A statistical and Wiener filtering algorithm based on the curvelet transform for SAR images

Synthetic aperture radar (SAR) images contain many kinds of noise. Speckle noise is multiplicative noise generated by the coherent imaging processes involved in SAR images and brings a great hindrance to the interpretation and application of SAR images, so it is considered the first major kind of noise in SAR images. SAR images also contain other incoherent additive noises generated by other factors, such as Gaussian noise, which are all considered the second major kind of noise. In order to reduce the impact of noise as much as possible, after an in-depth study of SAR imaging and noise-generating mechanism, curvelet transform principle, and Wiener filtering characteristic, a novel filtering method, here called the statistical and Wiener based on curvelet transform (SWCT) method is proposed. The SWCT algorithm processes two different kinds noise based on their properties. Specifically, it establishes a two-tiered filtering framework. For the first kind of noise, the algorithm uses the curvelet transform to decompose the SAR image and uses the statistical characteristics of the SAR image to generate an adaptive filtering threshold of the coefficients of decomposition to recover the original image. Then it filters every sub-band image at each decomposed scale and performs the inverse curvelet transform. The second kind of noise is directly filtered using the Wiener filter in the SWCT algorithm. Using the two-tiered filtering model and fully exploiting statistical characteristics, the SWCT algorithm not only reduces the amount of coherent speckle noise and incoherent noise effectively but also retains the edges and geometric details of the original SAR image. This is very good for target detection, classification, and recognition. Qualitative and quantitative tests were performed using simulated speckle noise, Gaussian noise, and real SAR images. The proposed SWCT algorithm was found to remove noise effectively and the performance of the algorithm was tested and compared to the mean filter, enhanced gamma-MAP (maximum a posterior probability) filter, wavelet transform filter, Wiener filter, and curvelet transform filter. Experiments carried out on real SAR images confirmed that the new method has a good filtering effect and can be used on different SAR images.     

Noise reduction in synthetic aperture radar images using fuzzy logic and genetic algorithm

Synthetic aperture radar (SAR) is a self-illuminating imaging technique; it produces high resolution images in all weather conditions, day and night. SAR images are widely accepted and used by many application scientists. However, the SAR images are corrupted with speckle noise. Speckle noises are caused by random interference of electromagnetic signals scattered by the object surface within one resolution element. The amount of noise and distribution of noise corrupting the image is unpredictable. Conventional noise filters are quantitative in nature; they are not well suited for uncertainty problems. Fuzzy logic is capable of handling uncertainty. In this work, noisy pixels in the images are identified by using fuzzy rules and filtered using fuzzy weighted mean, keeping the healthy pixels unchanged. The optimum value of parameters used in defining fuzzy membership function is determined by using genetic algorithm (GA). Reducing noise and simultaneously preserving image details are the two most desirable characteristics of noise filters. Peak signal-to-noise ratio (PSNR) and edge preserving factor (EPF) are used to evaluate the performance of the proposed fuzzy filter. SAR images affected by varying amounts of speckle noise are used to evaluate the performance. It was observed that the proposed filter suppresses noise and preserves image edges.

     

自适应加权镜像阈值层叠滤波器

与传统的阈值层叠滤波器相比,镜像阈值层叠滤波器不仅具有低通滤波的特性,还具有带通和高通的特性。但由于镜像阈值层叠滤波器比传统的阈值层叠滤波器的正布尔函数长度有显著增加,从而使计算量增加,为解决这一问题,提出了一种镜像自适应加权（MAW）算法。该方法充分考虑了镜像阈值分解的特点,并通过引入自适应领域加权误差准则建立了代价向量,在迭代过程中,对代价向量的层叠性进行快速约束,并判断其收敛性,最终获得了基于最优正布尔函数的自适应加权镜像阈值层叠滤波器（AWMSF）。为了验证该滤波器的滤噪性能,对最优AWMSF进行了性能分析,结果表明,AWMSF在滤除噪声的同时,能更好地保持图像的细节信息,并可减少迭代次数,从而使计算复杂度大大降低。     

Speckle reduction for the forest mapping analysis of multi-temporal Radarsat-1 images

As the number of satellite-borne synthetic aperture radar (SAR) systems increases, both the availability and the length of multi-temporal (MT) sequences of SAR images have also increased. Previous research on MT SAR sequences suggests that they increase the classification accuracy for all applications over single date images. Yet the presence of speckle noise remains a problem and all images in the sequence must be speckle filtered before acceptable classification accuracy can be attained. Several speckle filters designed specifically for MT sequences have been reported in the literature. Filtering in the spatial domain, as is usually done, reduces the effective spatial resolution of the filtered image. MT speckle filters operate in both the spatial and temporal dimensions, thus the reduction in resolution is not likely to be as severe (although a comparison between MT and spatial filters has not been reported). While this advantage may be useful when extracting spatial features from the image sequence, it is not quite as apparent for classification applications. This research explores the relative performance of spatial and MT speckle filtering for a particular classification application: mapping boreal forest types. We report filter performance using the radiometric resolution as measured by the equivalent number of looks (NL), and classification performance as measured by the classification accuracy. We chose representative spatial and MT filters and found that spatial speckle filters offer the advantage of higher radiometric resolution and higher classification accuracy with lower algorithm complexity. Thus, we confirm that MT filtering offers no advantage for classification applications; spatial speckle filters yield higher overall performance.     

基于静态小波分解的多尺度SAR图象滤波

由于雷达回波的相干性 ,合成孔径雷达 (SAR)图象上存在着斑点噪声 ,因此 ,为消除这种噪声 ,提出了一种基于静态小波分解的硬阈值滤波方法 ,该方法首先将 SAR图象分解至静态小波域 ,然后在静态小波域中将噪声的小波系数收缩至零 .将此算法应用于 ERS- 1SAR图象斑点噪声滤波 ,并与基于 Mallat分解的滤波算法和另外 3种典型的 SAR图象滤波算法进行比较 ,结果表明 ,该方法不仅可以有效地去除斑点噪声 ,并且可以保持 SAR图象的精细纹理结构     

基于静态小波分解的多尺度SAR图像滤波

由于雷达回波的相干性，合成孔径雷达（SAR）图象上存在着斑点噪声，因此，为消除这种噪声，提出了一种基于静态小波分解的硬阈值滤波方法，该方法首先将SAR图象分解至静态小波域，然后在静态小波域中将噪声的小波系数收缩至零，将此算法应用于ERS－1 SAR图象斑点噪声滤波，并与基于Mallat分解的滤波算法和另外3种典型的SAR图象滤波算法进行比较，结果表明，该方法不仅可以有效地去除斑点噪声,并且可以保持SAR图象的精细纹理结构。     

Soft morphological filtering

Stack filters are widely used nonlinear filters based on threshold decomposition and positive Boolean functions. They have shown to form a very large class of filters which includes rank-order operations as well as standard morphological operations. The stack filter representation of an order statistic filter provides an efficient tool for the theoretical analysis of the filter.Soft morphological filters form a large subclass of stack filters. They were introduced to improve the behavior of standard morphological filters in noisy conditions. In this paper, different properties of soft morphological filters are analysed and illustrated. Their connection to stack filters is established, and that connection is used in the statistical analysis of soft morphological filters. Soft morphological filters are less sensitive to additive noise than standard morphological filters. The deterministic properties of soft morphological filters are also analysed and it is shown that soft morphological filters form a class of filters with many desirable properties. For example, they preserve well details of images.     

改进的基于非局部均值的极化SAR相干斑抑制

贝叶斯形式的非局部均值模型在极化SAR图像相干斑抑制中有良好的应用,在实现抑制相干斑的同时较好地保持了边缘细节和点目标.通过分析合成孔径雷达(SAR)图像多视数据的空间统计分布,结合贝叶斯形式的非局部均值模型,得出在该模型下多视与单视SAR图像中像素间相似性度量函数一致性的结论,并对该相似性度量函数进行了修正,使之满足对称性;最后针对算法全局使用一个固定滤波参数影响滤波效果的问题,提出一种根据像素间相似程度自适应选取滤波参数的方法.实验结果验证了本文算法的有效性.     

一种改进的基于非局部均值的极化SAR相干斑抑制算法

贝叶斯形式的非局部均值模型在极化SAR图像相干斑抑制中有良好的应用,在实现抑制相干斑的同时较地保持了边缘细节和点目标。本文通过分析SAR图像多视数据的空间统计分布,结合贝叶斯形式的非局部均值模型,得出了在该模型下多视与单视SAR图像中像素间相似性度量函数一致性的结论,并对该相似性度量函数进行了修正,使之满足对称性;最后针对算法全局使用一个固定滤波参数影响滤波效果的问题,提出了一种根据像素间相似程度自适应选取滤波参数的方法。实验结果验证了本文算法的有效性。     

极化SAR相干斑抑制的非局部加权最小均方误差滤波算法

目的 相干斑的存在严重影响了极化合成孔径雷达(PolSAR)的影像质量.对相干斑的抑制是使用SAR数据的必不可少的预处理程序.提出一种基于非局部加权的线性最小均方误差(LMMSE)滤波器的极化SAR滤波的方法.方法 该方法的主要过程是利用非局部均值的理论来获取LMMSE估计器中像素样本的权重.同时,在样本像素的选取过程中,利用待处理像素的极化散射特性和邻域块的异质性来排除不相似像素以加速算法,同时达到保持点目标和自适应调节块窗口大小的目的.结果 模拟影像和真实影像上进行的实验结果表明,采用这种方法滤波后影像的质量得到明显改善.和传统的LMMSE算法相比,无论是单视的影像还是多视的影像,本文方法去噪结果的等效视数都高出8视以上;峰值信噪比也提升了5.8 dB.同时,去噪后影像分类的总体精度也达到了83％以上,该方法的运行效率也比非局部均值算法有了较大提升.结论 本文方法不仅能够有效抑制相干斑噪声,还能较好地保持边缘和细节信息以及极化散射特性.这将会为后续高效利用SAR数据提供保障.     

基于自适应堆滤波的边界检测

从被噪声干扰的图象中提取边界是图象测试与分析的关键之一。通常需要先滤除图象中的噪声，再用边界检测算子求出边界。本文介绍了一种边界直接检测法，即将边界检测与噪声滤波相结合，它是基于自适应堆滤波的边界检测法。首先非线性堆滤波器用于求出图象某象素点邻域内的灰度最大值与最小值的最优估计，然后以此两估计值之差代替原象素点灰度值。最后对之二值化求出边界。本文根据最小平均绝对误差准则，采用自适应方法求解堆滤波器。这种方法类似于线性自适应滤波器的ＬＭＳ方法，先任设一初始堆滤波器，利用期望图象与合噪声图象对堆滤波器进行迭代训练，最后求出最优化的自适应堆滤波器。文章最后给出了采用自适应堆滤波法求取图象边界的试验结果，表明这种方法可以有效地抑制各种分布的噪声干扰。     

An automatic filtering convergence method for iterative impulse noise filters based on PSNR checking and filtered pixels detection

Whether input images are corrupted by impulse noise and what the noise density level is are unknown a priori, and thus published iterative impulse noise filters cannot adaptively reduce noise, resulting in a smoothing image or unclear de-noising. For this reason, this paper proposes an automatic filtering convergence method using PSNR checking and filtered pixel detection for iterative impulse noise filters. (1) First, the similarity between the input image and the 1st filtered image is determined by calculating MSE. If MSE is equal to 0, then the input image is unfiltered and becomes the output. (2) Otherwise, one applies PSNR checking and filtered pixel detection to estimate the difference between the tth filtered image and the t–1th filtered image. (3) Finally, an adaptive and reasonable threshold is defined to make the iterative impulse noise filters stop automatically for most image details preservation in finite steps. Experimental results show that iterative impulse noise filters with the proposed automatic filtering convergence method can remove much of the impulse noise and effectively maintain image details. In addition, iterative impulse noise filters operate more efficiently.     

基于噪声检测的彩色图象脉冲噪声滤波

文章提出了具有细节保持能力的自适应彩色图像脉冲噪声滤波器,称为细节保持滤波器。新方法对图像中噪声像素进行检测,仅对噪声像素进行有序滤波而对非噪声像素则保持其原值不变,并根据图像噪声情况自适应地选择滤波窗口。从而,有效地滤除随机彩色脉冲噪声、保持图像边缘与细节,其性能优于经典的矢量中值滤波器（ＶＭＦ）、方向一距离滤波器（ＤＤＦ）、距离一幅度矢量滤波器（ＤＭＶＦ）等非线性滤波器。     

模糊加权中值滤波器

本文介绍了一种模糊加权中值滤波器,该滤波器由模糊布尔函数和滤波加权确定。本文用S型函数逼近模糊布尔函数。此外,用模糊理论领域中使用的S型函数逼近所滤波的加权。模糊加权中值滤波器只由4个参数确定。所提出的滤波在均方误差准则下能够由最小均方算法导出。图像复原的实验结果表明,本文介绍的模糊加权中值滤波方法既能去除脉冲噪声和平滑高斯噪声,又能同时有效地保持边缘和图像细节,漠糊加权中值滤波器明显优于加权中值滤波器,也优于Wiener滤波器。     

On the application of Gabor filtering in supervised image classification

Image texture can be an important source of data in the image classification process. Although not as easily measurable as image spectral attributes, image texture has proved in a number of cases to be a valuable source of data capable of increasing the accuracy of the classification process. In remote sensing there are cases in which classes are spectrally very similar, but present distinct spatial distribution, i.e. different textural characteristics. Image texture becomes then an important source of information in the classification process. The aim of this study is (1) to develop and test a supervised image classification method based on the image spatial texture as extracted by the Gabor filtering concept and (2) to investigate experimentally the performance of the classification process as a function of the Gabor filter's parameters. A set of Gabor filters is initially generated for the given image data. The filter parameters related to the relevant spatial frequencies present in the image are estimated from the available samples via the Fourier transform. Each filter generates one filtered image which characterizes the particular spatial frequency implemented by the filter parameters. As a result, a number of filtered images, sometimes referred to as 'textural bands', are generated and the originally univariate problem is transformed into a multivariate one, every pixel being defined by a vector with dimension identical to the number of filters used. The multidimensional image data can then be classified by implementing an appropriate supervised classification method. In this study the Euclidean Minimum Distance and the Gaussian Maximum Likelihood classifiers are used. The adequacy of the selected Gabor filter parameters (namely, the spatial frequency and the filter's spatial extent) are then examined as a function of the resulting classification accuracy. The proposed supervised methodology is tested using both synthetic and real image data. Results are presented and analysed.     

Evaluation of speckle noise MAP filtering algorithms applied to SAR images

This work proposes new speckle reduction filters for multi-look, amplitude-detected Synthetic Aperture Radar (SAR) images based on the maximum a posteriori (MAP) approach and compares their performance. The new filters use an adaptive approach based on the one-dimensional k-means clustering algorithm over the variance ratio and also a region-growing procedure. The trade-off between the loss of radiometric resolution and edge preservation is evaluated in the filtered images. In order to obtain quantitative measures of the speckle reduction and of the edge blurring, we used some parameters such as the classical equivalent number of looks and the Hough transform. Experiments have been carried out with natural images corrupted with synthetic speckle noise following the Rayleigh and square root of gamma distributions and with real SAR images.     

An image restoration by fusion

To deal with the problem of restoring images degraded with Gaussian white noise, the mean and adaptive Wiener filters are the most common methods to be implemented. Although these methods are both lowpass in character, they yield different results on the same problem. The mean filter reduces more noise than the adaptive Wiener but also blurs the image edges, whereas the adaptive Wiener filter can preserve edge sharpness but reduces less noise than the mean filter. Instead of trying to design a single mathematical technique to have the advantages of both methods, which is usually theoretically difficult, we propose an alternative solution to this image restoration by fusing multiple image filters using the mean, Sobel, and adaptive Wiener filters. Performance of the fusion algorithm is based on both redundant and complementary information provided by different filters. Several experimental results show the effective application of the proposed approach.     

The Nonlinear Prefiltering and Difference of Estimates Approaches to Edge Detection: Applications of Stack Filters

The theory of stack filtering, which is a generalization of median filtering, is used in two different approaches to the detection of intensity edges in noisy images. The first approach is a generalization of median prefiltering: a stack filter or another median-type filter is used to smooth an image before a standard gradient estimator is applied. These prefiltering schemes retain the robustness of the median prefilter, but allow resolution of finer detail. The second approach, called the Difference of Estimates (DoE) approach, is a new formulation of a morphological scheme [Lee et al., IEEE Trans. Robotics Automat. RA-3, Apr. 1987, 142-156, Maragos and Ziff, IEEE Trans. Pattern Anal. Mach. Intell. 12(5), May 1990.] which has proven to be very sensitive to impulsive noise. In this approach, stack filters are applied to a noisy image to obtain local estimates of the dilated and eroded versions of the noise-free image. Thresholding the difference between these two estimates yields the edge map. We find, for example, that this approach yields results comparable to those obtained with the Canny operator for images with additive Gaussian noise, but works much better when the noise is impulsive. In both approaches, the stack filters employed are trained to be optimal on images and noise that are "typical" examples of the target image. The robustness of stack filters leads to good performance for the target image, even when the statistics of the noise and/or image vary from those used in training. This is verified with extensive simulations.     

SAR图像MAP降噪的精细研究

本文推导出基于最大后验概率(MAP)滤波的一般形式,给出不同噪声分布和真实图像先验分布条件下的MAP滤波方程.从滤波方程在特定区间上解的分布情况以及区域统计特性分类两方面分析了MAP降噪性能,由此给出了MAP滤波的阈值表达形式.最后给出合成孔径雷达(SAR)图像的MAP降噪试验以及噪声滤除能力的量化指标.为了消除噪声强度对试验结果的影响,全面反映MAP降噪性能,本文给出了降噪能力随噪声大小的动态变化关系.结果表明,真实图像的先验分布对MAP滤波性能有着直接的影响,不合理的先验分布假定会严重降低MAP滤波的降噪能力.     

SRAD-CNN for adaptive synthetic aperture radar image classification

The performance of synthetic aperture radar (SAR) image classification based on a conventional convolutional neural network (CNN) is limited by a trade-off between immunity to speckle noise and the ability to locate boundaries accurately. Difficulties regarding the accurate location of boundaries are a result of the smoothing effect of the pooling layer. To address this issue, we propose a novel framework called SRAD-CNN for SAR image classification. In this framework, we apply a filtering layer constructed according to prior knowledge of the speckle reducing anisotropic diffusion (SRAD) filter. The filtering layer can not only reduce speckle but also enhance the boundaries. The main parameter that controls the degree of filtering can be optimized adaptively by a backpropagation algorithm. Image patches adaptively filtered by the filtering layer are then put into the CNN layers to assign a label. Due to the effect of the filtering layer, for our proposed SRAD-CNN, both the speckle noise immunity and the sensitivity to boundaries are superior to those of conventional CNN.To confirm the performance of the proposed SRAD-CNN, we conducted experiments using both simulated and real SAR images. The experimental results demonstrated that the parameter of the filtering layer could be optimized adaptively for different scenes, different noise levels, and different image resolutions. The SRAD-CNN outperformed the conventional CNN in both overall classification accuracy and maintenance of boundary accuracy on images with different resolutions and noise levels with limited training samples.