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A Frost filtering algorithm of synthetic aperture radar (SAR) images with adaptive windowing and adaptive tuning factor is proposed to resolve the problem that the traditional Frost filtering algorithm cannot balance speckle suppression and edge preservation effectively. The tuning factor and the window influence the performance of the Frost filter significantly. When the tuning factor and the window are too big or too small, the Frost filter cannot lead to effective balance between speckle suppression and edge preservation. Through the adaptive changing of the windowing and tuning factor, the proposed algorithm can not only suppress speckle effectively, but also keep the marginal information of image better. The proposed algorithm is applied to SAR images, and it is compared with the Lee filter, the Gamma MAP filter, the traditional Frost filter, and the modified frost filter only using adaptive tuning factor. Despeckling experiments demonstrate that the proposed algorithm can suppress speckle in homogeneous regions more sufficiently, while it can preserve edge information more effectively. Therefore, the proposed algorithm achieves a better balance between speckle suppression and edge preservation. Introduction Owing to coherent imaging system, speckle appears in synthetic aperture radar (SAR) images. The speckle degrades the quality of SAR images, and it affects the subsequent edge detection, image segmentation, and target recognition. Therefore, it is indispensable to reduce speckle effectively in SAR image processing [1,2]. Concerning this issue, many techniques have been proposed to suppress speckle. There are two major categories of techniques for speckle reduction in SAR images. The first technique is multi-look processing, and the second technique is image domain filtering. The multi-look processing improves SAR images by averaging several uncorrelated images of one terrain, but it results in a loss of spatial resolution. The image domain filtering tries to suppress speckle after the image is formed, including the local statistics filters such as Lee filter [3,4], Kuan filter [5,6], Frost filter [7-9], and Gamma MAP filter [10]. The Lee filter and Kuan filter are in the form of a linear weighted filtering. The Frost filter, on the contrary, is not just the simple linear weighted form. It is assumed that the impulse response of the system is constant under the conditions of limited bandwidth, and the actual image is estimated by the convolution of the observed image and the corresponding impulse. Finally, the filter equations can be derived by the minimum mean square error criterion [7,9]. For the traditional Frost filter, the window and the tuning factor are both fixed. When the tuning factor and the window are too big or too small, the Frost filter cannot yield an effective balance between speckle suppression and edge preservation. A modified Frost filter was proposed in [11], where the tuning factor is adaptively adjusted based on regional characteristics of SAR images. Compared to the traditional Frost filter, the modified Frost filter with adaptive tuning factor can achieve better performance. However, the size of window is still fixed, not reflecting the differences of various terrains such as homogeneous and heterogeneous regions. In this paper, we propose a Frost filter with adaptive windowing and adaptive tuning factor. The window size and the tuning factor are adaptively adjusted in terms of regional characteristics. In homogeneous regions, a large window is used to sufficiently suppress speckle. In heterogeneous regions, a small window is International Conference on Advances in Mechanical Engineering and Industrial Informatics (AMEII 2015) © 2015. The authors Published by Atlantis Press 538 adopted to well preserve edges and fine details. In order to demonstrate the performance of the proposed Frost filter, despeckling experiments on various SAR images are provided, which shows that the proposed double-adaptive Frost filter can suppress speckle as much as possible while preserve edge and fine details effectively. Modified Frost filter based on adaptive tuning factor The Frost filter was proposed in [7]. Similar to the Lee filter and the Kuan filter, the Frost filter is also based on the minimum mean square error criterion. However, the Frost filter does not owns the simple linear weighted form by the means of the real image and the observed image. It is assumed that the impulse response of the system is constant under the conditions of limited bandwidth, and the actual image is estimated by the convolution of the observed image and the corresponding impulse. Finally, the filter equations can be derived by the minmium mean square error criterion. The Frost filter can be expressed as [9] ( ) 2 ˆ , , I sh sh sh KC d s h sh sh s h P m I i j m e m − = = ∑∑ ∑∑ , (1) where ( ) , i j is the location of current pixel, ( ) ˆ , I i j denotes the output of the filter, sh P denotes the values of pixels among the window centered at ( ) , i j , K ( 0 K > ) is the tuning factor, I C is the coefficient of variation that is defined by the ratio of the sample standard deviation to the sample mean, and sh d is the distance between any pixel in the current window to the current pixel. Obviously, the value of the tuning factor K is important for the performance of the Frost filter. When the value of K is small, the Frost filter can suppress speckle well, but it cannot preserve edges and fine details effectively. As the value of K increases, the ability of speckle suppression of the Frost filter is getting worse, but the edge preserving has gradualy improved. Since the tuning factor in the Frost filter is important but not easy to predefined, a modified Frost filter based on adaptive tuning factor was proposed in [11]. This method computes the tuning factor adaptively by using the regional characterisics and the values of region pixels simultaneously. The centered pixel in current window is comtaminated by speckle, and, in some degree, the degree of such comtamination depends on whether the centered pixel is the most representative in current window. The t statisitcs were used to measure the representative of the centered pixel, because the sample mean and sample variance for t statistics can be estimated by the mean and variance of all pixels in current window [11]. In another word, the t statistics were adopted to measure the degree of speckle contamination for the centered pixel, and then the adaptive tuning factor was constructed as follows: ( ) ( ) ( ) 0 , , K s h T t Q s h = ⋅ , (2) ( ) ( ) ( ) ( ) 0 0 0 0 I t u t T t t δ − = , (3)

Frost Filtering Algorithm of SAR Images with Adaptive Windowing and Adaptive Tuning Factor