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.     

基于双树复数小波变换的SAR图像噪声抑制方法

利用双树复数小波变换(Dual Tree Complex Wavelet Transform,DTCWT)的近似平移不变性和多方向选择性,提出了一种基于DTCWT变换的SAR图像噪声抑制方法。首先对无噪声污染图像的复数小波系数的统计概率分布进行建模;然后利用此先验概率模型,采用最大后验概率方法从含噪小波系数中估计出无噪声污染的小波系数;最后经重构得到滤波后的图像。实验结果表明,此方法优于其他一些相干斑抑制方法。     

Speckle Suppression in SAR Images Using the 2-D GARCH Model

A novel Bayesian-based speckle suppression method for Synthetic Aperture Radar ( SAR) images is presented that preserves the structural features and textural information of the scene. First, the logarithmic transform of the original image is analyzed into the multiscale wavelet domain. We show that the wavelet coefficients of SAR images have significantly non-Gaussian statistics that are best described by the 2-D GARCH model. By using the 2-D GARCH model on the wavelet coefficients, we are capable of taking into account important characteristics of wavelet coefficients, such as heavy tailed marginal distribution and the dependencies between the coefficients. Furthermore, we use a maximum a posteriori (MAP) estimator for estimating the clean image wavelet coefficients. Finally, we compare our proposed method with various speckle suppression methods applied on synthetic and actual SAR images and we verify the performance improvement in utilizing the new strategy.     

A study of relative phase in complex wavelet domain: Property,statistics and applications in texture image retrieval and segmentation

In this paper, we develop a new approach which exploits the probabilistic properties from the phase information of 2-D complex wavelet coefficients for image modeling. Instead of directly using phases of complex wavelet coefficients, we demonstrate why relative phases should be used. The definition, properties and statistics of relative phases of complex coefficients are studied in detail. We proposed von Mises and wrapped Cauchy for the probability density function (pdf) of relative phases in the complex wavelet domain. The maximum-likelihood method is used to estimate two parameters of von Mises and wrapped Cauchy. We demonstrate that the von Mises and wrapped Cauchy fit well with real data obtained from various real images including texture images as well as standard images. The von Mises and wrapped Cauchy models are compared, and the simulation results show that the wrapped Cauchy fits well with the peaky and heavy-tailed pdf of relative phases and the von Mises fits well with the pdf which is in Gaussian shape. For most of the test images, the wrapped Cauchy model is more accurate than the von Mises model, when images are decomposed by different complex wavelet transforms including dual-tree complex wavelet (DTCWT), pyramidal dual-tree directional filter bank (PDTDFB) and uniform discrete curvelet transform (UDCT). Moreover, the relative phase is applied to obtain new features for texture image retrieval and segmentation applications. Instead of using only real or magnitude coefficients, the new approach uses a feature in which phase information is incorporated, yielding a higher accuracy in texture image retrieval as well as in segmentation. The relative phase information which is complementary to the magnitude is a promising approach in image processing.     

Bayesian Wavelet-Based Image Denoising Using the Gauss–Hermite Expansion

The probability density functions (PDFs) of the wavelet coefficients play a key role in many wavelet-based image processing algorithms, such as denoising. The conventional PDFs usually have a limited number of parameters that are calculated from the first few moments only. Consequently, such PDFs cannot be made to fit very well with the empirical PDF of the wavelet coefficients of an image. As a result, the shrinkage function utilizing any of these density functions provides a substandard denoising performance. In order for the probabilistic model of the image wavelet coefficients to be able to incorporate an appropriate number of parameters that are dependent on the higher order moments, a PDF using a series expansion in terms of the Hermite polynomials that are orthogonal with respect to the standard Gaussian weight function, is introduced. A modification in the series function is introduced so that only a finite number of terms can be used to model the image wavelet coefficients, ensuring at the same time the resulting PDF to be non-negative. It is shown that the proposed PDF matches the empirical one better than some of the standard ones, such as the generalized Gaussian or Bessel K-form PDF. A Bayesian image denoising technique is then proposed, wherein the new PDF is exploited to statistically model the subband as well as the local neighboring image wavelet coefficients. Experimental results on several test images demonstrate that the proposed denoising method, both in the subband-adaptive and locally adaptive conditions, provides a performance better than that of most of the methods that use PDFs with limited number of parameters.      

Bayesian wavelet-based image denoising using the gauss-hermite expansion

The probability density functions (PDFs) of the wavelet coefficients play a key role in many wavelet-based image processing algorithms, such as denoising. The conventional PDFs usually have a limited number of parameters that are calculated from the first few moments only. Consequently, such PDFs cannot be made to fit very well with the empirical PDF of the wavelet coefficients of an image. As a result, the shrinkage function utilizing any of these density functions provides a substandard denoising performance. In order for the probabilistic model of the image wavelet coefficients to be able to incorporate an appropriate number of parameters that are dependent on the higher order moments, a PDF using a series expansion in terms of the Hermite polynomials that are orthogonal with respect to the standard Gaussian weight function, is introduced. A modification in the series function is introduced so that only a finite number of terms can be used to model the image wavelet coefficients, ensuring at the same time the resulting PDF to be non-negative. It is shown that the proposed PDF matches the empirical one better than some of the standard ones, such as the generalized Gaussian or Bessel K-form PDF. A Bayesian image denoising technique is then proposed, wherein the new PDF is exploited to statistically model the subband as well as the local neighboring image wavelet coefficients. Experimental results on several test images demonstrate that the proposed denoising method, both in the subband-adaptive and locally adaptive conditions, provides a performance better than that of most of the methods that use PDFs with limited number of parameters.     

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。      

基于小波域统计建模及显著性修正的SAR图像相干斑抑制

该文提出了一种基于小波域统计建模与小波系数显著性修正相结合的斑点噪声滤波方法。这种方法首先通过对数变换将乘性噪声模型转化为加性噪声模型,对对数变换后的图像进行小波变换并对小波域的高频子带系数用混合高斯模型与隐马尔可夫树模型进行建模,并采用EM算法来估计模型参数。在模型参数估计的基础上;利用贝叶斯最小均方误差准则来估计干净的小波系数。在此基础上引入基于显著性准则的小波系数修正,最后通过小波逆变换与指数变换获得抑制斑点噪声后的图像。用真实SAR图像实验表明,该文提出的方法能够有效地抑制斑点噪声,同时能够很好地保存边缘细节结构与强散射中心。     

基于小波包算法的压缩传感SAR 成像方法

压缩传感SAR 成像能够大量减小采样率和数据量,但只对稀疏场景有效。该文提出基于小波包训练稀疏表示基的压缩传感SAR 成像方法。该方法通过对同类型的SAR 图像进行小波包训练,在小波包库中选择能够稀疏表示该类SAR 场景的稀疏表示基,并通过求解l1 范数最小化问题重构SAR 场景反射系数。文中提出的方法在严重降采样下仍能够实现无模糊的SAR 成像,仿真数据成像结果表明该文方法具有较好的效果。      

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。     

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.     

用小波变换抑制SAR图像中的斑点噪声

抑制合成孔径雷达图像中的斑点噪声一直是处理图像并得到准确图像信息的难点，提出了一种基于小波变换抑制合成孔径雷达（SAR）图像中的斑点噪声的方法，对原有的小波变换方法作了改进，能更好地保留图像的边缘信息，并能简化计算量。在仿真实验中使用了合成的模拟图像和真实的合成孔径雷图像，并与以往的小波去噪滤波方法以及一些经典的斑点噪声滤波方法（包括中值滤波，Lee滤波，Frost滤波）进行比较，在综合考虑了滤波算法在均匀区域对斑点噪声的抑制能力以及保留边缘信息能力的情况下，提出的算法有更好的效果。     

A New Statistical Detector for DWT-Based Additive Image Watermarking Using the Gauss–Hermite Expansion

Traditional statistical detectors of the discrete wavelet transform (DWT)-based image watermarking use probability density functions (PDFs) that show inadequate matching with the empirical PDF of image coefficients in view of the fact that they use a fixed number of parameters. Hence, the decision values obtained from the estimated thresholds of these detectors provide substandard detection performance. In this paper, a new detector is proposed for the DWT-based additive image watermarking, wherein a PDF based on the Gauss–Hermite expansion is used, in view of the fact that this PDF provides a better statistical match to the empirical PDF by utilizing an appropriate number of parameters estimated from higher-order moments of the image coefficients. The decision threshold and the receiver operating characteristics are derived for the proposed detector. Experimental results on test images demonstrate that the proposed watermark detector performs better than other standard detectors such as the Gaussian and generalized Gaussian (GG), in terms of the probabilities of detection and false alarm as well as the efficacy. It is also shown that detection performance of the proposed detector is more robust than the competitive GG detector in the case of compression, additive white Gaussian noise, filtering, or geometric attack.      

Supervised classification of K-distributed SAR images of naturaltargets and probability of error estimation

A radiometric and textural classification method for the single-channel synthetic aperture radar (SAR) image is proposed, which explicitly takes into account the probability density function (pdf) of the underlying cross section for K-distributed images. This method makes extensive use of adaptive preprocessing methods (e.g. Gamma-Gamma MAP speckle filtering), in order to ensure good classification accuracy as well as fair preservation of the spatial resolution of the final result. Error rates can be estimated during the training step, allowing one to select only relevant reflectivity classes and to save computation time in trials. The classification method is based on a maximum likelihood (ML) segmentation of the filtered image. Finally, a texture criterion is introduced to improve the accuracy of the classification result     

基于局部特征差异的异源图像融合算法

针对现有异源图像融合多以光学 图像为主、合成孔径雷达 (SAR)图 为辅和 光学图像 极易受 传播媒介 干扰 且 不 能同时保留纹理细节与颜色信息 等 问题, 提出一种新的基于局部特征差异的异源图像融合算法。 首先通 过 自适应分割 将 SAR 图像划分为规则特征区和不规则特征区两个区域;然后 进行 平移不变 离散 小波变换(SIDWT), 再根据 局部特征差异 性 设计 融合规 则,将 SAR 图像与全色遥感(PAN)图像的 小波系数 进行融合 , 以期保留图像的特征 信息与色彩信息 ;最后 通过 信息量 、 清晰度等 客观 评价指标 对 融合结果进行评价与分析 。 仿真实验 证明 了算法的有效性。     

基于稀疏表示和道路辅助的单幅SAR图像运动目标检测方法

本文提出一种利用单幅SAR(Synthetic Aperture Radar)图像实现运动目标检测的方法.首先提出一种基于压缩感知的SAR图像道路检测算法:根据SAR图像中道路的特点,使用模糊C均值方法将图像进行模糊分类,获得大致的道路区域,然后利用Hough变换域的稀疏性,用压缩感知精确定位图像中的道路信息.其次利用图像稀疏表示的方法对运动目标进行检测:不同速度运动目标的散焦量和距离单元跨越不同,由此生成样本图像,继而构造超完备字典.将待测图像分块,并计算子图像在字典下的稀疏系数,检测并匹配出运动目标的速度参数.最后,结合已检测出的道路辅助信息,消除多普勒模糊影响,剔除虚假的运动目标,并对运动目标速度参数进行校正.实验结果证明了所提方法的有效性.     

Locally adaptive wavelet domain Bayesian processor for denoising medical ultrasound images using Speckle modelling based on Rayleigh distribution

The authors present a statistical approach to speckle reduction in medical ultrasound B-scan images based on maximum a posteriori (MAP) estimation in the wavelet domain. In this framework, a new class of statistical model for speckle noise is proposed to obtain a simple and tractable solution in a closed analytical form. The proposed method uses the Rayleigh distribution for speckle noise and a Gaussian distribution for modelling the statistics of wavelet coefficients in a logarithmically transformed ultrasound image. The method combines the MAP estimation with the assumption that speckle is spatially correlated within a small window and designs a locally adaptive Bayesian processor whose parameters are computed from the neighboring coefficients. Further, the locally adaptive estimator is extended to the redundant wavelet representation, which yields better results than the decimated wavelet transform. The experimental results show that the proposed method clearly outperforms the state-of-the-art medical image denoising algorithm of Pizurica et al., spatially adaptive single-resolution methods and band-adaptive multi-scale soft-thresholding techniques in terms of quantitative performance as well as in terms of visual quality of the images. The main advantage of the new method over the existing techniques is that it suppresses speckle noise well, while retaining the structure of the image, particularly the thin bright streaks, which tend to occur along boundaries between tissue layers.     

基于局部平移瑞利分布模型的SAR图像相干斑抑制

该文提出了一种基于平稳小波域统计模型的SAR图像抑斑算法。首先对SAR图像应用非对数加性模型,接着针对该模型中的噪声在空域提出一种统计分布模型局部平移瑞利分布模型。最后基于该分布,在平稳小波域应用最大后验(MAP)方法获得真实信号平稳小波系数的解。实验表明,该文提出的局部平移瑞利分布模型是有效的,同时也表明该文给出的一种基于此分布模型的抑斑算法有很强的鲁棒性,抑斑性能优于许多现存的算法。     

Wavelet thresholding of multivalued images

In this paper, a denoising technique for multivalued images exploiting interband correlations is proposed. A redundant wavelet transform is applied and denoising is applied by thresholding wavelet coefficients. Specific functions of the wavelet coefficients are defined that exploit interscale and/or interband correlation of the signal. Three functions are studied: the square of the wavelet coefficients, products of coefficients at adjacent scales, and products of coefficients from different bands. For these functions, the signal and noise probability density functions (pdf) become more separated. The high signal correlation between bands is exploited by summing these products over all bands, in this way separating noise and signal pdfs even more. The noise pdf of the proposed quantities is derived analytically and from this, a wavelet threshold is derived. The technique is demonstrated to outperform single band wavelet thresholding on multispectral remote sensing images and on multimodal MRI images.     

基于广义高斯最大似然估计的小波域类LMMSE滤波算法

基于小波系数服从广义高斯分布,该文采用最大似然(ML)准则估计普通图像在子带上的系数方差。该文提出的估计子是一个子带自适应因子和一个次幂均值的乘积。与最近提出的SI-AdaptShr,LAWMAP和其它一些算法相比,所提出的算法取得了更好的去噪效果。进一步,一种简化的算法产生用于去除SAR图像的斑点噪声。这种新算法可以大大减少运算量,对大尺度的SAR图像后处理有帮助。