Analysis of SAR images using fractal dimension estimated by wavelet technique

了解合成孔径雷达(SAR)图像的统计特性对于许多应用具有重要意义。由于斑点和纹理的乘性相互作用，合成孔径雷达图像的强度在空间上会发生波动。纹理来源于场景相关的空间变异性，包含了关于目标的有用信息。对于纹理特征，考虑了分维，分数布朗运动(FBM)是随机分形过程的典型模型。最近，P.Flandrin提出了一种利用小波多分辨分析来估计一维FBM的Hurst参数的方法，该参数与分数维直接相关。我们将该方法推广到二维情况，证明了该方法可以用与L-D情形相同的步骤来估计二维图像的赫斯特参数，并将该方法应用于实际的合成孔径雷达图像。结果表明，该模型能很好地模拟合成孔径雷达图像，且在不同的频段和极化通道上，其分维不同。由于表面粗糙度被认为是表面粗糙度的直观表征，结果表明，不同的频率和极化程度对表面粗糙度的描述方式不同，并且研究了纹理与系统分辨率的关系，近年来，合成孔径雷达系统的分辨率有了显著的提高。然而，高分辨率数据的统计模型还没有完全建立起来。因此，在测量纹理和斑点的分维之前，我们检验了纹理和斑点乘积模型对高分辨率图像的有效性。在这一分析中，使用了全极化数据集，从而研究了纹理与极化之间的关系。

Understanding of the statistical properties of synthetic aperture radar (SAR) images is important for many applications. The intensity of SAR images fluctuates spatially by the multiplicative interaction of speckle and texture. Texture originates from the scene-dependent spatial variability, and contains useful information about targets. In this work, for a texture feature fractal dimension was considered.The fractional Brownian motion (fBm) is known to be a typical model for stochastically fractal processes. Recently, P.Flandrin introduced the method that estimates the Hurst parameter of a one-dimensional (1-D) fBm, which is directly related to the fractal dimension, by wavelet-based multiresolution analysis. We extended the method to the 2-D case, and showed that the Hurst parameter of a 2-D image can be estimated in the same procedure as the l-D case.Then the method was applied to actual SAR images. The results revealed that the SAR images were well modeled by the mm's, and the fractal dimensions of the SAR images were different in frequency bands and polarization channels. Since the fractal dimension is considered to feature the surface roughness intuitively, the results indicate that the manner of describing the roughness differs with frequency and polarization.Furthermore we studied the relation between texture and system resolution, In these years, the resolution of SAR systems has been enhanced remarkably. The statistical model of high resolution data, however, is not fully established. So we examined the validity of the product model of texture and speckle for high resolution images before measuring their fractal dimension. In this analysis, the full polarimetric datasets were used, so that the relation between texture and polarization was investigated.