## 6 Discussions  
Recent advancements in speckle noise mitigation for SAR images include wavelet-based methods [2] and machine learning approaches [51], which often face challenges in balancing noise reduction with detail preservation. However, fusion-based thresholding combined with non-linear diffusion represents a notable improvement. This technique merges multi-resolution image data through fusion-based thresholding, which enhances structural information retention. Non-linear diffusion then refines the image by adapting to local features, effectively reducing noise while preserving edges. Compared to existing filters, like Lee [10], HFLF [11], Kuan [12], Median [13], Frost [14], Log compression [15] filters, and recent methods, this approach shows superior performance in terms of PSNR and SSIM. Studies have demonstrated its efficacy in better noise suppression and detail retention, making it a more advanced solution for SAR image processing. This method's ability to integrate and refine multiple aspects of image quality provides a significant edge over past techniques.  
The proposed method demonstrates significant advancements in performance across key metrics, including SNR, PSNR, SSIM, and UIQI, when compared to previously reported techniques. Specifically, our method shows superior signal quality with higher SNR values than earlier studies, which reported values ranging from 10 to 20 [3]. This improvement underscores the effectiveness of our approach in enhancing signal clarity while minimizing noise. Similarly, the PSNR values from prior works, which ranged between 23 and 27 [52; 53; 54; 55], are consistently surpassed by our method, reflecting a marked enhancement in image fidelity and noise suppression. In terms of structural similarity, our method achieves better results in SSIM, a crucial metric for evaluating the preservation of structural details in images. We outperform recent machine learning benchmarks, which achieved SSIM values of 0.44 and 0.52 [55; 56], indicating our method's superior ability to maintain structural integrity, such as edges and textures. Furthermore, the UIQI values, which gauge overall image quality, from a recent wavelet-based intensity-hue-saturation method (ranging from 0.24 to 0.64) [57], are exceeded by our approach, demonstrating a significant improvement in preserving image features while reducing speckle noise. These collective improvements across all evaluated metrics highlight the substantial advancements offered by our proposed method, positioning it as a more effective approach than many previously reported techniques. However, it is important to acknowledge that direct comparative analysis is challenging, as each study employed distinct image datasets and varying noise levels, which can impact the performance results. Nevertheless, the consistent outperformance across multiple metrics suggests that our method holds strong potential for broader application in SAR image despeckling.  
The proposed despeckling method consistently outperforms contrast methods, showing higher mean values across all metrics, particularly at lower noise variances, indicating superior noise reduction and detail preservation. The UIQI and SSIM values highlight better structural similarity and visual quality retention, with the proposed method demonstrating more stable performance as reflected by narrower SD bars, suggesting greater reliability across various noise levels. This overall superior performance underscores the robustness of the proposed method in preserving fine image details while effectively reducing speckle noise. To improve this work, it is essential to compare the proposed method with a broad spectrum of state-of-the-art despeckling techniques, including both traditional and advanced methods. This comparison will highlight the strengths and limitations of the proposed approach, ensuring its effectiveness and superiority in preserving fine details and reducing noise.