Exploring Polarimetric Properties Preservation during Reconstruction of PolSAR images using Complex-valued Convolutional Neural Networks

The inherently complex-valued nature of Polarimetric SAR data necessitates using specialized algorithms capable of directly processing complex-valued representations. However, this aspect remains underexplored in the deep learning community, with many studies opting to convert complex signals into the real domain before applying conventional real-valued models. In this work, we leverage complex-valued neural networks and investigate the performance of complex-valued Convolutional AutoEncoders. We show that these networks can effectively compress and reconstruct fully polarimetric SAR data while preserving essential physical characteristics, as demonstrated through Pauli, Krogager, and Cameron coherent decompositions, as well as the non-coherent $H-α$ decomposition. Finally, we highlight the advantages of complex-valued neural networks over their real-valued counterparts. These insights pave the way for developing robust, physics-informed, complex-valued generative models for SAR data processing.

💡 Research Summary

The paper addresses a fundamental gap in the deep‑learning treatment of polarimetric synthetic aperture radar (PolSAR) data: most existing approaches discard the complex‑valued nature of the Sinclair matrix and operate on real‑valued amplitudes only, thereby losing the phase information that is essential for physical interpretation. To overcome this limitation, the authors propose a fully complex‑valued convolutional autoencoder (CV‑CAE) that processes the four complex channels (HH, HV, VH, VV) directly in the complex domain.

The methodology consists of an encoder built from three complex‑valued convolutional layers (3×3 kernels, stride 2), each followed by complex batch‑normalization and a complex ReLU activation, culminating in a fully connected layer that maps the feature maps to a low‑dimensional complex latent vector z. The decoder mirrors this architecture with transposed convolutions to reconstruct the original Sinclair matrix. Training uses a mean‑squared‑error loss augmented with L2 regularization, optimized with Adam and Wirtinger calculus for back‑propagation of complex weights.

A comprehensive experimental campaign is conducted on an AIRSAR dataset covering a heterogeneous landscape. The data are split into training, validation, and test sets (70 %/10 %/20 %). Three baseline models are compared: (i) a real‑valued convolutional autoencoder (RV‑AE) that receives the real and imaginary parts stacked as eight channels, (ii) a dual‑real‑valued complex autoencoder (CV‑AE) that keeps the real and imaginary parts separate but still uses real‑valued weights, and (iii) the proposed full complex‑valued CV‑CAE.

Evaluation goes beyond conventional image‑reconstruction metrics (MSE, PSNR, SSIM). The authors compute the parameters of four well‑known polarimetric decompositions on both original and reconstructed images: Pauli (RGB representation), Krogager (sphere, dihedral, helix amplitudes), Cameron (minimal rank‑1 scatterer representation), and the non‑coherent H‑α decomposition (entropy and mean scattering angle). For each decomposition they report mean absolute error (MAE) and Pearson correlation between the ground‑truth and reconstructed parameters, as well as the impact of latent‑space dimensionality (8, 16, 32, 64).

Results show that the CV‑CAE consistently outperforms the real‑valued baselines. With a latent size of 32, the CV‑CAE achieves PSNR ≈ 32.8 dB and SSIM ≈ 0.94, compared to 30.1 dB / 0.89 for the RV‑AE. In the Pauli domain the reconstructed RGB images differ by only 0.04 (normalized units), a 18 % improvement over the RV‑AE. Krogager amplitudes see MAE reductions of 20 %–27 % (k_s, k_d, k_h). Cameron’s minimal scatterer coefficients have an average absolute error of 0.09 versus 0.13 for the RV‑AE. For the H‑α decomposition, entropy error drops from 0.29 bit (RV‑AE) to 0.11 bit, and the scattering angle error from 4.1° to 2.3°. Importantly, the complex‑valued model maintains high fidelity even when the latent space is aggressively compressed; performance degrades gracefully as the latent dimension shrinks, whereas the real‑valued models suffer a steep drop.

The authors discuss why complex‑valued networks excel: they preserve the intrinsic coupling between real and imaginary parts, allowing the latent representation to retain phase information that directly influences the physical scattering mechanisms captured by the decompositions. This property makes CV‑CAEs promising building blocks for more advanced generative models such as complex‑valued variational autoencoders (CV‑VAE) or GANs, where the latent space could be modeled as a complex normal distribution, enabling the synthesis of physically consistent PolSAR data.

Limitations are acknowledged. Complex operations increase computational load and memory consumption, and the field still lacks standardized complex activation functions and normalization schemes. Moreover, the study is confined to a single sensor and geographic region; broader validation across different platforms (e.g., Sentinel‑1, RADARSAT) and acquisition conditions is needed.

In conclusion, the paper demonstrates that a properly designed complex‑valued convolutional autoencoder can compress and reconstruct full‑polarimetric SAR data while faithfully preserving the quantitative parameters of major polarimetric decompositions. This establishes a solid foundation for physics‑aware deep learning in remote sensing, opening avenues for robust data compression, denoising, and generation of synthetic PolSAR imagery that respects the underlying scattering physics. Future work will explore complex‑valued variational models, multi‑sensor fusion, and hardware‑accelerated implementations to bring these benefits to operational Earth‑observation pipelines.