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SAR Despeckling via Log-Yeo-Johnson Transformation and Sparse Representation

Xuran Hu, Mingzhe Zhu, Djordje Stanković, Zhenpeng Feng, Shouhan Mao, Ljubiša Stanković

TL;DR

This work tackles despeckling of SAR imagery corrupted by gamma speckle noise, where y = x · n with n gamma-distributed. It introduces a pipeline that first applies the Log-Yeo-Johnson transformation to convert multiplicative gamma noise into an approximate additive Gaussian form, enabling sparse coding in a non-local dictionary. The method formulates a MAP objective with noise- and sparsity-prior encoded via auxiliary matrices w1 and w2, solving a Lasso-type problem and reconstructing via a dictionary D derived from SVD. Experiments on synthetic and real SAR data demonstrate state-of-the-art performance on metrics such as PSNR, SSIM, ENL, EPI, and SQI, while preserving details and adapting to patchwise noise variance.

Abstract

Synthetic Aperture Radar (SAR) images are widely used in remote sensing due to their all-weather, all-day imaging capabilities. However, SAR images are highly susceptible to noise, particularly speckle noise, caused by the coherent imaging process, which severely degrades image quality. This has driven increasing research interest in SAR despeckling. Sparse representation-based denoising has been extensively applied in natural image processing, yet SAR despeckling requires addressing non-Gaussian noise and ensuring sparsity in the transform domain. In this work, we propose an innovative SAR despeckling approach grounded in compressive sensing theory. By applying the Log-Yeo-Johnson transformation, we convert gamma-distributed noise into an approximate Gaussian distribution, facilitating sparse representation. The method incorporates noise and sparsity priors, leveraging a non-local sparse representation through auxiliary matrices: one capturing varying noise characteristics across regions and the other encoding adaptive sparsity information.

SAR Despeckling via Log-Yeo-Johnson Transformation and Sparse Representation

TL;DR

This work tackles despeckling of SAR imagery corrupted by gamma speckle noise, where y = x · n with n gamma-distributed. It introduces a pipeline that first applies the Log-Yeo-Johnson transformation to convert multiplicative gamma noise into an approximate additive Gaussian form, enabling sparse coding in a non-local dictionary. The method formulates a MAP objective with noise- and sparsity-prior encoded via auxiliary matrices w1 and w2, solving a Lasso-type problem and reconstructing via a dictionary D derived from SVD. Experiments on synthetic and real SAR data demonstrate state-of-the-art performance on metrics such as PSNR, SSIM, ENL, EPI, and SQI, while preserving details and adapting to patchwise noise variance.

Abstract

Synthetic Aperture Radar (SAR) images are widely used in remote sensing due to their all-weather, all-day imaging capabilities. However, SAR images are highly susceptible to noise, particularly speckle noise, caused by the coherent imaging process, which severely degrades image quality. This has driven increasing research interest in SAR despeckling. Sparse representation-based denoising has been extensively applied in natural image processing, yet SAR despeckling requires addressing non-Gaussian noise and ensuring sparsity in the transform domain. In this work, we propose an innovative SAR despeckling approach grounded in compressive sensing theory. By applying the Log-Yeo-Johnson transformation, we convert gamma-distributed noise into an approximate Gaussian distribution, facilitating sparse representation. The method incorporates noise and sparsity priors, leveraging a non-local sparse representation through auxiliary matrices: one capturing varying noise characteristics across regions and the other encoding adaptive sparsity information.

Paper Structure

This paper contains 11 sections, 17 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Log-Yeo-Johnson Transformation for Noise Conversion
  4. Non-local Sparse-Guided SAR Despeckling
  5. Sparsity-guided Posterior Estimation
  6. Results and Analysis
  7. Experimental Setup
  8. Synthetic Experiment
  9. Real Experiment
  10. Ablation Study
  11. Conclusion

Figures (4)

  • Figure 1: Synthetic image despeckling, row from top to bottom: noisy image, ANLM, SAR2SAR, DnCNN, SARCAM, RDDPM, AGSDNet, SIFSDNet, MONet and our proposed method.
  • Figure 2: Real image despeckling, column from right to left: noisy image, ANLM, DnCNN, SARCAM, SAR2SAR, AGSDNet, SIFSDNet, MONet, RDDPM and our proposed method.
  • Figure 3: Images and Noise distributions before and after Log-Yeo-Johnson transformation: (a) Original image; (b) Image with gamma noise; (c) Residual noise; (d) Residual noise after transformation; (e) Original noise distribution; (f) Transformed noise distribution; (g) Noise distribution of stacking image patches; (h) Noise distribution of stacking transformed patches.
  • Figure 4: Ablation study, column from right to left: noisy image, denoised image (without Log-Yeo-Johnson transformation and auxiliary matrix), denoised image (without auxiliary matrix), denoised image (without Log-Yeo-Johnson transformation) and our proposed method.