GISdevelopment.net ---> AARS ---> ACRS 1998 ---> Poster Session 1 A Simple Sar Speckle Reduction by Wavelet Thresholding Punya Thitimajshima, Yuttapong Rangsanseri, and Prapon Rakprathanporn Department of Telecommunications Engineering, Faculty of Engineering King Mongkut's Institute of Technoloyg Ladkrabang, Bangkok 10520, Thailand E-mail: ktpunya@kmitl.ac.th, kryuttha@kmitl.ac.th Abstract This paper describes a method of speckle reduction in Synthetic Aperture Radar (SAR) images based on the wavelet transform. To deduce the problem of filtering the multiplicative noise to the case of an additive noise, the wavelete decomposition is performed on the logarithm of the image gray levels. A threshold value is estimated according to the noise variance and used for the soft-threshold performed on all the high frequency subimages. The filtered logarithmic image is then obtained by reconstruction from the thresholded coefficients. The exponential function on all the high frequency subimages. The filtered logarithmic image is then obtained by reconstruction from the thresholded coefficients. The exponential function of this reconstructed image gives the final filtered image. Experimental results on JERS-1/SAR images showed that the proposed method results in a significant removal. 1 Introduction Synthetic Aperture Radar (SAR) technology has resulted in marked improvements in the spatial resolution images when observing a ground scene from aircraft or satellites, and it can be used to estimate also features like the dampness of the soil, the thickness of a forest, or the roughness of the sea. Nevertheless, SAR images are contaminated by multiplicative noise, due to the coherence of the radar wavelength, labeled as speckle noise which results in an important reduction in the efficiency of target detection and classification algorithms. Typical noise-smoothing methods are not well suited to preserving edge structures in speckled images. Classical operators are based on the local variance statistics [1] [2]. The method proposed here starts from a wavelet representation of the image. A few attempts were made at filtering of SAR images by wavelet, essentially filtering can be reduced hence to the case of an additive noise that is mastered in the framework of threshold method930. The Discrete Wavelet Transform (DWT) is outlined in Section 2. In Section 3, we discuss briefly the method to reduce speckle noise by wavelet thresholding. Section 4 describes the threshold estimation. In Section 5, the experimental results using the proposed algorithm are presented. Finally, section 6 provides a conclusion of the paper. Discrete wavelet transform (DWT) The discrete wavelet transform [3] corresponds to multiresolution approximation expressions. In practice, mutiresolution analysis is carried out using 2 channel filter banks composed of a low-pass (G) and a high-pass (H) filter and each filter bank is then sampled at a half rate (1/2 down sampling) of the previous frequency. By repeating this procedure, it is possible to obtain wavelet transform of any order. The down sampling procedure keeps the scaling parameter constant (n = ½) throughout successive wavelet transforms so that is benefits for simple computer implementation. In the case of an image, the filtering is implemented in a separable way be filtering the lines and columns. For J-level wavelet decomposition, the image is decomposed into 3J high frequency subimages (SH, SLH, SHH) and one low frequency subimage (SLL). The SHL shows scale variations in the x-direction and its high values indicate the presence of vertical edges. Large values of SLH and SHHH indicates the presence of horizontal edges and corner points. 3 De-noising by soft thresholding Donoho [4] has proposed an algorithm for removing additive noise in signal based on thresholding its wavelet transform. The principle of this method, in the case of two-dimensional image, can be summarized as the following: decompose the image by using wavelet transform perform soft thresholding on the wavelet coefficients (Y): compute the inverse wavelet transform from the thresholded coefficient. A threshold value, T in eq. (1), can be estimated according to the noise variance within the image. This noise standard deviation s is estimated by [5]: where Med denote the median value. The threshold T is then computed by: Where N is the number of pixels in the image. 4 The proposed algorithm The basic idea of speckle reduction by wavelet thresholding is to convert the multiplicative noise to the case of an additive noise. This can be performed by the applications of logarithmic function at the input, and the exponential function at the output, as shown in Figure 1. Figure 1: block diagram of the proposed algorithm. 5 Experimental results Experiments were carried out for the proposed algorithm using different SAR images. An example is given in Figure 2. At first, the natural logarithm was taken for each pixel value of the original JERS-1/SAR image, which is shown in figure 2(a). Then the logarithmic image was decomposed by a 2-level wavelet transform. A threshold value was estimated according to eqs. (2)-(3) and used for the soft-thresholding, which was performed on all the high frequency subimages. The exponential function was applied to the reconstructed logarithmic image in order to get back the conventional pixel values of the filtered image, as shown in Figure 29c). An obvious reduction in the speckle can be seen inhomogeneous regions. On the right column, figure 2(b) and (d), are shown the corresponding histograms of the original and the filtered images, respectively. Figure 2: Experimental results. (a) Original JERS-1/SAR image. (b) Histogram of (a). (c) Filtered image. (d) Histogram of (c). 6 Conclusions A multriesolution filtering algorithm, based on thresholding the high-frequency wavelet subbands, was proposed for speckle reduction of SAR images. This algorithm is simple, but useful in general SAR image applications Acknowledgement The authors wish to thank the National Research Council of Thailand (NRCT) of providing the satellite image data. Reference J.S. Lee, "speckle suppression and Analysis for Synthetic Aperture Radar Images", Optical Engineering, vol. 25, no. 5 pp. 636-645, 1986. J.M. Durand, B.J. Gimonet, and J. Perbos, "SAR Data Filtering for Classification", IEEE Trans. Geosci, and Remote Sensing, vol. 25, no. 5 pp. 629-637, 1987. C.S. Burrus, R.A. Gopinath, and H. Guo, Introduction to Wavelets and Wavelet Transforms, New Jersey: Prentice-Hall Inc, 1998. D.L. Donoho, "De-noising by soft Thresholding", IEEE Trans. Inform. Theory, vol. 41, no. 3, pp. 613-627, 1995. S. Mallat, A Wavelet Tour of signal Processing, San Diago: Academic Press 1998.