ProSR: Semantic-Prototype-Guided Discrete Modeling for Physically Consistent SAR Super-Resolution

• High-resolution SAR imagery supports precision analysis but is costly to acquire, while smooth-approximation diffusion can blur nearby scattering edges and distort SAR structure.Source: §1 · p. 2
• ProSR reformulates SAR ISR as semantically guided discrete-token prediction over physically valid codebook entries, selecting categorical reconstructions instead of approximating a smooth density.Source: §1 · pp. 2–3
• A self-supervised representation provides label-free semantic guidance for SADE, which maps discrete codes to scattering classes, and a semantic-aware perceptual loss.Source: §1 · p. 3
• SPMG builds spatial-semantic maps that guide PMGA to restrict attention to semantically consistent regions, suppressing contextual leakage and inter-class interference.Source: §1 · p. 3
• ProSR establishes a large-scale 0.25 m resolution SAR ISR benchmark from the Umbra Open Dataset and reports state-of-the-art results with superior visual realism and scattering preservation.Source: §1 · p. 3

2.1 Single Image Super-Resolution (SISR)

• Diffusion models [9] [39] [65] improve perceptual fidelity and training stability over GANs, but smooth mode interpolation [52] [55] can cause structural hallucinations that undermine SAR physical integrity.Earlier pixel-wise architectures often over-smoothed results, while GANs frequently introduced unrealistic hallucinations from adversarial instability.Source: §2.1 · pp. 3–4

2.2 Discrete Latent Representations

• ProSR uses a discrete latent bottleneck with scattering-primitive guidance to avoid blurred intermediate values and preserve physical scattering distributions.Discrete token prediction [6] selects from a finite codebook rather than continuous latent values, suppressing averaging effects common in continuous spaces.Source: §2.2 · p. 4

2.3 SAR Image Super-Resolution (SAR ISR)

• SAR ISR methods synthesize high-frequency signatures using generative models and structural priors or downstream losses, but depend on scarce labeled data.Realistic scattering patterns can improve downstream tasks such as ATR; ProSR instead uses a self-supervised representation model as a semantic anchor to address label scarcity.Source: §2.3 · p. 4

2.4 Self-supervised Representation Learning in SAR

• SSL learns robust representations from unlabeled data, but its SAR use has focused on high-level tasks [44]; ProSR applies SSL-derived semantic priors to low-level reconstruction without manual labels.It aligns a detail codebook with LR-input semantic features and uses a semantic prototype map to guide cross-attention for input-consistent detail recovery and physical consistency.Source: §2.4 · pp. 4–5

3.1 Overview of ProSR

• The three-stage pipeline first pretrains SADE on HR ground-truth and LR image pairs, reuses its semantic encoder in SPMG, and uses pretrained encoders and adaptor for PMG training.At PMG inference, the pretrained semantic encoder, adaptor, and decoder are used.Source: §3.1 · pp. 5–6

3.2 Stage 1 - Semantic-Aligned Detail Encoding (SADE)

• SADE quantizes the residual between HR detail features and compact semantic features, separating high-frequency scattering signatures from low-frequency structure.A stochastic reconstruction branch uses p = 0.25 to train the semantic features to represent structure independently; SAR self-supervised perceptual loss supplies domain-specific supervision without labels.Source: §3.2 · pp. 6–7

3.3 Stage 2 - Semantic Prototype Map Generation (SPMG)

• SPMG maps semantic features to three learnable target, shadow, and clutter prototypes, then dynamically discretizes high-confidence scattering regions into a non-overlapping map for Stage 3 guidance.The method uses relative thresholds for target and shadow assignments and filters clutter using the top 30% of global clutter-similarity pixels.Source: §3.3 · pp. 7–8

3.4 Stage 3 - Prototype-Map-Guided Masked Generative Modeling

• PMG predicts discrete high-frequency scattering tokens and uses prototype-guided attention to restrict cross-attention to semantically consistent regions, then iteratively refines tokens at inference.This is intended to prevent mode interpolation and inter-class feature leakage while preserving SAR intensity distributions and speckle statistics.Source: §3.4 · pp. 8–9

4.1 Dataset Construction

• The benchmark contains 132,452 VV-polarized patches from 502 Umbra SAR images, with 0.25 m HR references and 1.0 m LR counterparts.LR references were generated by spectral-domain cropping rather than image-space interpolation to preserve speckle statistics and phase integrity; the curated data are publicly available.Source: §4.1 · pp. 9–10

4.2 Implementation Details

• ProSR uses three trained stages: SADE with a 1,024-entry, 32-dimensional Gumbel-VQ codebook; SPMG aligns embeddings to ViT-Tiny features; PMG predicts tokens.PMG uses a 20-layer Transformer and MaskGIT sampling over 8 steps; training and inference details are specified for each stage.Source: §4.2 · pp. 10–11

4.3 Performance Comparison

• On the SAR ISR (×4) benchmark, ProSR dominates in Target and Structural Integrity (|∆TCR|, IW-SSIM, HaarPSI) and excels in FID, Density, and Coverage, indicating superior statistical realism.Source: §4.3 · p. 13, Table 1 · p. 13
• On MSTAR ATR, ProSR reaches 88.39% accuracy, versus 23.87% for oversampled LR and 84.18% for the strongest baseline.All methods use a fixed classifier trained only on original HR images, without SR-specific adaptation.Source: §4.3 · p. 14

4.4 Ablation Studies

• Detail-VQ outperforms standard HR-VQ and avoids the structural errors of Dual-VQ, while K = 1024 balances reconstruction performance with Stage 3 classification complexity.Standard HR-VQ produces over-vivid artifacts; Dual-VQ reduces PSNR/SSIM. K = 512 is insufficient for complex textures, while K = 1024 and 2048 yield comparable LPIPS and SSIM; 1024 achieves highest PSNR.Source: §4.4 · pp. 14–15
• PMGA semantic guidance reduces FID by 1.69 and yields Density 0.9741 and Coverage 0.8592, while its attention discriminates scattering centers.The reported attention behavior prevents blurred merging and suppresses structural hallucinations while preserving high-frequency integrity.Source: Figure 5 · p. 14, §4.4 · p. 15
• The continuous DiT-style variant performs worse than ProSR on LPIPS and FID, with values of 0.3211/40.43 versus 0.3010/23.70.It struggles with dense, impulse-like scatterers and often produces stochastic structural distortions.Source: §4.4 · p. 15

5 Conclusion

• ProSR predicts discrete tokens in a SADE-defined detail latent space to address stochastic distortions and over-smoothed textures in diffusion-based SAR ISR.The paper presents this as an alternative to smooth-approximation-based diffusion models.Source: §5 · p. 15
• On the 0.25 m benchmark, ProSR achieved superior physical realism and structural accuracy while suppressing structural hallucinations.The conclusion also reports that extensive experiments validate these results.Source: §5 · p. 15
• SPMG extracts label-free semantic priors and constructs Msem to guide PMGA in routing information within consistent categories, mitigating inter-class confusion without manual labels.This mechanism supports sharp, physically consistent scattering restoration.Source: §5 · p. 15
• Future work will extend ProSR to downstream tasks such as object detection and develop physics-informed no-reference metrics for signal authenticity.Source: §5 · p. 15

Supplementary Overview · Sec. A Dataset Analysis

• The supplement covers dataset characteristics and data distributions in Sec. A.It expands the analysis of the SAR dataset.Source: Supplementary Overview · p. 21

Supplementary Overview · Sec. B Additional Experiments

• Sec. B adds qualitative results, MSTAR ATR evaluation, DiT-style modeling and prototype ablations, and AE stochastic-training analysis.These experiments include discrete-versus-continuous DiT-style modeling analysis.Source: Supplementary Overview · p. 21

Supplementary Overview · Sec. C Additional Discussions

• Sec. C discusses a toy theoretical analysis of diffusion-based modeling and factors affecting SSIM in SAR super-resolution.Source: Supplementary Overview · p. 21

Supplementary Overview · Sec. D Model Complexity and Efficiency

• Sec. D analyzes model complexity and efficiency using parameter counts, FLOPs, and inference runtime.Source: Supplementary Overview · p. 21

Supplementary Overview · Sec. E Failure Cases and Limitations

• Sec. E discusses limitations involving sub-resolution targets, SSL capacity constraints, and validation-set diversity.Source: Supplementary Overview · p. 21

Supplementary Overview

• The supplementary material provides further details and extensive experimental results to complement the main paper.Source: Supplementary Overview · p. 21

A Dataset Analysis

• The 502 SAR images were manually categorized as Airport, Urban, Industrial, Port, or Natural using predominant environmental context and site metadata, merging minor subclasses for statistical coherence.Source: A Dataset Analysis · pp. 21–22
• The 502 unique scenes span diverse locations across continents and environmental conditions, with image and patch statistics detailed by category and incidence angles of 10°–50°.Source: A Dataset Analysis · p. 21, Figure 6 · p. 22, Table 6 · p. 22
• The split used 468 training images (124,749 patches) and 34 geographically disjoint validation images (7,703 patches), avoiding random splitting and image-level data leakage.The selected validation scenes comprise complex environments and diverse scattering phenomena to test spatial generalization.Source: A Dataset Analysis · p. 22
• To prevent generative mode collapse, quality control discarded many homogeneous, low-backscatter sea patches from port scenes, balancing target structures against homogeneous speckle areas.Source: A Dataset Analysis · pp. 22–23

B.1 MSTAR ATR: A Probe for HR Scattering Fidelity

• 88.39% accuracy for ProSR exceeded oversampled LR (23.87%) and UPSR (84.18%), while ProSR also achieved the best FID (12.40) and LPIPS (0.1869).A frozen ResNet-50 trained only on HR images evaluated all outputs; oversampling and UPSR had the highest SSIM and PSNR, respectively.Source: Table 8 · p. 23, §B.1 · p. 23

B.2 Additional Qualitative Comparison

• Additional qualitative comparisons show reconstruction of tiny scattering points and results in cities, residential areas, and natural terrains.Source: §B.2 · p. 23

B.3 Analysis of Discrete vs. Continuous DiT-style Modeling

• Under ill-posed LR-to-HR reconstruction, continuous denoising can average plausible solutions and merge neighboring scatterers, whereas ProSR’s categorical dictionary preserves sharp, distinct impulses.The passage attributes ProSR’s effect to a finite dictionary of learned scattering primitives that reduces interpolated intermediate representations.Source: Figure 9 · p. 26, §B.3 · pp. 26–27
• The controlled DiT-style variant predicts continuous latents before quantization, replacing token embeddings and the classification head with linear projections.The transformer, iterations, semantic conditionings, and noise-prediction objective were held identical; inference used 15-step DDIM sampling.Source: §B.3 · p. 26
• DiT-style FID was 40.43 vs. ProSR 23.70, and DiT-style LPIPS was 0.3211 vs. ProSR 0.3010.The comparison reports degradation in perceptual and statistical realism for the continuous variant.Source: Table 9 · p. 26, §B.3 · p. 26

B.4 Effect of the Number of Prototype tokens K

• With K = 3, the semantic maps clearly separate target, clutter, and shadow with high confidence, aligning with SAR physical structure.For K = 2 and K = 4, configurations were otherwise identical to the proposed K = 3 setting.Source: §B.4 · p. 27
• At K = 2, too few prototype tokens cause under-segmentation, with target and clutter regions overlapping rather than separating properly.The figure’s K = 2 and K = 4 maps use dynamic thresholding without residual region extraction logic for clutter areas.Source: §B.4 · p. 27, Figure 10 · p. 27
• When K ≥4, redundant tokens overfit non-physical background patterns, absorb probability mass from valid regions, and reduce target, shadow, and clutter confidence.The passage notes that the clutter slot’s confidence is completely degraded, reducing overall semantic coherence and suppressing valid-region assignments.Source: §B.4 · p. 27

B.5 Sensitivity Analysis of Relative Masking Threshold (γ)

• The semantic prototype masks use the top c = 30% of pixels ranked by global clutter score to isolate stable scattering signatures.A separate visual ablation of c is omitted because c = 30% is described as providing representative coverage of the predicted clutter distribution.Source: §B.5 · p. 31
• The selected γ = 0.7 maintains semantic purity and structural connectivity, while γ = 0.5 expands regions and γ = 0.9 omits structure.The passage identifies γ = 0.7 as yielding a balanced representation of scattering geometry.Source: Figure 14 · p. 31, §B.5 · p. 32
• Naive argmax creates boundary ambiguity and can misclassify clutter within target regions, failing to preserve distinctive clutter characteristics.The passage also describes semantic contamination from mixing heterogeneous features within a single mask, which hinders class-specific information exchange.Source: §B.5 · pp. 31–32
• Excessively high γ leaves too few valid structural segments for intra-class exchange, producing fragmented, disconnected scattering representations that miss scene geometry.The comparison identifies structural omission at γ = 0.9.Source: Figure 14 · p. 31, §B.5 · p. 32

B.6 Effectiveness of Stochastic Training Strategy in Autoencoder

• Stochastically including LR patches regularizes the autoencoder, discouraging HR-texture memorization and encouraging consistent structural features from LR inputs.At p = 0, the autoencoder behaves like standard HR-only quantization and over-relies on information-rich HR features, failing to disentangle LR structure from high-frequency detail.Source: §B.6 · p. 32
• SSIM peaks at p = 0.25, LPIPS is best at p = 0.1, and PSNR is best at p = 0.5, reflecting different structural-detail tradeoffs.The passage interprets peak SSIM at p = 0.25 as preserving essential SAR scattering patterns while reconstructing HR details from LR structure.Source: Table 10 · p. 32, §B.6 · p. 32

C.1 Toy analysis of close-mode separation in diffusion models

• When σ_t falls below a, the score’s center changes from a peak to a valley, separating the two modes.For σ_t > a, x=0 is the peak of a merged unimodal distribution; for σ_t < a, it becomes the valley between two modes.Source: §C.1 · p. 33
• Smaller mode spacing delays separation until later reverse-sampling stages, where score errors and finite steps can leave smeared responses; ProSR uses hard codebook selection to reduce interpolation between structural codes.The categorical selection encourages reconstructions consistent with learned scattering patterns.Source: §C.1 · p. 33

C.2 Factors Affecting SSIM in Generative SAR ISR

• Generative SAR outputs can score below oversampled LR images on SSIM because scatterer shifts and independent speckle realizations reduce pixel-aligned cross-covariance.A 1–2 pixel scatterer displacement can sharply penalize SSIM’s structural factor, while the covariance between conditionally independent true and generated speckle approaches zero; this reflects the regression-generation trade-off.Source: §C.2 · pp. 33–34

D Model Complexity and Efficiency

• ProSR has the most compact generative core at 85.83M and fewer FLOPs than ResShift, but higher inference runtime than the baselines.The 20-layer global attention supports early MaskGIT decoding by capturing long-range dependencies and suppressing content-inconsistent hallucinations; the paper treats latency as a fidelity trade-off and proposes linear-complexity attention and fewer inference steps for future acceleration.Source: D Model Complexity and Efficiency · p. 34, Table 11 · p. 34

E.1 Failure Case

• Dense sub-resolution targets and low-contrast boundaries can become indistinguishable from clutter after downsampling, so ProSR reconstructs prominent scatterers better than these ambiguous regions.Resolution-cell expansion causes coherent vector addition between target signal and background clutter during sub-aperture downsampling.Source: §E.1 · p. 35, Figure 15 · p. 35
• Coherent phase mixing can destructively interfere with structural cues, irreversibly erasing geometric evidence and leaving semantic priors insufficient to recover the original topology.Under this severe physical degradation, recovering the exact scattering points remains highly ill-posed; ProSR and other baselines fail to faithfully reconstruct them.Source: §E.1 · p. 35, Figure 15 · p. 35

E.2 Limitations

• ProSR’s reconstruction precision is limited by SSL feature capacity: semantic ambiguity can cause local Msem inaccuracies and minor misalignments, motivating a larger SSL ViT-tiny backbone [20] [44].Even without PMGA, ProSR outperforms other SR baselines in statistical fidelity; PMGA further refines structural details and individual scattering primitives, while the discrete framework models global scattering distributions and characteristics more effectively than diffusion-based baselines.Source: §E.2 · p. 36
• Validation is concentrated in port patches because the authors used non-overlapping, highly complex environments rather than a random split to avoid image-level leakage and maximize training volume; broader sources are future work.Port scenarios include challenging scattering phenomena such as ships and metallic structures, as well as urban and natural topographies, providing a composite testbed for evaluating complex SAR characteristics and generalization across terrains.Source: §E.2 · p. 36