Project Summary

Reconstructing single look complex (SLC) synthetic aperture radar (SAR) images from masked data, while preserving image quality.

Development Tools and Outputs

• The research works with a conditional diffusion model developed by Mikolaj Czerkawski
• The pipeline is implemented in Python 3.12
• GitHub Repository for undersampled SAR SLC reconstruction

Project Description

Introduction

Synthetic Aperture Radar (SAR) is a cornerstone of modern Earth observation. Unlike optical sensors, SAR provides all-weather, day-and-night imaging capabilities, making it indispensable for disaster response, environmental monitoring, and defense. However, the active nature of coherent radar imaging strains on-board resources such as power, thermal load, and data capacity. This limits the operation of Sentinel-1 to only 25 minutes per orbit in stripmap mode. To reduce the strain applied to the system the research at Φ-lab investigated the reduction of data acquired while maintaining image quality (i.e., spatial resolution, phase coherence, and radiometric quality). Traditional despeckling and reconstruction methods (such as spatial filters or standard CNNs) often force a compromise: they either fail to remove the noise entirely, or they aggressively blur the image, destroying critical high-frequency details like urban infrastructure and terrain edges.

This project explores a paradigm shift by applying a Conditional Denoising Diffusion Probabilistic Model (DDPM) (PixelDiffusionConditional) to SAR image reconstruction. Diffusion models have demonstrated state-of-the-art performance in optical image generation by learning the fundamental data distribution. The overarching goal of this research is to harness the generative prior of diffusion models to transform noisy, heavily skewed SAR signals into crisp, high-fidelity physical reconstructions, bridging the gap between theoretical generative AI and complex remote sensing applications.

Methods: Architecture, Conditioning, and Masking Strategy

The core of the methodology relies on a conditional pixel-space diffusion framework designed to reconstruct missing or degraded SAR information. Instead of generating images from pure noise, the model's generative process is explicitly guided by a contextual prior. The original SAR image is decomposed in the Doppler frequency spectrum to create a reference (FA) and 3 identically sized – but lower resolution – subapertures (SA1, SA2, SA3). The reduction in acquired data is represented by removing one of the subapertures from the input and reconstructing the FA from the remaining subapertures. Inputs, Outputs, and Data Mapping: The network operates on paired image batches defined as $(x,y)$ :

• Condition Tensor $(x)$: The input observation. Depending on the specific masking strategy applied during dataset generation, x represents the remaining, degraded subapertures.
• Target Tensor $(y)$: The ground-truth, uncorrupted FA SAR patch the model aims to reconstruct.
• Radiometric Scaling: To map the extreme values of SAR data to the strict bounds required by diffusion, both tensors are log-normalized into a $[-1,1]$ range before entering the UNet.

The Conditioning Mechanism: The DenoisingDiffusionConditionalProcess utilizes a 1000-timestep reverse diffusion loop. During training, forward diffusion gradually adds Gaussian noise to the target y. In the reverse loop, the UNet predicts this noise to recover y. Crucially, the condition tensor x (with its designated condition_channels) is injected into the network at every timestep. This spatial conditioning restricts the generative feature space, forcing the model to continuously reference the unmasked/known structural features of x while hallucinating the missing data in the masked regions.

Loss Formulation: The network optimizes its conditional reconstruction by minimizing the difference between the predicted and actual noise. While originally designed with a configurable loss architecture, empirical testing during this term primarily utilized Mean Absolute Error (MAE/L1) to prioritize the preservation of sharp, high-frequency terrain edges over the blurring effect typical of standard L2 loss.

Results: Magnitude Reconstruction Performance

Following the resolution of early-stage mathematical instabilities, the conditional diffusion pipeline successfully converged. The model demonstrated a strong capacity to learn the structural prior of the SAR landscape and infer missing conditional data. Quantitative evaluation of the generated reconstructions against the validation set yielded promising baseline metrics:

• Peak Signal-to-Noise Ratio (PSNR): Reached 18 dB.
• Structural Similarity Index Measure (SSIM): Reached 0.35.

In the context of optical imagery, these metrics might appear modest; however, in the domain of SAR – where the ground-truth target is itself heavily corrupted by random multiplicative speckle – an SSIM of 0.35 represents a significant achievement. It indicates that the model is successfully reconstructing the underlying structural geometries and high-frequency edges of the terrain, rather than simply guessing mean pixel values.

Crucial Limitation: It is important to note that these metrics represent the reconstruction of magnitude data only. The log-scaled amplitude was isolated for this phase of the research, serving as a proof-of-concept that conditional DDPMs can successfully navigate SAR's asymmetric data distribution.

Future Directions: Transitioning to Phase Information

While the current PixelDiffusionConditional architecture has proven successful for magnitude-based reconstruction, it ignores a fundamental physical reality of radar imaging. SAR is an active, coherent microwave sensor. Raw SAR data is intrinsically Single Look Complex (SLC), consisting of both amplitude (magnitude) and phase information. By discarding the phase component, the current pipeline treats SAR data purely as a noisy optical photograph. However, the complex phase contains invaluable physical data regarding scattering mechanisms, target elevation, and millimeter-scale surface deformations.

The Next Evolution of the Project: To make the generated reconstructions viable for true downstream remote sensing applications (such as Interferometric SAR [InSAR] or coherent change detection), the diffusion model must be upgraded to process full SLC data. Future research building upon this term's foundation should focus on:

Conclusion

This visiting researcher term successfully established a highly robust DDPM pipeline tailored specifically for conditional SAR image reconstruction. By systematically diagnosing the interactions between diffusion mathematics and extreme data distributions, the project engineered a stable, magnitude-based baseline capable of achieving 18 dB PSNR and 0.35 SSIM. More importantly, this term laid the structural and codebase groundwork required for the next critical phase of research: the transition toward fully coherent, Single Look Complex (SLC) generative modeling.