Wavelet-based image denoising with the normal inverse Gaussian prior and linear MMSE estimator

A new spatially adaptive wavelet-based method is introduced for reducing noise in images corrupted by additive white Gaussian noise. It is shown that a symmetric normal inverse Gaussian distribution is highly suitable for modelling the wavelet coefficients. In order to estimate the parameters of the distribution, a maximumlikelihood- based technique is proposed, wherein the Gauss?Hermite quadrature approximation is exploited to perform the maximisation in a computationally efficient way. A Bayesian minimum mean-squared error (MMSE) estimator is developed utilising the proposed distribution. The variances corresponding to the noisefree coefficients are obtained from the Bayesian estimates using a local neighbourhood. A modified linear MMSE estimator that incorporates both intra-scale and inter-scale dependencies is proposed. The performance of the proposed method is studied using typical noise-free images corrupted with simulated noise and compared with that of the other state-of-the-art methods. It is shown that the proposed method gives higher values of the peak signal-to-noise ratio compared with most of the other denoising techniques and provides images of good visual quality. Also, the performance of the proposed method is quite close to that of the state-of-the-art Gaussian scale mixture (GSM) method, but with much less complexity.     

基于多尺度小波变换的高斯混合模型SAR图像去噪

针对合成孔径雷达图像斑点噪声去除问题,提出了一种滤波算法。该算法根据SAR图像小波系数分布的特点,采用高斯混合模型对其进行精确拟舍,并用贝叶斯估计来恢复原图。为了有效地克服对数图像均值不为零对小波滤波的影响,在多尺度小波变换前先对取对数后的图像作了归一化处理。仿真实验结果表明,该方法克服了常用的小波阈值去噪只有一个阈值的缺点,可在去除噪声的同时有效保留图像的边缘细节。     

小波与双边滤波的医学超声图像去噪

目的：医学超声图像中的斑点噪声降低了图像质量并且限制了超声图像自动化诊断技术的发展。针对斑点噪声问题,提出了一种新型的基于小波和双边滤波的去噪算法。方法：首先,根据医学超声图像在小波域内的统计特性,在通用小波阈值函数的基础之上,改进了小波阈值函数。其次,将无噪信号的小波系数和斑点噪声的小波系数分别建模为广义拉普拉斯分布模型和高斯分布模型,利用贝叶斯最大后验估计方法得到了新型的小波收缩算法,利用小波阈值法对小波域内的高频信号分量进行去噪。最后,对小波域内的低频信号分量进行双边滤波处理,然后利用小波逆变换便得到去噪后的图像。结果：在仿真实验中,通过与其它7种去噪算法作对比,观察峰值信噪比(PSNR)等图像质量评价指标,结果表明本文算法的去噪效果优于其他相关算法。临床超声图像的实验结果进一步验证了本文算法的去噪性能。结论：本文提出了一种新型的去噪算法,实验表明本文算法能够很好地抑制斑点噪声,并且能保留图像病灶边缘等细节。     

基于复小波噪声方差显著修正的SAR图像去噪

提出了一种基于复小波域统计建模与噪声方差估计显著性修正相结合的合成孔径雷达(Synthetic Aperture Radar,SAR)图像斑点噪声滤波方法。该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,然后对变换后的图像进行双树复小波变换(Dualtree Complex Wavelet Transform,DCWT),并对复数小波系数的统计分布进行建模。在此先验分布的基础上,通过运用贝叶斯估计方法从含噪系数中恢复原始系数,达到滤除噪声的目的。实验结果表明该方法在去除噪声的同时保留了图像的细节信息,取得了很好的降噪效果。     

基于冗余小波变换的医学超声图像去斑噪算法

医学超声图像中固有的斑点噪声严重降低了图像的可解译程度,影响了后续的图像分析和诊断。提出了一种基于冗余小波变换的超声图像去斑算法,首先对含斑图像进行对数变换,将乘性噪声变成加性噪声;再对转换后图像做冗余小波分解;在小波系数服从广义高斯分布的前提下,计算每个小波高频子带的贝叶斯萎缩阈值,利用软阈值方法修正小波系数。实验结果表明,该算法去斑性能优于传统的空间域滤波和正交小波阈值去噪方法。     

Speech Enhancement, Gain, and Noise Spectrum Adaptation Using Approximate Bayesian Estimation

This paper presents a new approximate Bayesian estimator for enhancing a noisy speech signal. The speech model is assumed to be a Gaussian mixture model (GMM) in the log-spectral domain. This is in contrast to most current models in frequency domain. Exact signal estimation is a computationally intractable problem. We derive three approximations to enhance the efficiency of signal estimation. The Gaussian approximation transforms the log-spectral domain GMM into the frequency domain using minimal Kullback-Leiber (KL)-divergency criterion. The frequency domain Laplace method computes the maximum a posteriori (MAP) estimator for the spectral amplitude. Correspondingly, the log-spectral domain Laplace method computes the MAP estimator for the log-spectral amplitude. Further, the gain and noise spectrum adaptation are implemented using the expectation-maximization (EM) algorithm within the GMM under Gaussian approximation. The proposed algorithms are evaluated by applying them to enhance the speeches corrupted by the speech-shaped noise (SSN). The experimental results demonstrate that the proposed algorithms offer improved signal-to-noise ratio, lower word recognition error rate, and less spectral distortion.     

Spatially adaptive thresholding in wavelet domain for despeckling of ultrasound images

Ultrasound imaging is widely used for diagnostic purposes among the clinicians. A major problem concerning the ultrasound images is their inherent corruption by the multiplicative speckle noise that hampers the quality of the diagnosis, and reduces the efficiency of the algorithms for automatic image processing. In this paper, we propose a new spatially adaptive wavelet-based method in order to reduce the speckle noise from ultrasound images. A spatially adaptive threshold is introduced for denoising the coefficients of log-transformed ultrasound images. The threshold is obtained from a Bayesian maximum a posteriori estimator that is developed using a symmetric normal inverse Gaussian probability density function (PDF) as a prior for modelling the coefficients of the log-transformed reflectivity. A simple and fast method is provided to estimate the parameters of the prior PDF from the neighbouring coefficients. Extensive simulations are carried out using synthetically speckled and ultrasound images. It is shown that the proposed method outperforms several existing techniques in terms of the signal-to-noise ratio, edge preservation index and structural similarity index and visual quality, and in addition, is able to maintain the diagnostically significant details of ultrasound images.     

一种新型的空域SAR图像相干斑抑制方法

为了有效抑制SAR强度图像中的相干斑噪声,提出一种改进Sigma滤波并结合Gamma MAP滤波的空域相干斑抑制方法。首先利用阈值判断法判断并保留强点目标,然后结合SAR图像分布模型和MMSE准则判断Sigma区间,其中可以根据图像局部统计特性自适应调整窗口尺寸,最后选择Sigma区间内像素进行Gamma MAP滤波。实验结果表明:对于星载和机载SAR图像,在相干斑噪声抑制和边缘纹理细节信息保持方面,该方法较其他常用的空域相干斑抑制方法具有明显的优越性,能极大地提高SAR图像判读和目标识别能力。     

侧扫声呐图像的3维块匹配降斑方法

斑点噪声是影响侧扫声呐图像质量的主要因素,降斑处理对侧扫声呐图像的判别与分析非常重要。针对侧扫声呐图像自身特性和斑点噪声分布特点,提出一种基于3维块匹配(BM3D)的降斑方法。根据海底散射模型,得到侧扫声呐图像斑点噪声的瑞利分布模型,然后通过高斯光滑函数幂变换将瑞利分布的噪声转化为高斯分布,通过对数变换将乘性噪声转变为加性噪声,再进行自适应的BM3D滤波,最后采用逆变换得到降斑图像。实验结果表明,该方法在降噪、边缘和纹理保持等方面均优于空间域、小波域、Curvelet域的一些降斑方法。     

基于双树复小波二元统计模型的图像去噪方法

为了更有效地进行图像去噪,提出了一种基于双树复小波二元统计模型的图像去噪方法,该方法先用带参数的二元广义高斯分布(GGD)来模拟原图双树复小波系数的统计分布;然后结合最大似然估计(MLE)得到优化的参数估计;最后在此先验分布的基础上,运用最大后验概率(MAP)来估计从噪声图的小波系数中恢复原图的系数,从而达到去噪的目的。实验表明该新方法不仅可以干净地去除图像的噪声,还可以有效地保留图像细节,取得了良好的去噪效果,尤其是去噪图像的视觉效果要明显优于目前的很多算法。     

Non-Gaussian model-based fusion of noisy images in the wavelet domain

This paper describes a new methodology for multimodal image fusion based on non-Gaussian statistical modelling of wavelet coefficients. Special emphasis is placed on the fusion of noisy images. The use of families of generalised Gaussian and alpha-stable distributions for modelling image wavelet coefficients is investigated and methods for estimating distribution parameters are proposed. Improved techniques for image fusion are developed, by incorporating these models into a weighted average image fusion algorithm. The proposed method has been shown to perform very well with both noisy and noise-free images from multimodal datasets, outperforming conventional methods in terms of fusion quality and noise reduction in the fused output.     

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。     

区域GMM聚类的SAR图像分割

高斯混合模型(GMM)聚类算法近年来广泛应用于图像分割领域。但在SAR图像分割中,由于忽略了图像像素间的空间相关性,使其对相干斑噪声十分敏感。提出一种基于区域的GMM聚类算法,它将空间相关性引入聚类分类中,利用分水岭分割得到基本同质区域,计算区域的灰度均值作为GMM聚类算法的输入样本,将聚类特征从像素水平提升到区域水平,减少了噪声对分割结果的影响;并将自身反馈机制引入期望最大化(EM)算法中,进一步提高了GMM模型参数估计的精度。还对合成图像和真实SAR图像进行了分割实验,结果表明新算法可有效地提高分割的     

基于多小波域SOT结构的SAR图像去噪与压缩算法*

合成孔径雷达（SAR）图像固有的相干斑噪声严重影响了SAR图像的判读和进一步压缩处理,提出一种在多小波域将空间方向树（SOT）去噪与压缩相结合的SAR图像压缩算法。首先利用SOT对高频子带的多小波系数进行软阈值去噪,滤除相干斑噪声;然后采用改进的多级树集合分裂（SPIHT）算法编码形成嵌入式码流。利用大量的机载SAR图像对该算法进行了仿真验证,实验结果表明采用该算法进行SAR图像压缩提高了重建图像的PSNR,同时对相干斑噪声进行了有效的抑制。     

基于小波域隐马尔可夫树模型的超声图象贝叶斯去噪

提出了一种新的医学超声图象去噪方法 .首先 ,原始超声图象经对数变换 ,其乘性散粒噪声变为了加性噪声 ;然后再经小波变换后 ,基于隐马尔可夫树模型 ,应用贝叶斯方法去除加性噪声 ;最后 ,经小波反变换和指数变换恢复去噪后的原始超声图象 .测试结果表明 ,此方法在有效去除噪声的同时 ,能保留原始图象的细节边缘 .针对超声图象还对几种去噪算法作出定性比较 ,并对去噪性能给出定量分析 ,实验结果表明 ,该方法是可行的     

改进权值非局部均值超声图像去噪

目的 超声图像斑点噪声会影响诊断的准确性和可靠性。通过分析超声图像斑点噪声统计模型,结合非局部均值滤波算法,提出一种基于超声斑点噪声模型的改进权值非局部均值（NLM）滤波算法。方法 算法针对超声图像灰度信息对图像进行预处理,利用超声图像斑点噪声模型改进传统NLM算法的权值计算函数,基于图像特征确定最优采样间隔进行下采样,利用改进后的权值计算函数对图像进行NLM去噪处理。结果 分别采用人工合成与真实超声图像对本文算法性能进行测试,并与传统非局部均值滤波算法、非局部总变分（NLTV）等算法进行去噪效果比较,同时采用均方误差、峰值信噪比和平均结构相似性作为滤波算法性能的客观评价指标。本文算法能快速完成超声图像的去噪处理,峰值信噪比较其他算法可以提高0.2 dB以上,可以降低均方误差,提高平均结构相似性,缩短处理时间,并得到较好的图像质量和视觉效果。结论 根据超声图像斑点噪声模型对NLM算法的权值计算函数进行优化,使得NLM图像滤波算法能更好地适用于超声图像的去噪,基于超声斑点噪声模型的改进权值NLM算法相较于其他算法,滤波效果更佳,适合超声图像去噪。     

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.     

λ-WMAP: a statistical speckle filter operating in the wavelet domain

In this paper we introduce the Γ-WMAP filter, a wavelet based equivalent to the classical Γ-MAP filter. We model speckle as additive signal-dependent noise, and propose to use the normal inverse Gaussian (NIG) distribution as a statistical model for the wavelet coefficients of both the reflectance image and the noise image. A method for estimating the parameters of the proposed statistical models is presented, and we show that the NIG distribution makes excellent fits to the distributions of the wavelet coefficients of single-look synthetic aperture radar (SAR) images. The performance of the Γ-WMAP filter is tested on three single-look SAR images. We find that when the filter is used in a global mode it may severely blur the image. However, when applied in a local, adaptive mode the new algorithm has excellent de-speckling performance. Visual comparisons with the Γ-MAP filter show that Γ-WMAP tends to give better de-speckling. Quantitative comparisons in homogeneous regions using both the equivalent number of looks and the log standard deviation as measures definitely show that the Γ-WMAP gives better speckle filtering.     

基于小波域HMT模型的序列图像超分辨率重建*

鉴于基于小波域隐马尔可夫树的噪声抑制性和较好的边缘保持性,提出一种基于小波域隐马尔可夫树的序列图像的超分辨率重建算法。针对小波系数进行统计建模,讨论了不同尺度小波系数之间的隐马尔可夫树结构,利用了序列图像的运动信息,运用极大后验概率估计和贝叶斯原理,将小波域HMT作为图像先验知识并给出了超分辨率重建算法,最终通过EM算法和共轭梯度算法的交替迭代进行优化计算。实验结果表明方法的重建效果得到了明显的改进。