Estimation of the Equivalent Number of Looks in Polarimetric Synthetic Aperture Radar Imagery

This paper addresses estimation of the equivalent number of looks (ENL), an important parameter in statistical modeling of multilook synthetic aperture radar (SAR) images. Two new ENL estimators are discovered by looking at certain moments of the multilook polarimetric covariance matrix, which is commonly used to represent multilook polarimetric SAR (PolSAR) data, and assuming that the covariance matrix is complex Wishart distributed. First, a second-order trace moment provides a polarimetric extension of the ENL definition and also a matrix-variate version of the conventional ENL estimator. The second estimator is obtained from the log-determinant matrix moment and is also shown to be the maximum likelihood estimator under the Wishart model. It proves to have much lower variance than any other known ENL estimator, whether applied to single-polarization or PolSAR data. Moreover, this estimator is less affected by texture and thus provides more accurate results than other estimators should the assumption of Gaussian statistics for the complex scattering coefficients be violated. These are the first known estimators to use the full covariance matrix as input, rather than individual intensity channels, and therefore to utilize all the statistical information available. We finally demonstrate how an ENL estimate can be computed automatically from the empirical density of small sample estimates calculated over a whole scene. We show that this method is more robust than procedures where the estimate is calculated in a manually selected region of interest.     

Probability density functions for multilook polarimetric signatures

Derives closed-form expressions for the probability density functions (PDF's) for copolar and cross-polar ratios and for the copolar phase difference for multilook polarimetric SAR data, in terms of elements of the covariance matrix for the backscattering process. The authors begin with the case in which scattering-matrix data are jointly Gaussian-distributed. The resulting copolar-phase PDF is formally identical to the phase PDF arising in the study of SAR interferometry, so the authors' results also apply in that setting. By direct simulation, they verify the closed-form PDF's. They show that estimation of signatures from averaged covariance matrices results in smaller biases and variances than averaging single-look signature estimates. They then generalize their derivation to certain cases in which backscattered intensities and amplitudes are K-distributed. They find in a range of circumstances that the PDF's of polarimetric signatures are unchanged from those derived in the Gaussian case. They verify this by direct simulation, and also examine a case that fails to satisfy an important assumption in their derivation. The forms of the signature distributions continue to describe data well in the latter case, but parameters in distributions fitted to (simulated) data differ from those used to generate the data. Finally, the authors examine samples of K-distributed polarimetric SAR data from Arctic sea ice and find that their theoretical distributions describe the data well with a plausible choice of parameters. This allows the authors to estimate the precision of polarimetric-signature estimates as a function of the number of SAR looks and other system parameters     

Statistics of the Stokes parameters and of the complex coherenceparameters in one-look and multilook speckle fields

Barakat [1987] derived the Stokes parameter statistics, applicable to one-look synthetic aperture radar (SAR) images, of a partially polarized wave backscattered from a Gaussian area. In this paper, the statistics of the Stokes parameters and of the phase difference are derived as a function of the mean effective phase difference and the degree of coherence for one-look and multilook SAR data. The statistics of the degree of coherence are also derived for multilook SAR data. It is shown that the estimator currently used for calculation of the degree of coherence is biased under low coherence conditions     

A method for estimating the parameters of the K distribution

A method that combines the maximum likelihood and the method of moments for estimating the parameters of the K distribution is proposed. The method results in the lowest variance of parameter estimates when compared with existing non-ML techniques     

Improved Poisson intensity estimation: denoising application using Poisson data

Recently, Timmermann and Nowak developed algorithms for estimating the means of independent Poisson random variables. The algorithms are based on a multiscale model where certain random variables are assumed to obey a beta-mixture density function. Timmermann and Nowak simplify the density estimation problem by assuming the beta parameters are known and only one mixture parameter is unknown. They use the observed data and the method of moments to estimate the unknown mixture parameter. Taking a different approach, we generate training data from the observed data and compute maximum likelihood estimates of all of the beta-mixture parameters. To assess the improved performance obtained by the proposed modification, we consider a denoising application using Poisson data.     

Polarimetric Characteristics of sea ice in the sea of Okhotsk observed by airborne L-band SAR

The Phased-Array L-Band SAR (PALSAR) aboard the Advanced Land Observing Satellite (ALOS) is capable of globally acquiring fully polarimetric data. In order to confirm the ability of L-band polarimetric synthetic aperture radar (SAR) to investigate sea ice before the ALOS launch, we conducted a field experiment using an airborne Polarimetric and Interferometric SAR (Pi-SAR) in the Sea of Okhotsk in 1999. This paper presents the analyzed results of data acquired in that experiment. The extracted polarimetric parameters of several ice types suggested that polarimetric coherences and phase differences between right-right (RR) and left-left (LL) are good candidates for discriminating ice types. The polarimetric anisotropy as well as the beta angle of the first eigenvector calculated in the polarimetric decomposition procedure are alternative parameters that are sensitive to ice type differences. Due to the low depolarization characteristics of open water, it could be discriminated from sea ice by scattering entropy in all incidence angle ranges. From the relation between ice thickness and the polarimetric parameters, we found that backscattering coefficients and vertical (VV) to horizontal (HH) backscattering ratio are highly correlated with ice thickness. Since the ratio is sensitive to ice surface dielectric constants, a simple simulation using the integral equation method surface model was conducted by using the physical parameters of typical sea ice. A two-dimensional ice thickness map was derived from an empirical relation between the VV-to-HH backscattering ratio and ice thickness.     

Observation of sea-ice thickness in the sea of Okhotsk by using dual-frequency and fully polarimetric airborne SAR (pi-SAR) data

To investigate the possibilities of using dual-frequency, multipolarization synthetic aperture radar (SAR) data to monitor sea ice, we derived the relationship between various polarization characteristics and the physical parameters of sea ice. We discuss the frequency and polarization characteristics of the backscattering coefficients of sea ice and then characterize its thickness by comparing the corresponding backscattering coefficient for each polarization with the physical parameters of the ice. We first propose a methodology for classifying sea-ice types by using a polarimetric decomposition technique, before comparing an estimation of the sea-ice thickness with the corresponding dual-frequency, multipolarization SAR data. We utilized the backscattering ratio to estimate the thickness of the sea ice. This ratio canceled the effect of roughness on the backscattering. The method was validated using Pi-SAR (polarimetric and interferometric airborne SAR) observation data obtained at ground-truth sites.     

A microwave backscattering model for deformed first-year sea iceand comparisons with SAR data

Like-polarized backscattering from randomly tilted ice blocks in deformed first-year sea ice is modeled. An approximation for the coherent and incoherent scattering cross section of a single ice block is formulated and validated by comparison with moment method computations. It is found that the model is accurate for lossy ice blocks but underestimates the scattering when the loss is low, which is attributed to multiple scattering within the blocks. The backscattering coefficient is evaluated by averaging over an ensemble of blocks with a distribution of slopes and effects of shadowing are estimated. In situ measurements of ice ridge properties in the Baltic Sea are used as input when comparing the model results with coincident ERS-1 SAR data. The model is found to agree with the data to within 1.5 dB, where the discrepancies are mainly due to the uncertainty of the dielectric loss factor in the ice blocks. The model also shows good agreement with airborne 5.3 GHz SAR data of a first-year shear ridge in the Beaufort Sea for incidence angles between 25-50     

Segmentation of polarimetric synthetic aperture radar data

A statistical image model is proposed for segmenting polarimetric synthetic aperture radar (SAR) data into regions of homogeneous and similar polarimetric backscatter characteristics. A model for the conditional distribution of the polarimetric complex data is combined with a Markov random field representation for the distribution of the region labels to obtain the posterior distribution. Optimal region labeling of the data is then defined as maximizing the posterior distribution of the region labels given the polarimetric SAR complex data (maximum a posteriori (MAP) estimate). Two procedures for selecting the characteristics of the regions are then discussed. Results using real multilook polarimetric SAR complex data are given to illustrate the potential of the two selection procedures and evaluate the performance of the MAP segmentation technique. It is also shown that dual polarization SAR data can yield segmentation resultS similar to those obtained with fully polarimetric SAR data     

基于Mellin变换的K分布参数估计新方法

 K分布是目前SAR图像建模领域应用最广泛、最著名的统计模型之一.当前普遍采用的是基于矩估计的参数估计方法,但其存在等效视数值需要经验获取、容易出现错误估计以及造成K分布失效等问题.为此,本文提出了一种基于Mellin变换的K分布参数估计新方法.该方法以Mellin变换为基础,详细推导了K分布对应的第一个、第二个第二类型的特征函数和它们各自对应的对数矩和对数累积量,最终获得了K分布参数估计简洁的迭代表达式.所提方法不但有效克服了K分布失效的问题,更为重要的是,其把视数同形状参数、尺度参数一样视为待估计的参数,且能够快速准确地迭代出它们的估计值,保证了K分布的拟合精度.实验结果证明了所提方法的有效性.     

Intensity and phase statistics of multilook polarimetric andinterferometric SAR imagery

Polarimetric and interferometric SAR data are frequently multilook processed for speckle reduction and data compression. The statistical characteristics of multilook data are quite different from those of single-look data. The authors investigate the statistics of their intensity and phase. Probability density function (PDF's) of the multilook phase difference, magnitude of complex product, and intensity and amplitude ratios between two components of the scattering matrix are derived, and expressed in closed forms. The PDF's depend on the complex correlation coefficient and the number of looks. Comparisons of these theoretically derived PDF's are made to measurements from NASA/JPL AIRSAR data. The results of this paper can be applied to feature classification using polarimetric SAR and to the estimation of decorrelation effects of the interferometric SAR     

基于Fisher分布的极化合成孔径雷达统计建模及其参数估计方法

为更准确地描述高分辨极化合成孔径雷达(Synthetic Aperture Radar, SAR)图像的尖峰和长拖尾等统计分布特性, 提出了基于Fisher分布的极化图像多变量乘积模型, 并研究了其参数估计方法.首先给出了柯西分布相干斑噪声等效纹理分量的概率密度函数及其低阶矩特征;然后利用散射因子服从F分布的等效纹理变量与高斯散斑变量相乘形成的多变量乘积统计模型, 得到了Fisher分布模型的概率密度函数, 并推导了其多视协方差矩阵的概率密度函数和矩阵行列式值的低阶矩特征;最后提出了基于矩阵行列式值的矩估计和基于Mellin变换的对数累积量估计等两种参数估计方法, 并进行了对比, 同时通过仿真数据和实测数据验证了理论模型和新参数估计方法的有效性.这为高分辨极化SAR图像建模、目标检测和识别等领域的理论研究和工程实现提供了新途径.     

Restoration of polarimetric SAR images using simulated annealing

Filtering synthetic aperture radar (SAR) images ideally results in better estimates of the parameters characterizing the distributed targets in the images while preserving the structures of the nondistributed targets. However, these objectives are normally conflicting, often leading to a filtering approach favoring one of the objectives. An algorithm for estimating the radar cross-section (RCS) for intensity SAR images has previously been proposed in the literature based on Markov random fields and the stochastic optimization method simulated annealing. A new version of the algorithm is presented applicable to multilook polarimetric SAR images, resulting in an estimate of the mean covariance matrix rather than the RCS. Small windows are applied in the filtering, and due to the iterative nature of the approach, reasonable estimates of the polarimetric quantities characterizing the distributed targets are obtained while at the same time preserving most of the structures in the image. The algorithm is evaluated using multilook polarimetric L-band data from the Danish airborne EMISAR system, and the impact of the algorithm on the unsupervised H-α classification is demonstrated     

SAR image statistics related to atmospheric drag over sea ice

The possibility of using synthetic aperture radar (SAR) data to distinguish sea-ice regions with different atmospheric drag is explored. Both the amplitude of the radar return and statistics derived from SAR image data are examined. Roughness statistics data from several pack-ice areas are used in a backscatter model to predict the return from surfaces with measured drag coefficients. The results suggest that the scattering coefficient for typical radar wavelengths is insensitive to the roughness elements responsible for the observed drag coefficient variations over pack ice free of major ridges. For marginal ice zones, where ice concentration and floe deformation contribute to atmospheric drag, a simple model for the atmospheric boundary layer is used to provide qualitative relationships between drag coefficient and regional ice properties (ice concentration, floe size distribution, floe edge density) derivable from SAR data. Simple algorithms to produce maps of ice concentration and edge density are outlined and applied to 23.5-cm SAR digital image data     

基于EM算法的G0分布参数最大似然估计

 G0分布是目前合成孔径雷达(Synthetic Aperture Radar,SAR)图像数据建模的一个重要模型,建模能力强、实用性好,受到了广泛的关注.G0分布的应用离不开准确有效的参数估计,而由于G0分布表达式复杂,统计意义上最优的最大似然估计法一直没能用在G0分布上.本文首先给出了一种新的方式来推导得出G0分布,在此基础上,采用最大期望(Expectation Maximization,EM)算法为G0分布给出一种有效的最大似然参数估计方法.文中的方法与现有的G0分布参数估计方法通过实验进行了比较,实验结果充分证明了所提方法的有效性.     

Retrieving snowpack properties and accumulation estimates from a combination of SAR and scatterometer measurements

This study combines two satellite radar techniques, low-resolution C-/Ku-band scatterometer and high-resolution C-band synthetic aperture radar (SAR) for glaciological studies, in particular mass-balance estimations. Three parameters expressing the mean backscattering and its dependency on azimuth and incidence angle are used to describe and classify the Antarctic ice sheets backscattering behavior. Simple linear regression analyses are carried out between ground truth accumulation data and the SAR backscattering coefficient along continuous profile lines. From this we parameterize the accumulation rate separately for certain snow pack regimes. We find that SAR data can be used to map mass-balance changes, however only within limited areas. Applying this method therefore generally requires accurate ground truth for regional calibration together with additional information regarding mean air temperature or elevation. This investigation focuses on the area of Dronning Maud Land, Antarctica. We present the first high-resolution accumulation map based on SAR data for the surrounding area of the EPICA deep ice core drilling site Kohnen, which is compared to reliable ground truth records as well as to a surface-mass-balance map interpolated from these at low resolution.     

Multiple Comparison for Weibull Parameters

Two problems are considered: 1) testing the hypothesis that the shape parameters of k 2-parameter Weibull populations are equal, given a sample of n observations censored (Type II) at r failures, from each population; and 2) Under the assumption of equal shape parameters, the problem of testing the equality of the p-th percentiles. Test statistics (for these hypotheses), which are simple functions of the maximum likelihood estimates, follow distributions that depend only upon r,n,k,p and not upon the Weibull parameters. Critical values of the test statistics found by Monte Carlo sampling are given for selected values of r,n,k,p. An expression is found and evaluated numerically for the exact distribution of the ratio of the largest to smallest maximum likelihood estimates of the Weibull shape parameter in k samples of size n, Type II censored at r = 2. The asymptotic behavior of this distribution for large n is also found.     

Application of neural networks for sea ice classification inpolarimetric SAR images

Several automatic methods have been developed to classify sea ice types from fully polarimetric synthetic aperture radar (SAR) images, and these techniques are generally grouped into supervised and unsupervised approaches. In previous work, supervised methods have been shown to yield higher accuracy than unsupervised techniques, but suffer from the need for human interaction to determine classes and training regions. In contrast, unsupervised methods determine classes automatically, but generally show limited ability to accurately divide terrain into natural classes. In this paper, a new classification technique is applied to determine sea ice types in polarimetric and multifrequency SAR images, utilizing an unsupervised neural network to provide automatic classification, and employing an iterative algorithm to improve the performance. The learning vector quantization (LVQ) is first applied to the unsupervised classification of SAR images, and the results are compared with those of a conventional technique, the migrating means method. Results show that LVQ outperforms the migrating means method, but performance is still poor. An iterative algorithm is then applied where the SAR image is reclassified using the maximum likelihood (ML) classifier. It is shown that this algorithm converges, and significantly improves classification accuracy. The new algorithm successfully identifies first-year and multiyear sea ice regions in the images at three frequencies. The results show that L- and P-band images have similar characteristics, while the C-band image is substantially different. Classification based on single features is also carried out using LVQ and the iterative ML method. It is found that the fully polarimetric classification provides a higher accuracy than those based on a single feature. The significance of multilook classification is demonstrated by comparing the results obtained using four-look and single-look classifications     

Change detection in multisensor SAR images using bivariate gamma distributions.

This paper studies a family of distributions constructed from multivariate gamma distributions to model the statistical properties of multisensor synthetic aperture radar (SAR) images. These distributions referred to as multisensor multivariate gamma distributions (MuMGDs) are potentially interesting for detecting changes in SAR images acquired by different sensors having different numbers of looks. The first part of this paper compares different estimators for the parameters of MuMGDs. These estimators are based on the maximum likelihood principle, the method of inference function for margins, and the method of moments. The second part of the paper studies change detection algorithms based on the estimated correlation coefficient of MuMGDs. Simulation results conducted on synthetic and real data illustrate the performance of these change detectors.     

On the Extension of Multidimensional Speckle Noise Model From Single-Look to Multilook SAR Imagery

Speckle noise represents one of the major problems when synthetic aperture radar (SAR) data are considered. Despite the fact that speckle is caused by the scattering process itself, it must be considered as a noise source due to the complexity of the scattering process. The presence of speckle makes data interpretation difficult, but it also affects the quantitative retrieval of physical parameters. In the case of one-dimensional SAR systems, speckle is completely determined by a multiplicative noise component. Nevertheless, for multidimensional SAR systems, speckle results from the combination of multiplicative and additive noise components. This model has been first developed for single-look data. The objective of this paper is to extend the single-look data model to define a multilook multidimensional speckle noise model. The asymptotic analysis of this extension, for a large number of averaged samples, is also considered to assess the model properties. Details and validation of the multilook multidimensional speckle noise model are provided both theoretically and by means of experimental SAR data acquired by the experimental synthetic aperture radar system, operated by the German Aerospace Center