## 1 Introduction  
Synthetic Aperture Radar (SAR) is an active coherent microwave imaging sensor, which is used to form 2-D or 3-D images from back scattered signals of complex target terrain (CTT) in all time and all weather conditions [1; 2]. For the purpose of SAR imaging, specific waveforms in the shape of pulses are transmitted by the sensor in phases, and interact with the illuminated CTI. After reflection, these pulses are no longer in phases, even though they are coherent in frequency. This is mainly caused by the difference in the distance of the pulses travelling back from point scatterers due to surface roughness, antenna-platform displacements or similar, and makes the received pulses have random phase shiftswhen received [1; 3]. The out-of-phase pulses interfere constructively or destructively to produce stronger or weaker signals when received, according to their spatial configuration. When a SAR image is formed by coherently processing the backscattered 2-D signals from successive transmitted pulses, these interferences cause variations in the signal magnitude and random pixel-to-pixel intensity changes, which is presented as a specific pattern called speckle noise [4; 5]. This explains why SAR gray-scale images can have a granular pattern that produces dark spots, corresponding to destructive interferences, and bright spots, due to constructive ones [6]. The presence of speckles makes interpretation of the images difficult, and may lead to misinterpretation and erroneous detection because of the pixel quality degradation [5; 6; 7; 8]. SAR speckle noise has a standard deviation linearly related to the mean and the variance, which is often modeled as multiplicative signal-dependent noise [6; 7; 8; 9; 10]. Dozens of de-speckling filters have been proposed in order to remove such multiplicative effects, have been widely studied, and are the topic of literature on the modeling and analysis of the data [11; 12; 13; 14; 15; 16; 17]. Spatial de-speckling filters with good noise suppression capabilities often result in image resolution loss and quality deterioration. Hence, for the purpose of precise image processing, the suppression of speckle must be balanced with the implementation of the filter in order to preserve fine details, so that the subtle textures of the de-speckled image can be detected within the image [16; 17; 18; 19; 20]. In other words, the resolution preservation of the SAR images is directly related to how the speckles are suppressed from the image with the help of the spatial de-speckling filter application [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. Hence, an adverse effects analysis of the speckle on the radar system resolution and the image resolution might be helpful to avoid further information loss and resolution degradation, as an index for de-speckling filter selection [14]. The previous literature regarding this [4; 10; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25] not only does not include a comprehensive study on the speckle noise behavioral formulation and modeling, as well as the resolution loss effects analysis, but also lacks spatial de-speckling filter objective quality assessment and evaluation. To our best knowledge, this is the first time that SAR spatial resolution analysis and image resolution evaluation are being investigated simultaneously on the same SAR image under different spatial de-speckling filters. According to the proposed method, the multiplicative noise behavioral investigation includes speckle distribution formulation and PSD function modeling, system resolution analysis on the basis of RDG and RFP extraction, and image resolution information analysis based on objective quality assessment. The PSD function modeling is carried out with the help of image statistics and noise distribution based on the amplitude, the intensity, and the phase of the pixels, which determines the level of the embedded multiplicative speckle noise presence within the texture.