## 4 Discussion  
SAR systems are an established technology for remote sensing applications [1]. Owing to the complex recording and processing of the received 2-D backscattered data, SAR sensors are able to form high-resolution complex images of the terrain [3]. The inherent complex nature of SAR data is also one of the main drawbacks of this sensor, as it affects the phase history of the raw data with a specific type of noise known as speckles [4]. Speckles are modeled as multiplicative interference in a destructive or constructive manner in the SAR phase history, and its suppression or de-speckling has been always a major challenge in SAR image processing [5]. In general, speckle reduction techniques are applied prior to texture feature extraction, and the de-speckling has been considered as an active field of research in remote sensing processing [8]. However, the main problem of SAR image de-speckling is resolution preservation, because both the speckle presence and de-speckling procedure degrade the quality of the image and might lead to misinterpretation [21]. These considerations motivate the increasingly intense research for speckle analysis and precise de-speckling methods with the help of spatial de-speckling filters, without impairing potentially valuable SAR image information [19]. Considering the complexity of spatial de-speckling filter implementation, it is necessary to perform an objective quality analysis on the embedded multiplicative noise within the SAR images for the purpose of speckle behavioral analysis and proper filter selection. To retrieve such objective metrics, this paper considers a reference SAR image under seven different spatial de-speckling filter implementations for the purpose of speckle presence analysis and filtering evaluation. This is the first time that this type of evaluation scenario has been categorized into three major procedures. The evaluation scenario not only covers the spectral simulation of the speckle on the basis of the image and the noise, but also covers the objective quality assessment in the case of system resolution and image resolution analysis. The spectral simulation includes the PSD function formulation and modeling, while the system resolution and the image resolution contain the RDG, RFP, pixel-based, correlation-based, local entropy, and local range measurements. All the resulting qualitative and quantitative metrics verify that not only are the multiplicative speckle-noise presented in the high-frequency part of the image information with no specific pattern within the texture, but also that no spatial de-speckling filter consistently outperforms the others in suppression. In other words, the novel results of this research analysis show that every specific aforementioned category, such as spectral modeling, system resolution and image resolution, has its own filter or filters with the best and the worst performance. Hence, in the case of the aforementioned spatial de-speckling filters, the results are listed as follows: (i) According to the spectral modeling of the spatial filters, Gamma has the best and Lee sigma has the worst de-speckling performance. (ii) For the purpose of residue speckle measurement, Local sigma has the best performance, while Gamma has the worst ability to measure the level of the remaining noise presence. (iii) According to system resolution measurement based on the RDG index, Lee has the best system performance while Local sigma has the worst evaluation, and Kuan has the best performance in comparison to Lee sigma if the RFP is going to be considered. (iii) Finally, in the case of the image resolution analysis, the spatial filter selection is completely relativistic and dependent on criteria such as pixel-based, correlation based, local entropy, or range line results. This research study not only verifies that multiplicative speckle noise is located within the high-frequency part of the image information with no specific pattern within the texture, but also the proposed spatial de-speckling filter for the proper application.