Nonlinear restoration of noisy images

The restoration of images degraded by an additive white noise is performed by nonlinearly filtering a noisy image. The standard Wiener approach to this problem is modified to take into account the edge information of the image. Various filters of increasing complexity are derived. Experimental results are shown and compared to the standard Wiener filter results and other earlier attempts involving nonstationary filters.     

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。     

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.     

基于均值操作的快速自适应滤波器

为了满足图象实时处理对算法速度和高斯噪声,脉冲噪声混合的噪声环境对算法鲁棒性的要求,以及适应能够同时抑制高斯噪声和脉冲噪声的需要,提出了一种可以有效滤除混合噪声（高斯噪声和正负脉冲噪声）,而且可以快速实现的自适应滤波器－－ＡＢＡ滤波器,ＡＢＡ滤波器,ＡＢＡ滤波器应用了自适应的滤波结构,它将以脉冲噪的结果充分利用在自适应处理中,实验仿真所得的数据显示,在脉冲噪声的密度小于１０％的情况下,与其它一些滤     

基于决策分析的高椒盐噪声轮胎痕迹图像滤波方法

决策分析能准确判断出噪声像素与信号像素,均值滤波能较好平滑噪声,而自适应中值滤波能较好地保持原始图像的细节及边缘。为了恢复被高密度椒盐噪声污染的轮胎痕迹图像,提出三者相结合的新算法。该算法结合三者的优点,与传统中值滤波器、自适应中值滤波器等非线性滤波器相比,能得到更好的图像质量。实验表明,算法能有效消除灰度轮胎痕迹图像中的高密度椒盐噪声和彩色轮胎痕迹图像中的中低密度椒盐噪声,较好地保护了图像的细节及边缘信息。     

一种图像自适应Wiener组合滤波方法

利用小波域Wiener滤波和空间域自适应Wiener滤波的特点,提出一种基于小波域自适应Wiener滤波和空间域自适应Wiener滤波的组合滤波方法。该方法首先在小波域进行自适应Wiener滤波,对恢复图像中的残留噪声方差进行重新估计,再在空间域进行自适应Wiener滤波,这种方法提高了恢复图像的精度。仿真实验表明,与单独的小波域和空间域Wiener滤波相比,该方法的均方误差最小,去噪效果更优。     

基于修正维纳滤波的小波包变换图像去噪

图像去噪是图像处理中一个非常重要的环节。为了改善降质图像质量,根据Donoho提出的小波阈值去噪算法,分析了维纳滤波原理,提出了一种基于修正维纳滤波的小波包变换图像去噪方法。利用修正维纳滤波对噪声图像进行处理,用处理后的图像计算噪声的标准方差,以此作为小波包的阈值。利用小波包对维纳滤波后的图像进行分解,实现对图像的低频和高频部分分别进行分解,用计算出的阈值对小波包树系数进行软阈值处理。利用小波包逆变换来获取去噪后的图像。结果表明：在噪声方差为0.01时,经该算法去噪后图像的PSNR比小波包自适应阈值去噪后的PSNR高出8.8 dB。该算法不仅能有效地去除加性高斯白噪声,而且能很好地保留边缘信息,极大地改善了图像的视觉质量。     

基于多小波基维纳滤波图像去噪

提出一种多小波基维纳图像去噪方法。它把多个小波基用于小波维纳滤波图像去噪，利用多个小波各自独有的特性和维纳滤波估计最小误差估计的优点，达到对图像更有效去噪的目的。实验结果表明，该方法可以有效降低图像噪声，同时，较好地保持图像视觉效果。     

基于改进约束最小二乘方法的图像复原算法

约束最小二乘方法(约束最小二乘方滤波器)在图像复原的应用过程中普遍只要求噪声方差和均值的知识,对处理的每一幅图像都能产生最优效果,因而得到了广泛应用。文中提出的图像复原算法就是基于约束最小二乘方法的,并对其进行了改进。通过实验证明,用该改进的图像复原处理方法复原的图像比用维纳滤波方法复原的图像更加平滑,复原图像的信噪比也更大。另一方面,改进的约束最小二乘方法复原的图像比平滑约束最小平方法复原的图像具有更加突出的边缘,而且同样具有更高的信噪比。适当应用该方法,能够体现出维纳滤波和平滑约束最小平方滤波这两种基本的约束最小二乘方滤波相结合的效果优势。     

Comparison of different speckle-reduction techniques in SAR images using wavelet transform

Speckle noise is always present in Synthetic Aperture Radar (SAR) images. Many methods that reduce speckle noise while preserving texture and detail have been presented previously. In this paper, a comparison of different methods using wavelet decomposition is performed and new improvements for traditional methods are introduced. These techniques are: Wiener filtering, classical soft threshold, a new adaptive soft threshold and Bayesian reconstruction. First, speckle noise in a SAR image was analysed statistically. Then, a simulated image following these characteristics was created in order to evaluate noise reduction. The mean squared error was classified depending on the spatial characteristics of a local region. This tool gave valuable information for algorithm assessment. In the comparison, the new adaptive soft threshold method provided excellent results concerning noise reduction and detail preservation compared with classical soft threshold and Wiener methods. In addition, it gave as much noise reduction as the most sophisticated Bayesian method, but much more efficiently. Hence, the adaptive version of soft thresholding outperformed the other techniques. This study also presents a rigorous framework for speckle noise simulation and noise reduction evaluation.     

A new adaptive center weighted median filter for suppressing impulsive noise in images

In this work, a new adaptive center weighted median (ACWM) filter is proposed for improving the performance of median-based filters, preserving image details while effectively suppressing impulsive noise. The proposed filter is an adaptive CWM filter with an adjustable central weight obtained by partitioning the observation vector space. To obtain the optimal weight for each block, the efficient scalar quantization (SQ) method is used to partition the observation vector space. The center weight within each block is obtained by using a learning approach based on the least mean square (LMS) algorithm. The noise filtering procedure is progressively applied through several iterations so that the mean square error of the output can be minimized. Experimental results have demonstrated that the proposed filter outperforms many well-accepted median-based filters in terms of both noise suppression and detail preservation. The proposed new filter also provides excellent robustness at various percentages of impulsive noise.     

A new gaussian noise filter based on interval type-2 fuzzy logic systems

In this paper, a new selective feedback fuzzy neural network (SFNN) based on interval type-2 fuzzy logic systems is introduced by partitioning input and output spaces and based upon which a new FLS filter is further studied. The experimental results demonstrate that this new FLS filter outperforms other filters (e.g. the mean filter and the Wiener filter) in suppressing Gaussian noise and maintaining the original structure of an image.     

Two empirical methods for improving the performance of statistical multirate high-resolution signal reconstruction

The problem of reconstructing a known high-resolution signal from a set of its low-resolution parts exposed to additive white Gaussian noise is addressed in this paper from the perspective of statistical multirate signal processing. To enhance the performance of the existing high-resolution signal reconstruction procedure that is based on using a set of linear periodically time-varying (LPTV) Wiener filter structures, we propose two empirical methods combining empirical mode decomposition- and least squares support vector machine regression-based noise reduction schemes with these filter structures. The methods originate from the idea of reducing the effects of white Gaussian noise present in the low-resolution observations before applying them directly to the LPTV Wiener filters. Performances of the proposed methods are evaluated over one-dimensional simulated signals and two-dimensional images. Simulation results show that, under certain conditions, considerable improvements have been achieved by the proposed methods when compared with the previous study that only uses a set of LPTV Wiener filter structures for the signal reconstruction process.     

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。     

基于二级修复的多方向加权均值滤波算法

针对目前算法不能有效去除高概率的椒盐噪声并保护图像边缘和细节特征的缺点,提出了一种基于二级修复的多方向加权均值滤波算法。在噪声检测阶段,首先利用一个方差参数判断当前像素点与其邻域像素点之间的灰度差异程度,再通过将方差参数和灰度极值相结合的方法检测出图像中的椒盐噪声点。在噪声修复阶段,提出一种二级修复方法来修复噪声点的灰度值。首先利用改进的自适应中值滤波器对椒盐噪声点进行第一级噪声修复;然后利用方差参数将第一级修复后的噪声点划分为两类,并采用不同的修复方法对这两类像素点进行第二级噪声修复,一类像素点采用均值滤波器进行再修复,另外一类像素点采用多方向加权均值滤波器进行再修复。数值实验结果表明,所提算法的滤波性能和边缘保护能力均优于当下很多先进的滤波器。     

Edge-detection-based filter for SAR speckle noise reduction

Some adaptive filters, such as the Kuan, Lee, minimum mean square error (MMSE) and Frost filters, have been tested on synthetic aperture radar (SAR) data without considering the level of homogeneity in the pixels. Therefore, they degrade the spatial resolution of images and smooth details, while also decreasing the speckle noise level. There are other filters, such as the enhanced Lee and gamma maximum a posteriori (MAP), that utilize the level of homogeneity, but they cannot adequately suppress speckle noise. In addition to these weaknesses, pixels surrounding a point scatterer are also treated as point scatterers due to inadequacy of the method based on evaluating the coefficient of variation for differentiating between them and the point scatterer. We have developed a new method based on the assessment of similarity of homogeneity levels in the image, incorporating edge-detection filters to identify meaningful features and an algorithm to filter the pixels surrounding point scatterers. This method, called the UNSW (University of New South Wales) adaptive filter (UAF), was compared to nine filters using different quantitative and qualitative methods. The results show the ability of the UAF to simultaneously reduce speckle and preserve details as well as its ability to filter more pixels. The effect of increasing the damping factor on speckle noise reduction performance has also been assessed using this method.     

基于联合滤波的聚类稀疏表示图像去噪算法

针对非局部均值去噪算法中噪声对结构聚类影响的问题,提出了一种基于联合滤波预处理的聚类稀疏表示图像去噪算法。利用维纳滤波和巴特沃斯滤波联合滤波处理提取含噪图像中的高频分量,同时减小了噪声对聚类的影响;利用非局部均值去噪的思想将高频图像块进行聚类,每一类图像块单独进行字典学习,增强字典的自适应性;利用多循环字典更新的K-SVD算法进行类内字典学习,增强字典的描述能力。实验结果表明,与传统的K-SVD算法相比,该算法能有效保留图像的结构信息,并且提升了图像的去噪效果。     

SAR image processing using adaptive stack filter

Stack filters are a special case of non-linear filters. They have a good performance for filtering images with different types of noise while preserving edges and details. A stack filter decomposes an input image into several binary images according to a set of thresholds. Each binary image is filtered by a Boolean function. The Boolean function that characterizes an adaptive stack filter is optimal and is computed from a pair of images consisting of an ideal noiseless image and its noisy version. In this work the behavior of adaptive stack filters on synthetic aperture radar (SAR) data is evaluated. With this aim, the equivalent number of looks for stack filtered data are calculated to assess the speckle noise reduction capability of this filter. Then a classification of simulated and real SAR images is carried out on data filtered with a stack filter trained with selected samples. The results of a maximum likelihood classification of these data are evaluated and compared with the results of classifying images previously filtered using the Lee and the Frost filters.     

Speech enhancement with an adaptive Wiener filter

This paper proposes an adaptive Wiener filtering method for speech enhancement. This method depends on the adaptation of the filter transfer function from sample to sample based on the speech signal statistics; the local mean and the local variance. It is implemented in the time domain rather than in the frequency domain to accommodate for the time-varying nature of the speech signals. The proposed method is compared to the traditional frequency-domain Wiener filtering, spectral subtraction and wavelet denoising methods using different speech quality metrics. The simulation results reveal the superiority of the proposed Wiener filtering method in the case of Additive White Gaussian Noise (AWGN) as well as colored noise.     

基于高斯马尔可夫随机场的MAP估计在高斯噪声滤波中的应用

提出了基于高斯马尔可夫随机场(GMRF)的最大后验概率(MAP)估计在图像高斯噪声滤波中的应用方法。根据高斯噪声的先验特点,建立基于高斯马尔可夫随机场的退化图像恢复模型,从而将图像高斯噪声滤波问题转化为求解最大后验概率问题。先验概率可以根据马尔可夫随机场(MRF)和吉布斯分布(GD)的等效性, 用GD的概率估计。为了求解最大后验概率,第一,通过期望最大化(EM）算法对GMRF模型进行参数估计。第二,用共轭梯度法将目标函数最小化。实验结果表明,与其他滤波器（如高斯滤波、维纳滤波等）相比,本文所阐述的方法在滤除高斯噪声、保持图像原有结构方面效果更好。