guarantees decomposability for disjoint image masks and underlies the interpretability of multi-mask combinations in sinogram space (Huang et al., 11 Sep 2025). Given the full sinogram $$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$1, RMAS constructs complementary positive and negative masked targets as

$$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$2

and

$$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$3

These are linked by a positive–negative consistency loss:

$$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$4

In the main text, the same constraints are summarized channel-wise as

$$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$5

where $$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$6 denotes the full sinogram and $$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$7 are the positive/negative masked channels (Huang et al., 11 Sep 2025). These relations are algebraic and applied on the inputs and targets, so they act as zero-cost, implicit regularizers. This suggests that RMAS encodes consistency not by adding trainable layers, but by restricting admissible channel relations during training.

3. Augmentation pipeline and Dynamic Multi-Mask mechanism

The augmentation process begins in the image domain and is carried through a Radon projector to sinogram space (Huang et al., 11 Sep 2025). The paper specifies that mask blocks of $$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$8 are used to seed the image-domain occlusions. In each iteration, $$R[f](s, 0) = \int\!\!\int f(x, y)\,\delta(x \cos 0 + y \sin 0 - s)\,dx\,dy$$9 non-overlapping spatial masks $0$0 are sampled, and the number $0$1, sizes, and spatial distributions vary dynamically. Morphological operations and exact distributional parameters for shapes, connectivity, or intensity are not elaborated in the text; masks are treated as binary or weighted occlusions whose geometric variation is the primary driver of diversity (Huang et al., 11 Sep 2025).

Each mask is forward projected via the Radon transform, the resulting sinogram masks are summed, and the aggregate is normalized by either linear rescaling or clipping. All experiments use sinogram tensors of size $0$2, and composite inputs are constructed as 3-channel arrays (Huang et al., 11 Sep 2025).

The DMM mechanism varies the number of masks per sample, their sizes, and placements, while enforcing non-overlap to preserve clear decomposition. Because the sinogram masks from multiple image masks are additive, the aggregated mask can still gate complementary positive and negative targets after normalization (Huang et al., 11 Sep 2025). The paper states that DMM exponentially increases data diversity without changing the model architecture or parameter count. In low-shot settings, the network is thus exposed to many instances of the same geometric rules under different mask configurations.

The high-level training loop is described in the paper as follows: sample $0$3 non-overlapping $0$4 image-domain masks with randomized positions and sizes; project each mask using the Radon projector and kernel approximation; aggregate and normalize the sinogram masks; construct $0$5 and $0$6; form the composite $0$7 by stacking $0$8; encode to latent space; and apply the diffusion denoising step (Huang et al., 11 Sep 2025). This sequence shows that augmentation, geometric constraint, and generative modeling are tightly coupled rather than staged independently.

4. Integration with latent diffusion training

RMAS is integrated into an LDM by assembling the masked composites as a 3-channel input,

$0$9

A sinogram autoencoder $s$0 maps the composite to a latent representation,

$s$1

Diffusion training then follows standard objectives, including DDPM, DDIM, and DDBM (Huang et al., 11 Sep 2025). For DDPM, the denoising loss on the latent is given by

$s$2

DDIM and DDBM are used for efficient sampling and supervised bridge constraints, respectively, while RMAS supplies the physically constrained masked inputs and targets that condition latent learning without extra trainable parameters (Huang et al., 11 Sep 2025). The system uses DDIM sampling with 250 steps for training and 72 for generation.

This integration is significant because RMAS is not formulated as a separate regularizer attached after model design. Instead, it changes the statistics and geometry of the training inputs reaching the autoencoder and diffusion backbone. A plausible implication is that the LDM learns a structured factorization of sinogram content into masked, unmasked, and full channels, with the Radon-space partition acting as an implicit inductive bias.

5. Empirical behavior and reported performance

The reported empirical effect of RMAS, together with DMM and the positive/negative constraints, is the expansion of 500 real sinograms per tracer or anatomy into over 200,000 structured training examples (Huang et al., 11 Sep 2025). Under this regime, ALL-PET achieves high-quality sinogram generation using only 500 samples, with performance comparable to models trained on larger datasets, and generalizes across low-dose reconstruction, attenuation correction, delayed-frame prediction, and tracer separation (Huang et al., 11 Sep 2025).

The paper reports superior projection and image-domain FID/KID relative to VAE, GAN, and SGM under the same 500-sample regime (Huang et al., 11 Sep 2025). In the reconstructed image domain, the reported ALL-PET FID values are 68.01 for $s$3F-FDG brain, 65.21 for $s$4F-FDG trunk, 131.65 for $s$5F-DOPA, and 304.04 for $s$6Ga-PSMA; the corresponding KID values are 0.043, 0.033, 0.087, and 0.084 (Huang et al., 11 Sep 2025).

A PAC-Bayes analysis is also reported. At confidence levels 0.999–0.95, the certified upper bounds after augmentation are lower by about 0.027, which the paper interprets as improved stability (Huang et al., 11 Sep 2025). At the same time, the paper does not present an ablation isolating RMAS versus no-RMAS or fixed single-mask versus DMM. Consequently, the evidence is framed at the level of the combined RMAS/DMM/constraint formulation rather than as a clean decomposition of each component’s marginal effect.

That limitation shapes how the results should be read. The paper attributes the data diversity and constraint-driven regularization to RMAS and DMM as key enablers of quality under low-shot conditions, but the exact quantitative contribution of RMAS alone is not separately measured (Huang et al., 11 Sep 2025).

6. Relation to other augmentation paradigms

The paper contrasts RMAS with image-domain augmentations such as Cutout, random erasing, Mixup, and masked autoencoding (MAE), noting that those methods operate on reconstructed images and do not enforce measurement-space physics (Huang et al., 11 Sep 2025). RMAS differs in three explicitly stated ways: it uses Radon-based masking that directly matches PET acquisition geometry in angles and radial positions; it enforces complementary positive/negative consistency in the sinogram domain as a zero-parameter regularizer grounded in physical decomposability; and it integrates with LDM in latent space via composite inputs, shifting complexity to data design while preserving physical interpretability (Huang et al., 11 Sep 2025).

This distinction is methodological rather than merely representational. Classical image-domain augmentation alters already reconstructed content, whereas RMAS perturbs a mask representation whose forward projection is tied to the acquisition operator. That difference suggests a stronger alignment between augmentation and inverse-problem structure. The paper’s Figure 1, as described in the text, contrasts RMAS, DMM, and TMA with classical data augmentation and attention, emphasizing that ALL-PET attains low-shot learning with far less compute by exploiting sinogram physics rather than increasingly large models (Huang et al., 11 Sep 2025).

A common misconception would be to view RMAS as equivalent to generic masking. The formulation in ALL-PET is narrower: masks are generated in image space, projected into sinogram space by the Radon transform, constrained through positive/negative complementarity, and then embedded into a 3-channel latent diffusion pipeline. The geometry-preserving projection step is therefore constitutive, not incidental.

7. Practical configuration, limitations, and future directions

The paper provides specific implementation guidance for RMAS (Huang et al., 11 Sep 2025). It recommends using $s$7 image-domain mask blocks as building units, sampling $s$8 non-overlapping masks per iteration with $s$9 varied dynamically, and forward projecting masks into sinogram space with a Radon projector and kernel approximation for $K(\cdot)$0. The sinogram masks should be normalized with either linear rescaling or clipping to keep values in $K(\cdot)$1, and composite inputs should be assembled as $K(\cdot)$2 before training the sinogram autoencoder and latent diffusion model with the standard denoising objective (Huang et al., 11 Sep 2025).

The paper also identifies several practical pitfalls. Geometric consistency must be preserved so that the algebraic constraints $K(\cdot)$3 and $K(\cdot)$4 remain valid; otherwise, the zero-cost regularization effect is undermined. Boundary artifacts can arise from kernel choice and discretization in $K(\cdot)$5, and clipping helps bound activations. Coverage balance matters: DMM should vary coverage so that both lesion-related and background regions are represented, because overly aggressive masking can deprive the model of contextual cues. For reproducibility, the paper recommends logging random seeds, mask configurations, and projector settings, as well as any clinician-driven ROI edits if TMA is used downstream (Huang et al., 11 Sep 2025).

The stated limitations concern both data scope and modeling assumptions. Although 500 samples per task suffice in the reported experiments, optimal sample size depends on tracer heterogeneity, scanner hardware, and clinical endpoints; multi-center validation is needed (Huang et al., 11 Sep 2025). RMAS and DMM assume that forward-projected image masks produce sinogram variations representative of anatomical and acquisition variability. Extreme cases such as severe motion, unusual scatter, and atypical tracer kinetics may require task-specific mask priors or additional physics-based simulation (Huang et al., 11 Sep 2025). The downstream ROI guidance introduced by TMA also adds user-dependent variability through thresholding or clinician edits, so calibrated interfaces and logging are recommended for reproducibility and regulatory traceability.

Taken together, these considerations place RMAS within a specific design space: it is a projection-domain augmentation strategy for PET that prioritizes physical consistency, low-shot generalization, and low-resource training, while leaving open questions about transfer across sites, scanners, and atypical acquisition regimes (Huang et al., 11 Sep 2025).