## 1 Introduction  
Synthetic Aperture Radar (SAR) is used to create high-resolution 2D and 3D images through reflected radar signals, functioning effectively in all weather conditions [1]. SAR uses reflection, scattering, refraction, or absorption of targeted areas to generate precise topographic images [2], making it valuable in defense, surveillance, object detection, remote sensing, and global positioning [3; 4; 5]. However, SAR images are often degraded by speckle noise, which challenges image quality [6]. While SAR synthesizes a large antenna from radar echoes, enabling precise distance calculations through microwave radiation [7], the received signals may differ from transmitted ones, causing further degradation [8; 9]. Traditional noise reduction methods tend to smooth images but fail to preserve critical details like edges and textures, necessitating more robust approaches to enhance SAR image quality while retaining fine details. Lee [10] is a widely used method for speckle-noise suppression in coherent imaging systems like SAR and ultrasound. It operates on an adaptive filtering approach, assuming a multiplicative noise model, where noise is proportional to the signal. The filter adapts based on local mean and variance to smooth homogeneous areas while preserving edges and important features. Homomorphic Filtering with Log Function (HFLF) [11] is a technique for reducing speckle noise in SAR images by converting the multiplicative noise into an additive form using a logarithmic transformation. This simplifies noise handling, allowing conventional filters to effectively reduce noise while preserving important features. After filtering, the image is restored to its original form, resulting in a clearer, despeckled SAR image, ideal for further analysis. This approach enhances noise suppression and edge preservation, making it effective in radar and medical imaging. However, its main limitation is that it can be computationally intensive, requiring complex algorithms for frequency decomposition and filtering. Additionally, improper tuning of frequency bands may lead to over-smoothing or loss of fine details. Balancing these aspects is crucial to achieving optimal noise reduction while maintaining image quality. The Kuan filter [12] is an adaptive technique for speckle-noise suppression in coherent imaging systems, such as SAR and ultrasound. It operates by estimating local statistics and adapting its smoothing based on the image's local variance, which helps to reduce noise while preserving edges. Despite its effectiveness, the Kuan filter has limitations, including its sensitivity to parameter settings, which can affect its performance. It may also struggle with highly variable noise environments or non-uniform textures, potentially leading to either over-smoothing or inadequate noise reduction. Balancing these factors is crucial for optimal results. The median filter [13] is a non-linear technique used for speckle-noise suppression in images, including those from SAR and ultrasound. It replaces each pixel's value with the median of the pixel values in a local neighborhood, effectively reducing noise while preserving edges. However, its limitations include reduced performance in preserving fine details and texture, as it can blur edges and structures if it is not properly configured. Additionally, the median filter may not handle high levels of speckle noise as effectively as adaptive filters, leading to suboptimal noise reduction in complex or highly textured regions. The Frost filter [14] is an adaptive technique designed for speckle-noise suppression in radar and medical imaging. It smooths images based on local statistics while preserving edges, using a weight function that decreases with distance from the central pixel, allowing for adaptive noise reduction. Despite its effectiveness, the Frost filter has limitations, including sensitivity to the selection of its parameters, such as the smoothing parameter and window size.