## 3 Resolutional Analysis Results
### HMS Image Resolution Analysis Based on Objective Quality Assessment  
The implementation of the objective quality assessment technique on the de-speckled SAR images will not only help to evaluate the HMS presence in the SAR images, but also verify the procedure of the spatial de-speckling filter implementation based on image resolution and information analysis. These objective metrics include the mean square error (MSE), the mean intensity value (MIV), the variance (Var), the signal-to-noise ratio (SNR), the peak signal-to-noise ratio (PSNR), the structural similarity index map (SSIM), the mean SSIM (MSSIM), the normalized cross correlation (NCC), the local entropy, and the local range. The MSE, MIV, Var, SNR, PSNR, SSIM and MSSIM are pixel-based  
Figure 11: Reference RFP evaluation in the presence of noise and compensated noise conditions. Figure 10: Resulting RFP presentation (**a**–**c**). measurements, the NCC is correlation-based, and the local entropy and local range are based on image information statistics. MIV contributes to individual pixel intensity for the entire image, and Var is normally used to find how each pixel varies from the neighboring pixel or the central one. The SNR is the ratio of the mean value of the image and the standard deviation of the HMS within an image. The higher the SNR, the sharper the SAR image will be. The PSNR is the ratio between the maximum possible power of the SAR image and the power of HMS that affects the quality of the image, with the help of MSE as a scaled definition of power by the number of pixels in the images. There is an inverse relationship between PSNR and MSE. Therefore, a higher PSNR value will introduce a lower value of errors. The SSIM index is a quality metric of one of the images being compared to another image, which is regarded as the reference image. The NCC is used as a correlation-based technique to evaluate the degree of similarity between pixel entities of the reference SAR image and the de-speckled images. The local entropy and local range are also 2-D presentations of the images based on pixel and neighboring pixel statistics calculations, which in turn are based on the texture content related to their variations in intensity values or gray levels. The results of image resolution analysis on the pixel-based quality assessment are listed in Table 4. As can be seen from the listed results, every spatial de-speckling filter has its own specification, and in the case of pixel-based image resolution analysis the texture, the image structure, and the parameter of interest play a key role for spatial filter selection. It can also be deduced that Frost and Gamma have the best SSIM values and have great similarity with the reference SAR image, while Kuan and Lee have the lowest values of errors. With the help of correlation-based measurement, the NCC between the reference SAR image and the other de-speckled images is also calculated and presented in Figure 12. Accordingly, the maximum NCC value is related to the Local adaptive median filter with the value of 0.8, while the minimum value is about 0.52, which is related to the Kuan filter. It is clear that in the case of correlation metric evaluation, the Kuan filter, with the best level of pixel-based error measurement, has not achieved the same performance based on correlation index measurements. Figure 12 also presents the NCC of the Local adaptive median filter as having the best performance according to the NCC index.