SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling

Synthetic aperture radar (SAR) images are inherently affected by multiplicative speckle noise, which is due to the coherent nature of the scattering phenomenon. This paper proposes a novel Bayesian-based algorithm within the framework of wavelet analysis, which reduces speckle in SAR images while preserving the structural features and textural information of the scene. First, we show that the subband decompositions of logarithmically transformed SAR images are accurately modeled by alpha-stable distributions, a family of heavy-tailed densities. Consequently, we exploit this a priori information by designing a maximum a posteriori (MAP) estimator. We use the alpha-stable model to develop a blind speckle-suppression processor that performs a nonlinear operation on the data and we relate this nonlinearity to the degree of non-Gaussianity of the data. Finally, we compare our proposed method to current state-of-the-art soft thresholding techniques applied on real SAR imagery and we quantify the achieved performance improvement.     

Modeling SAR images with a generalization of the Rayleigh distribution

Synthetic aperture radar (SAR) imagery has found important applications due to its clear advantages over optical satellite imagery one of them being able to operate in various weather conditions. However, due to the physics of the radar imaging process, SAR images contain unwanted artifacts in the form of a granular look which is called speckle. The assumptions of the classical SAR image generation model lead to a Rayleigh distribution model for the histogram of the SAR image. However, some experimental data such as images of urban areas show impulsive characteristics that correspond to underlying heavy-tailed distributions, which are clearly non-Rayleigh. Some alternative distributions have been suggested such as the Weibull, log-normal, and the k-distribution which had success in varying degrees depending on the application. Recently, an alternative model namely the alpha-stable distribution has been suggested for modeling radar clutter. In this paper, we show that the amplitude distribution of the complex wave, the real and the imaginery components of which are assumed to be distributed by the alpha-stable distribution, is a generalization of the Rayleigh distribution. We demonstrate that the amplitude distribution is a mixture of Rayleighs as is the k-distribution in accordance with earlier work on modeling SAR images which showed that almost all successful SAR image models could be expressed as mixtures of Rayleighs. We also present parameter estimation techniques based on negative order moments for the new model. Finally, we test the performance of the model on urban images and compare with other models such as Rayleigh, Weibull, and the k-distribution.     

基于ROEWA和Gabor滤波的SAR图像边缘提取

针对合成孔径雷达(SAR)图像特有的乘性噪声和非恒虚警统计特性很难正确提取目标边缘的问题,提出了在指数加权均值比(ROEWA)算子基础上寻找自适应的最佳局域Gabor滤波器进行目标边缘提取的方法。利用Gabor滤波器具有的多方向特性确定边缘方向,然后用最大似然估计纠正错误边缘方向,重新结合视觉细胞倍频程计算出Gabor函数的最佳局域滤波参数,提取出SAR图像的正确边缘。实验表明,该方法取得很好边缘提取效果,并且后期分割出的目标更符合实际目标形态,具有较强的通用性。     

An Improved SAR Image Denoising Metho d Based on Bo otstrap Statistical Estimation with ICA Basis

A new method for Synthetic aperture radar (SAR) image denoising is proposed. The prior information of speckle statistical model can be exploited to judge its distribution. The basis of SAR image can be estimated by Independent component analysis (ICA), and these bases can be divided into two different subspaces (noise and real signal subspaces) through a linear classifier. Then para-metric Bootstrap estimates the parameters of speckle sta-tistical model on the noise signal subspace, and the non-parametric Bootstrap can estimate the distribution of real image on the real signal subspace. According to different results estimated by Bootstrap, corresponding Maximum a posterior probability (MAP) filter will be selected for im-age denoising, using the noise model’s parameter for adap-tive filtering. Experiments show that the image processed by this new method can achieve a better visual perception and ob jective evaluation results.     

Restoration of speckle noise corrupted SAR images using regularization by denoising

Speckle noise removal is a well-established problem in synthetic aperture radar (SAR) image processing. Among different methods focused on the reconstruction of SAR images, variational models have achieved state-of-the-art performance. In this paper, a Rayleigh based speckle reduction algorithm is developed using the variational framework. The forward model is combined with recently proposed regularization by denoising (RED) prior. However, RED has been proposed in literature for the additive noise model. Multiplicative noise in SAR images prevents the direct application of RED to variational models. Hence, logarithm transformation is applied to change the multiplicative noise model to additive model, and the forward model from Rayleigh to Fisher–Tippett distribution. The resulting optimization problem is solved using the alternating direction method of multipliers. Further, the proof of the convergence analysis is carried out for the above framework. Simulations convey that the proposed method has better despeckling performance compared to that of state-of-the-art methods.     

SAR image despeckling using heavy-tailed Burr distribution

Multiplicative speckle noise diminishes the radiometric resolution of the synthetic aperture radar (SAR) images and all the coherent images. Speckle removal adds an extra value to an automated SAR image interpretation and analysis. In this paper, dual-tree complex wavelet-transform-based Bayesian method is proposed for despeckling the SAR images. In each subband, the reflectance and noise of the logarithmically transformed wavelet coefficients are modeled using heavy-tailed Burr and zero-mean Gaussian distributions. The closed-form expression for the shape parameter of Burr distribution is derived by employing the Mellin transform. The resultant complex-free quadratic maximum a posteriori solution with suitable shrinkage function yields despeckled SAR images. Extensive experiments are carried out using real SAR images as well as simulated images. The proposed method performs well in terms of equivalent number of looks with 3.5751 dB improvement in homogeneous region1 of Pipe river SAR image, edge preservation with 0.6158 improvement, peak signal to noise ratio of 51.3305 dB, and mean structural similarity index measure of 0.9397 at 0.05 noise variance for synthetically speckled image in comparison to the existing methods and takes averagely 2.3461 times less computing time. The proposed method provides a computationally efficient better speckle reduction in homogeneous regions while still preserving the edge.     

冗余轮廓波变换的构造及其在SAR图像降斑中的应用

构造了由非抽样塔式分解和方向滤波器组实现的冗余轮廓波变换。文中利用McClellan变换设计非抽样塔式分解中满足精确重构条件的圆对称滤波器组。利用冗余轮廓波变换系数的自适应局部统计模型及最大后验概率法对SAR图像进行降斑处理,并与基于平稳小波和轮廓波变换的降斑算法进行比较。结果表明,提出的算法能有效地去除散斑噪声,并且具有更强的边缘保持能力。     

基于上下文和隐类属的小波域马尔可夫随机场SAR图像分割

该文针对合成孔径雷达(Synthetic Aperture Radar, SAR)图像含有大量的乘性斑点噪声的特点,提出了一种小波域隐类属的马尔可夫随机场(Markov Random Field, MRF)图像分割算法来抑制噪声的影响。考虑到小波的聚集性和持续性,该算法重新构造了待分图像小波域模型以类属为隐状态的混合长拖尾模型,将隐类属的马尔可夫随机场推广到小波域上,并用改进的上下文模型估计尺度间转移概率,最后推导出了新的最大后验(Maximum A Posteriori, MAP)分割公式。仿真结果证明,该算法具有鲁棒性能够有效地抑制噪声对图像的影响,得到准确的分割结果。     

基于统计理论的SAR图像斑点噪声滤波算法分析

合成孔径雷达图像固有的斑点噪声严重降低了图像的可解译程度,影响了后续目标检测、分类和识别等应用。文中通过对基于统计理论的SAR图像斑点噪声滤波方法进行比较分析,得出单个滤波器难以从去噪和边缘保持方面均达到最佳效果的结论。     

Statistical properties of logarithmically transformed speckle

In synthetic aperture radar (SAR) image processing and analysis, the logarithmic transform is often employed to convert the multiplicative speckle model to an additive noise model. However, this nonlinear operation totally changes the statistics of SAR images. In this communication, we first review the statistical properties of speckle noise in both the intensity and the amplitude formats. Then, we derive the probability density functions, the mean values, and the variances to characterize the log-transformed speckle. Finally we discuss the problems introduced by the logarithmic transform on statistical analysis of SAR images. The statistical models developed in this communication will facilitate subsequent SAR image processing tasks based on the additive noise model     

SAR Image Regularization With Fast Approximate Discrete Minimization

Synthetic aperture radar (SAR) images, like other coherent imaging modalities, suffer from speckle noise. The presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms. Numerous approaches have been proposed to filter speckle noise. Markov random field (MRF) modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image. In this context, total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges. Speckle noise follows heavy-tailed distributions, and the MRF formulation leads to a minimization problem involving nonconvex log-likelihood terms. Such a minimization can be performed efficiently by computing minimum cuts on weighted graphs. Due to memory constraints, exact minimization, although theoretically possible, is not achievable on large images required by remote sensing applications. The computational burden of the state-of-the-art algorithm for approximate minimization (namely the alpha -expansion) is too heavy specially when considering joint regularization of several images. We show that a satisfying solution can be reached, in few iterations, by performing a graph-cut-based combinatorial exploration of large trial moves. This algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area SAR images.     

基于斑点方差估计的非下采样Contourlet域SAR图像去噪

 合成孔径雷达(SAR)图像固有的相干斑噪声严重影响图像质量,使得SAR图像的自动解译十分困难.本文联合SAR图像的统计特性和非下采样Contourlet对SAR图像细节信息的良好刻画能力,提出一种新的非下采样Contourlet域SAR图像去噪算法,通过估计到的各个高频方向子带的斑点噪声方差和变换系数模值的局部均值,对非下采样Contourlet变换系数进行判定,保留信号系数,抑制斑点噪声系数,实现SAR图像去噪.仿真实验结果表明,本文方法在斑点抑制的同时可以有效保持细节信息.     

A convex variational method for super resolution of SAR image with speckle noise

Super resolution (SR) is an attractive issue in image processing. In the synthetic aperture radar (SAR) image, speckle noise is a crucial problem that is multiplicative. Therefore, numerous custom SR methods considering additive Gaussian noise cannot respond to this image degradation model. The main contribution of this paper is to propose a novel variational convex optimization model for the single SAR image SR reconstruction with speckle noise that is one of the first works in this field. Employing maximum a posteriori (MAP) estimator and proposing an effective regularization based on combination of sparse representation, total variation (TV) and a novel feature space based soft projection tool to use merits of them is the main idea. To solve the proposed model, the split Bregman algorithm is employed efficiently. Experimental results for the multiple synthetic and realistic SAR images show the effectiveness of proposed method in terms of both fidelity and visual perception.     

Speckle filtering of SAR images based on adaptive windowing

Speckle noise usually occurs in synthetic aperture radar (SAR) images owing to coherent processing of SAR data. The most well-known image domain speckle filters are the adaptive filters using local statistics such as the mean and standard deviation. The local statistics filters adapt the filter coefficients based on data within a fixed running window. In these schemes, depending on the window size, there exists trade-off between the extent of speckle noise suppression and the capability of preserving fine details. The authors propose a new adaptive windowing algorithm for speckle noise suppression which solves the problem of window size associated with the local statistics adaptive filters. In the algorithm, the window size is automatically adjusted depending on regional characteristics to suppress speckle noise as much as possible while preserving fine details. Speckle noise suppression gets stronger in homogeneous regions as the window size increases succeedingly. In fine detail regions, by reducing the window size successively, edges and textures are preserved. The fixed-window filtering schemes and the proposed one are applied to both a simulated SAR image and an ERS-1 SAR image to demonstrate the excellent performance of the proposed adaptive windowing algorithm for speckle noise     

基于几何模型的SAR图像斑点噪声的抑制

斑点噪声的抑制一直是合成孔径雷达(SAR)图像处理的重要研究课题。本文利用几何模型对合成孔径雷达图像进行滤波。通过对几何模型除噪性能进行分析,提出了一个数值计算的改进格式。新的迭代格式能较好地保留图像的边缘、尖点和细节信息。最后对合成孔径雷达图像进行去噪实验,与小波阈值除噪、Lee滤波进行比较具有更好的滤波效果。     

Two-dimensional adaptive block Kalman filtering of SAR imagery

A method for removing speckle from synthetic aperture radar (SAR) imagery by using 2-D adaptive block Kalman filtering is introduced. The image process is represented by an autoregressive model with a nonsymmetric half-plane (NSHP) region of support. New 2-D Kalman filtering equations are derived which taken into account not only the effect of speckles as multiplicative noise but also the effects of the additive receiver thermal noise and the blur. This method assumes local stationarity within a processing window, whereas the image can be assumed to be globally nonstationary. A recursive identification process using the stochastic Newton approach is also proposed which can be used on-line to estimate the filter parameters based upon the information within each new block of the image. Simulation results on several images are provided to indicate the effectiveness of the proposed method when used to remove the effects of speckle noise as well as those of the additive noise     

基于自相关函数建模的小波域SAR图像去斑方法

合成孔径雷达（SAR）图像的小波系数间存在重要的相关性．通过对这种相关性的精确建模可以改善图像的去斑效果。提出了一种新的基于自相关函数建模的小波域SAR图像去斑方法。首先对原始SAR图像进行对数变换．再用可控金字塔作多尺度和多方向分解．分别对图像和噪声系数的自相关函数精确建模．并在图像自相关函数中引入方向性解析式．再利用维纳滤波得到去噪后的小波对数图像,最后经指数变换得到去斑后的SAR图像。对合成图像和实际sAR图像的去斑实验表明,该方法较其他经典方法的去斑效果要好。     

基于复小波方向信息的SAR图像斑点噪声抑制

针对一般小波去噪方法在去除合成孔径雷达(Synthetic Aperture Radar-SAR)图像斑点噪声时不能有效保持图像边缘信息的问题,提出结合双密度双树复小波变换（Double-Density Dual Tree Complex Wavelet Transform –DD_DTCWT）方向信息进行边缘检测的SAR图像噪声抑制算法。本文对边缘检测指标进行改进,利用DD_DTCWT方向复小波系数的相对方差作为边缘检测指标,通过相对方差分布密度函数获取阈值处理的自适应门限,由此实现SAR图像的自适应滤波。实验结果表明,本文提出的边缘检测和主方向高频复系数提升方法可以有效保持并增强图像的边缘信息。与SRAD算法和基于DD_DTCWT的双变量收缩函数（Bivariate Shrinkage Function--BSF）算法相比较,本文算法具有更好的边缘保持能力。      

高分辨率星载SAR单视图像斑点噪声抑制实现方法

本文提出了实现高分辨率星载合成孔径雷达单视图像斑点噪声抑制的TDRGMAP方法.它以最大后验概率滤波器实现斑点平滑,以无偏修正使其适用于单视图像,结合边缘和线条检测,并加以点目标检测及保持,获得高空间分辨率和高辐射分辨率的SAR单视图像.本文详细阐述了TDRGMAP方法的机理和实现,最后利用仿真生成的星载SAR单视图像进行实验,证明了TDRGMAP方法的有效性.     

合成孔径雷达图像斑点噪声抑制与滤波

斑点噪声的存在,严重阻碍了合成孔径雷达（SAR）图像的应用。根据斑点噪声的形成机理,分析并比较了抑制SAR斑点噪声的传统滤波算法及统计滤波算法的原理,利用ERS-2的SAR图像数据比较了这几种算法对SAR图像斑点噪声的滤除效果,根据噪声滤波效果评价参数得出Gamma滤波抑制斑点噪声的综合性能最好。