SAR amplitude probability density function estimation based on a generalized Gaussian model.

In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed "method-of-log-cumulants" (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena.     

Novel distribution model of transformed coefficients in video coding using quad-tree structured block partitioning

Today’s video coding standard such as high efficiency video coding uses a full quad-tree structured block partitioning, so the underlying statistics of transformed coefficients becomes more complicated to estimate than the previous standards due to the coding structure. However, a statistical distribution of transformed residue is important for a design of a smart encoder. Thus, in this paper, we present a theoretic analysis of a distribution of transformed coefficients produced from an encoder using different transform sizes, and derive a probability density function (pdf) for the estimation. The proposed density model provides a more accurate distribution model than the conventional pdfs. Parameters are theoretically estimated, and rate-distortion model is established from the proposed pdf. We also apply the proposed method to a rate control problem to show the efficiency of the proposed density model. Our experimental results show that the proposed method is better capable of modeling the mixed sources of multiple-type transform coefficients occurred from the quad-tree coding structure of transform and provides an accurate estimate in rate control.

     

Wavelet-Based SAR Image Despeckling and Information Extraction, Using Particle Filter

This paper proposes a new-wavelet-based synthetic aperture radar (SAR) image despeckling algorithm using the sequential Monte Carlo method. A model-based Bayesian approach is proposed. This paper presents two methods for SAR image despeckling. The first method, called WGGPF, models a prior with Generalized Gaussian (GG) probability density function (pdf) and the second method, called WGMPF, models prior with a Generalized Gaussian Markov random field (GGMRF). The likelihood pdf is modeled using a Gaussian pdf. The GGMRF model is used because it enables texture parameter estimation. The prior is modeled using GG pdf, when texture parameters are not needed. A particle filter is used for drawing particles from the prior for different shape parameters of GG pdf. When the GGMRF prior is used, the particles are drawn from prior in order to estimate noise-free wavelet coefficients and for those coefficients the texture parameter is changed in order to obtain the best textural parameters. The texture parameters are changed for a predefined set of shape parameters of GGMRF. The particles with the highest weights represents the final noise-free estimate with corresponding textural parameters. The despeckling algorithms are compared with the state-of-the-art methods using synthetic and real SAR data. The experimental results show that the proposed despeckling algorithms efficiently remove noise and proposed methods are comparable with the state-of-the-art methods regarding objective measurements. The proposed WGMPF preserves textures of the real, high-resolution SAR images well.     

Statistical analysis of multilook SAR interferograms for CFAR detection of ground moving targets

This paper examines the statistics of the phase and magnitude of multilook synthetic aperture radar (SAR) interferograms toward deployment of along-track interferometry (ATI) for slow ground moving-target indication (GMTI). While the known probability density function (pdf) of the interferogram's phase (derived under the assumption of Gaussian backscatter) is shown to agree almost perfectly for a wide variety of backscatter conditions, the corresponding magnitude's pdf tends to deviate strongly in most cases. Motivated by this discrepancy, a novel distribution is derived for the interferogram's magnitude. This pdf, called the polynomial or p-distribution, matches the real data much more accurately, particularly for heterogeneous composite terrain. For extremely heterogeneous terrain, such as urban areas, both pdfs for interferometric phase and magnitude fail and are extended. Based on these statistics, a completely automatic detection scheme with constant false-alarm rates (CFARs) for slow moving targets is proposed. All involved parameters required to determine the detection thresholds are estimated from the sample data. It is demonstrated, on the basis of experimental airborne SAR data, that this detector is capable of detecting slow moving vehicles within severe ground clutter.     

一种基于非参数密度估计和马尔可夫上下文的SAR图像分割算法

在研究传统的基于参数的合成孔径雷达(SAR)图像统计模型基础上,为了精确估计高分辨率SAR图像的统计分布,该文提出了一种结合基于核函数的非参数估计和马尔可夫上下文的SAR图像分割算法。该算法首先采用基于核函数的非参数方法估计SAR图像的统计分布,然后将此统计量作为图像分割的似然函数,利用马尔可夫上下文约束进行SAR图像分割。该文通过软件仿真对新算法和基于参数的统计模型的算法的效果进行了比较。研究发现,基于核函数的非参数估计方法仅仅依赖实际数据,在无法准确获取分布函数解析式的情况下往往具有更好的效果。实验证明,基于核函数的非参数估计方法对高分辨率SAR图像中较为复杂的场景如城区的提取取得了更为满意的结果。     

基于模型迭代匹配的单幅高分辨SAR图像遮挡建筑物高度估计方法

分析了高分辨SAR图像中受遮挡建筑物的特点,提出了一种针对遮挡情况建筑物的高度估计方法。该方法基于模型迭代匹配的思想,将一系列高度参数假设依所提构建的计算模型变换为特征信号并与SAR图像进行匹配,使似然函数达到最大的高度假设即为待估计的遮挡建筑物高度。基于仿真和实测SAR数据的实验结果表明,和已有方法相比,所提方法可以更准确地实现对部分被遮挡建筑物的高度估计。     

Parametric autofocus of SAR imaging - inherent accuracy limitations and realization

In synthetic aperture radar (SAR) imaging, low scene contrast may degrade the performance of most of the existing autofocus methods. In this paper, by dividing a slow-time signal into three isolated components, namely target, clutter, and noise, in SAR imaging, a novel parametric statistical model is proposed during the coherent processing interval. Based on the model, Cramer-Rao bounds (CRBs) of the estimation of unknown parameters are derived. It is shown that the CRBs of the target parameter estimation strongly depend on the background, i.e., clutter and noise, and the CRBs of the background parameter estimation may be obtained regardless of the target component. Motivated from this result and using the estimated background parameters, a novel effective parametric autofocus method is developed, which is applicable to any scene contrast. In addition, a preprojection is also introduced to simplify the subsequent parameter estimation. Finally, the proposed model and the novel method are illustrated by some real SAR data.     

一种基于SAR稀疏采样数据的动目标运动参数估计方法

该文针对地面动目标运动参数估计问题进行研究,提出一种利用单天线合成孔径雷达(SAR)稀疏采样数据的动目标2维速度估计方法。首先以目标2维速度为参数构建一个等效参数化模型将动目标回波数据转化为小斜视回波数据,然后利用改进的迭代阈值算法实现不同参数条件下的动目标2维成像,最后以成像结果的图像熵值为优化准则对初始模型参数进行搜索,从而获得准确的动目标运动参数。该方法以稀疏采样数据为输入,可以减少所需数据量,并且能够有效避免多普勒模糊问题,在较低信杂比条件下仍然能够准确估计出目标运动参数。仿真实验结果验证了所提动目标参数估计方法的有效性。     

The Rician inverse Gaussian distribution: a new model for non-Rayleigh signal amplitude statistics.

In this paper, we introduce a new statistical distribution for modeling non-Rayleigh amplitude statistics, which we have called the Rician inverse Gaussian (RiIG) distribution. It is a mixture of the Rice distribution and the inverse Gaussian distribution. The probability density function (pdf) is given in closed form as a function of three parameters. This makes the pdf very flexible in the sense that it may be fitted to a variety of shapes, ranging from the Rayleigh-shaped pdf to a noncentral chi2-shaped pdf. The theoretical basis of the new model is quite thoroughly discussed, and we also give two iterative algorithms for estimating its parameters from data. Finally, we include some modeling examples, where we have tested the ability of the distribution to represent locale amplitude histograms of linear medical ultrasound data and single-look synthetic aperture radar data. We compare the goodness of fit of the RiIG model with that of the K model, and, in most cases, the new model turns out as a better statistical model for the data. We also include a series of log-likelihood tests to evaluate the predictive performance of the proposed model.     

A new statistical model for Markovian classification of urban areas in high-resolution SAR images

We propose a classification method suitable for high-resolution synthetic aperture radar (SAR) images over urban areas. When processing SAR images, there is a strong need for statistical models of scattering to take into account multiplicative noise and high dynamics. For instance, the classification process needs to be based on the use of statistics. Our main contribution is the choice of an accurate model for high-resolution SAR images over urban areas and its use in a Markovian classification algorithm. Clutter in SAR images becomes non-Gaussian when the resolution is high or when the area is man-made. Many models have been proposed to fit with non-Gaussian scattering statistics (K, Weibull, Log-normal, Nakagami-Rice, etc.), but none of them is flexible enough to model all kinds of surfaces in our context. As a consequence, we use a mathematical model that relies on the Fisher distribution and the log-moment estimation and which is relevant for one-look data. This estimation method is based on the second-kind statistics, which are detailed in the paper. We also prove its accuracy for urban areas at high resolution. The quality of the classification that is obtained by mixing this model and a Markovian segmentation is high and enables us to distinguish between ground, buildings, and vegetation.     

Multiresolution MAP despeckling of SAR images based on locally adaptive generalized Gaussian pdf modeling.

In this paper, a new despeckling method based on undecimated wavelet decomposition and maximum a posteriori MIAP) estimation is proposed. Such a method relies on the assumption that the probability density function (pdf) of each wavelet coefficient is generalized Gaussian (GG). The major novelty of the proposed approach is that the parameters of the GG pdf are taken to be space-varying within each wavelet frame. Thus, they may be adjusted to spatial image context, not only to scale and orientation. Since the MAP equation to be solved is a function of the parameters of the assumed pdf model, the variance and shape factor of the GG function are derived from the theoretical moments, which depend on the moments and joint moments of the observed noisy signal and on the statistics of speckle. The solution of the MAP equation yields the MAP estimate of the wavelet coefficients of the noise-free image. The restored SAR image is synthesized from such coefficients. Experimental results, carried out on both synthetic speckled images and true SAR images, demonstrate that MAP filtering can be successfully applied to SAR images represented in the shift-invariant wavelet domain, without resorting to a logarithmic transformation.     

A spatially selective approach to Doppler estimation for frame-based satellite SAR processing

When Doppler centroid estimators are applied to satellite synthetic aperture radar (SAR) data, biased estimates are often obtained because of anomalies in the received data. Typical anomalies include areas of low SNR, strong discrete targets, and radiometric discontinuities. In this paper, a new method of Doppler centroid estimation is presented that takes advantage of principles such as spatial diversity, estimator quality checks, geometric models, and the fitting of a "global" estimate over a wide area of a SAR scene. In the proposed scheme, Doppler estimates are made over small blocks of data covering a whole frame, so that all parts of the scene are potentially represented. The quality of each block estimate is examined using data statistics or estimator quality measures. Poor estimates are rejected, and the remaining estimates are used to fit a surface model of the Doppler centroid versus the range and azimuth extent of the scene. A physical model that relates the satellite's orbit, attitude, and beam-pointing-direction to the Doppler centroid is used to get realistic surface fits and to reduce the complexity (dimensionality) of the estimation problem. The method is tested with RADARSAT-1 and Shuttle Radar Topography Mission X-band SAR (SRTM/X-SAR) spaceborne data and is found to work well with scenes that do have radiometric anomalies, and in scenes where attitude adjustments cause the Doppler to change rapidly.     

烟花算法在SAR图像属性散射中心参数估计中的应用

针对合成孔径雷达（SAR）属性散射中心估计问题,提出基于烟花算法的方法。首先,在图像域对SAR图像中高能量区域进行分割解耦,获得单个独立散射中心在图像域的表现形式。在此基础上,以属性散射中心参数化模型为基础,构建优化问题,对分离出来的单个散射中心进行最优参数的搜索。在此阶段,引入烟花算法进行参数寻优。该算法具有强大的全局和局部搜索能力,在保证优化精度的条件下避免陷入局部最优,从而保证散射中心参数估计的可靠性。在原始图像中剔除求解后的单个散射中心,对残余图像进行高能量区域分割,序惯估计下一个散射中心的属性参数。最终,获取输入SAR图像上所有散射中心的参数集。实验中,首先基于MSTAR数据集中的SAR图像进行参数估计验证,通过参数估计结果与原始图像的对比以及基于估计参数集对原始图像进行重构,反映了提出算法的有效性。此外,实验还基于估计得到的属性参数进行SAR目标识别算法验证,通过与其他参数估计算法在相同条件下进行识别性能的对比,进一步体现了提出方法在属性散射中心参数估计上的性能优势。     

基于可变参数化几何模型的SAR图像飞机目标特征提取方法

基于飞机目标的轮廓特点和成像特性,提出了一种基于可变参数化几何模型的合成孔径雷达（SAR）图像飞机目标特征提取方法。首先,利用飞机目标的先验知识构造一个描述飞机目标外形轮廓的参数化模型;然后,对于输入的实测飞机目标切片图像,构建目标函数来度量模型与实测图像中目标区域的拟合程度,通过遗传算法求解最优参数;最后,在最优参数模型的基础上计算目标的几何特征。基于仿真和实测数据的实验结果验证了该方法的有效性。     

Statistical Classification of Buried Unexploded Ordnance Using Nonparametric Prior Models

We used kernel density estimation (KDE) methods to build a priori probability density functions (pdfs) for the vector of features that are used to classify unexploded ordnance items given electromagnetic-induction sensor data. This a priori information is then used to develop a new suite of estimation and classification algorithms. As opposed to the commonly used maximum-likelihood parameter estimation methods, here we employ a maximum a posteriori (MAP) estimation algorithm that makes use of KDE-generated pdfs. Similarly, we use KDE priors to develop a suite of classification schemes operating in both "feature" space as well as ldquosignal/datardquo space. In terms of feature-based methods, we construct a support vector machine classifier and its extension to support M-ary classification. The KDE pdfs are also used to synthesize a MAP feature-based classifier. To address the numerical challenges associated with the optimal data-space Bayesian classifier, we have used several approximation techniques, including Laplacian approximation and generalized likelihood ratio tests employing the priors. Using both simulations and real field data, we observe a significant improvement in classification performance due to the use of the KDE-based prior models.     

Bayesian inference of models and hyperparameters for robust optical-flow estimation

Selecting optimal models and hyperparameters is crucial for accurate optical-flow estimation. This paper provides a solution to the problem in a generic Bayesian framework. The method is based on a conditional model linking the image intensity function, the unknown velocity field, hyperparameters, and the prior and likelihood motion models. Inference is performed on each of the three levels of this so-defined hierarchical model by maximization of marginalized a posteriori probability distribution functions. In particular, the first level is used to achieve motion estimation in a classical a posteriori scheme. By marginalizing out the motion variable, the second level enables to infer regularization coefficients and hyperparameters of non-Gaussian M-estimators commonly used in robust statistics. The last level of the hierarchy is used for selection of the likelihood and prior motion models conditioned to the image data. The method is evaluated on image sequences of fluid flows and from the "Middlebury" database. Experiments prove that applying the proposed inference strategy yields better results than manually tuning smoothing parameters or discontinuity preserving cost functions of the state-of-the-art methods.     

合成孔径雷达参数化成像技术进展

传统合成孔径雷达(SAR)成像可视为点目标散射模型约束下数据空间到图像空间的映射.然而,真实目标多为延展目标,与传统线性成像处理中的点目标散射模型存在失配,会导致SAR图像表征失真.常见的现象是使延展目标多呈现为孤立强点,阻碍了基于SAR图像的目标辨识等应用.SAR参数化成像技术是为解决上述模型失配问题而诞生的一种非线...     

Direct reconstruction of kinetic parameter images from dynamic PET data

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.     

System-independent threshold and BER estimation in optical communications using the extended generalized gamma distribution

Two important tasks with respect to the optimized configuration of an optical communications system are those of the performance evaluation and the receiver decision threshold estimation. In this paper, a new training-based BER and threshold estimation technique is proposed relaxing the assumption of Gaussian distributed received signals. The proposed method is similar in philosophy to the Gaussian Approximation one, and is system-independent and simulation-based. This means that the probability density function (pdf) of the sampled electrical current is estimated based on training data provided via simulations without any assumptions on the specific configuration of the communications system under consideration. The novelty of the paper is that for the first time a combination of a generalized form of the gamma distribution together with the noncentral chi-square distribution have been used for the modeling of the pdfs of the spaces and the marks, respectively.     

一种差分SAR层析高分辨成像方法

城区建筑的4维成像是差分SAR层析的重要应用领域之一。此种应用背景下,如何利用空间-时间2维平面内稀疏分布的观测数据,在保持方位向-距离向分辨率的同时实现高程向-形变速率向的高分辨成像是差分SAR层析面临的难点问题。在确定性点目标模型下,基于松弛(RELAX)算法,该文提出了一种适用于城区建筑目标的差分SAR层析高分辨成像方法。与统计模型下的空间谱估计方法相比,该方法无需多视处理,能够保持方位向-距离向分辨率。与奇异值分解方法相比,该方法具有更优的高程向-形变速率向分辨能力。在仿真实验和Envisat-ASAR实测数据处理中,该方法的有效性得到了验证。