Speckle-Aware Representation Enhancement

• SARE is a methodology that integrates physical speckle noise models into representation learning to improve image fidelity and semantic consistency.
• In SAR applications, it employs noise injection and Vision Transformer-based autoencoding to enhance denoising and semantic separability despite speckle interference.
• In optical imaging, SARE uses controlled speckle modulation and autocorrelation enhancement to enable robust reconstruction through scattering media.

Speckle-Aware Representation Enhancement (SARE) denotes a class of methodologies that explicitly incorporate physical models of speckle noise into the process of representation learning or image reconstruction, with the principal objective of boosting robustness and fidelity under speckle-contaminated observation regimes. The SARE approach has found distinct technical realizations in remote sensing—specifically Synthetic Aperture Radar (SAR) imagery in deep learning frameworks—and in computational imaging through scattering media via optical speckle modulation and correlated inverse algorithms. In both domains, SARE augments traditional systems by physically modeling, injecting, or modulating speckle noise, thereby making learned or recovered representations less sensitive to the deleterious effects of coherent noise and enhancing semantic or structural recoverability.

1. Physical and Statistical Principles of Speckle

Speckle is a stochastic, high-frequency interference pattern arising from the coherent summation of scattered waves—whether radio-frequency as in SAR or optical as in tissue imaging. In SAR, the observed intensity within a resolution cell is formed by the incoherent average of $L$ independent, exponentially distributed single-look intensities,

$$Z = \frac{1}{L}\sum_{i=1}^L I_i\,,\quad I_i \sim \mathrm{Exp}(\bar I),$$

yielding a gamma-distributed measurement with mean $\bar I$ and variance proportional to $1/L$ (Liu et al., 18 Dec 2025). This multiplicative noise is scene-dependent, grainy, and statistically non-Gaussian. In optical systems, the speckle pattern is dictated by the complex-valued, random Green’s function $h(x_s,x_o)$ mapping object-points to sensor-coordinates. The resultant memory effect (ME) correlations preserve some tilt-shift structure over small spatial displacements, enabling computational inversion via autocorrelation-based techniques (Chen et al., 2022).

2. SARE in SAR Self-Supervised Representation Learning

The SARE module within the SARMAE architecture is tailored to address the challenge posed by SAR’s multiplicative speckle during self-supervised masked autoencoding (Liu et al., 18 Dec 2025). In this context, direct MAE reconstruction of speckled inputs does not promote semantic separability or denoising. SARE addresses this as follows:

• Noise Injection: For each input patch $x$, a synthetically more severe speckle is applied by resampling according to a gamma distribution with a lower look parameter $L_\mathrm{syn}$ (i.e., higher variance), such that

$$x'(i, j) \sim \mathrm{Gamma}\big(L_\mathrm{syn}, x(i, j)/L_\mathrm{syn}\big).$$

To further generalize the model to various noise types, four noise models are used:

| Model Type | Functional Form | Parameterization | |----------------------|--------------------------------------------------------------|--------------------------------------------------| | Additive Gaussian | $x' = x + \mathcal{N}(0,\sigma^2)$ | $\sigma \sim U(0,0.5)$ | | Multiplicative Rayleigh | $x' = x \odot R$, $R \sim \mathrm{Rayleigh}(\sigma)$ | $\sigma \sim U(0,0.5)$ | | Multiplicative Gamma | As above | $L_\mathrm{syn} \in \{1,2,3,4\}$ | | Additive Uniform | $x' = x + U(-\alpha, \alpha)$ | $\alpha \sim U(0,0.5)$ |

• Architectural Placement: The speckled or clean patch $x'$ is batched, masked (mask ratio 0.75), and encoded via a Vision Transformer (ViT) branch prior to MAE reconstruction.
• Training Objective: The denoising MAE is optimized with a mean-squared error over masked patches,

$$\mathcal{L}_\mathrm{SARE} = \frac{1}{|\mathcal{M}|} \sum_{p \in \mathcal{M}} \| D(E_\mathrm{SAR}(\tilde{x}'))_p - x_p \|_2^2,$$

where $D$ is the decoder and $E_\mathrm{SAR}$ is the SAR encoder.

This methodology compels the latent representation to become invariant to speckle statistics, capturing intrinsic SAR backscatter while discarding idiosyncratic speckle variations.

3. SARE in Optical Imaging through Scattering Media

In the domain of fluorescence imaging through highly scattering tissue, SARE refers to a technique for boosting the statistical contrast of memory effect (ME) speckle correlations (Chen et al., 2022). The workflow is:

• Speckle Modulation: A phase-only spatial light modulator (SLM) applies controlled phase ramps to generate $T$ uncorrelated realizations of the speckle response, each corresponding to an interferometric shear $\tau_t$ exceeding one speckle grain.
• Acquisition Protocol: For each shear, three phase-shifted exposures are acquired per classical phase-shifting interferometry, yielding modulated intensity frames.
• Autocorrelation Enhancement: Averaging autocorrelations over all $T$ uncorrelated speckles raises statistical ME contrast linearly with $T$, overcoming photon noise and the fragility of single-shot ME recovery.

This strategy enables megapixel-scale reconstructions behind thick ($\sim150\,\mu\mathrm{m}$) scattering slabs, using a local-support ptychographic cost function and enforcing sparsity or total variation regularization in the object domain.

4. Loss Functions and Optimization Strategies

In SARMAE, the SARE loss function is strictly a denoising reconstruction error over masked patches, as formalized above, and is typically combined with semantic consistency constraints such as the Semantic Anchor Representation Constraint (SARC) when paired optical data is used (Liu et al., 18 Dec 2025). In computational imaging SARE, optimization minimizes the local-support difference between measured and predicted speckle autocorrelations (including known tilts from modulation), augmented by regularization (e.g., total variation or $\ell_1$ sparsity). Both domains employ gradient-based optimizers (Adam) with carefully tuned schedules.

5. Hyperparameter Selection and Architectural Choices

Both SARMAE SARE and optical SARE place significant importance on key hyperparameters:

SARMAE SARE (Liu et al., 18 Dec 2025):

• Masking ratio: 0.75
• Noise injection probability: 0.5 per batch
• Synthetic gamma look $L_\mathrm{syn}$: 1–4
• Noise model parameters: Drawn uniformly from [0, 0.5]
• Batch size: 1024, AdamW (learning rate $10^{-3}$, weight decay 0.05), 300 epochs.

Optical SARE (Chen et al., 2022):

• Number of interferometric shears: $T \approx 18$, giving $3T=54$ exposures
• Field-of-view: Up to $10^6$ pixels ($300 \times 300\,\mu\mathrm{m}^2$)
• Regularization: Total variation or $\ell_1$ sparsity
• Computational load: $O(N_\mathrm{pix} \times T)$, solved on GPU in $\sim5$ minutes.

6. Empirical Outcomes and Limitations

SARE has demonstrated robust improvements in empirical evaluation:

Dataset/Task	Baseline	+SARE	Δ
FUSAR-SHIP classification accuracy	82.22%	86.80%	+4.58%
SSDD ship detection mAP	64.20%	64.40%	+0.2%
AIR-PolSAR-Seg mIoU	64.36%	65.15%	+0.79%

(Liu et al., 18 Dec 2025)

Qualitative results indicate attention to semantically meaningful structures and reduced speckle bias. In imaging through tissue, SARE achieves accurate recovery of fluorescent bead positions with RMS error $<1$ pixel, and contrast increases from $\sim0.1$ to $\sim5$ as the number of speckle modulations increases from 1 to 54 (Chen et al., 2022).

Key limitations in the optical regime include sensitivity to ME correlation range (failing beyond $\approx200\,\mu$m thickness) and requirement for sparse or moderately dense objects. In both domains, SARE’s effectiveness depends on the fidelity of the speckle noise model and on sufficient noise diversity during training or modulation.

7. Context, Extensions, and Significance

SARE represents a principled progression beyond “denoising” by directly integrating physical noise modeling and augmentation into core learning or reconstruction mechanisms, rather than treating noise as a nuisance post hoc. In the self-supervised representation learning setting, this methodology can be seen as a SAR-specific generalization of noise-aware masked encoding, with downstream benefits in data efficiency and domain robustness. In computational imaging, SARE’s physical modulation breaks the speckle correlation bottleneck, enabling wide-field inversion through substantially thicker media at the cost of increased acquisition and computational effort.

A plausible implication is that SARE-style strategies, by matching the augmentation or modulation to the underlying physics of the noise process, could be broadly applicable across modalities with structured, non-i.i.d. noise, provided suitable models and domain-appropriate constraints are identified.