Image denoising with complex ridgelets

In this paper, we propose a novel image denoising method by incorporating the dual-tree complex wavelets into the ordinary ridgelet transform. The approximate shift invariant property of the dual-tree complex wavelet and the high directional sensitivity of the ridgelet transform make the new method a very good choice for image denoising. We apply the digital complex ridgelet transform to denoise some standard images corrupted with additive white noise. Experimental results show that the new method outperforms VisuShrink, the ordinary ridgelet image denoising, and wiener2 filter both in terms of peak signal-to-noise ratio and in visual quality. In particular, our method preserves sharp edges better while removing white noise. Complex ridgelets could be applied to curvelet image denoising as well.     

A new wavelet-based fuzzy single and multi-channel image denoising

In this paper, we propose a new wavelet shrinkage algorithm based on fuzzy logic. In particular, intra-scale dependency within wavelet coefficients is modeled using a fuzzy feature. This feature space distinguishes between important coefficients, which belong to image discontinuity and noisy coefficients. We use this fuzzy feature for enhancing wavelet coefficients' information in the shrinkage step. Then a fuzzy membership function shrinks wavelet coefficients based on the fuzzy feature. In addition, we extend our noise reduction algorithm for multi-channel images. We use inter-relation between different channels as a fuzzy feature for improving the denoising performance compared to denoising each channel, separately. We examine our image denoising algorithm in the dual-tree discrete wavelet transform, which is the new shiftable and modified version of discrete wavelet transform. Extensive comparisons with the state-of-the-art image denoising algorithm indicate that our image denoising algorithm has a better performance in noise suppression and edge preservation.     

Image denoising using statistical model based on quaternion wavelet domain

Image denoising is the basic problem of image processing.Quaternion wavelet transform is a new kind of multiresolution analysis tools.Image via quaternion wavelet transform,wavelet coefficients both in intrascale and in interscale have certain correlations.First,according to the correlation of quaternion wavelet coefficients in interscale,non-Gaussian distribution model is used to model its correlations,and the coefficients are divided into important and unimportance coefficients.Then we use the non-Gaussian distribution model to model the important coefficients and its adjacent coefficients,and utilize the MAP method estimate original image wavelet coefficients from noisy coefficients,so as to achieve the purpose of denoising.Experimental results show that our algorithm outperforms the other classical algorithms in peak signal-to-noise ratio and visual quality.     

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。     

An adaptive edge-preserving image denoising technique using patch-based weighted-SVD filtering in wavelet domain

Image denoising has always been one of the standard problems in image processing and computer vision. It is always recommendable for a denoising method to preserve important image features, such as edges, corners, etc., during its execution. Image denoising methods based on wavelet transforms have been shown their excellence in providing an efficient edge-preserving image denoising, because they provide a suitable basis for separating noisy signal from the image signal. This paper presents a novel edge-preserving image denoising technique based on wavelet transforms. The wavelet domain representation of the noisy image is obtained through its multi-level decomposition into wavelet coefficients by applying a discrete wavelet transform. A patch-based weighted-SVD filtering technique is used to effectively reduce noise while preserving important features of the original image. Experimental results, compared to other approaches, demonstrate that the proposed method achieves very impressive gain in denoising performance.     

Wavelet based speech presence probability estimator for speech enhancement

A reliable speech presence probability (SPP) estimator is important to many frequency domain speech enhancement algorithms. It is known that a good estimate of SPP can be obtained by having a smooth a-posteriori signal to noise ratio (SNR) function, which can be achieved by reducing the noise variance when estimating the speech power spectrum. Recently, the wavelet denoising with multitaper spectrum (MTS) estimation technique was suggested for such purpose. However, traditional approaches directly make use of the wavelet shrinkage denoiser which has not been fully optimized for denoising the MTS of noisy speech signals. In this paper, we firstly propose a two-stage wavelet denoising algorithm for estimating the speech power spectrum. First, we apply the wavelet transform to the periodogram of a noisy speech signal. Using the resulting wavelet coefficients, an oracle is developed to indicate the approximate locations of the noise floor in the periodogram. Second, we make use of the oracle developed in stage 1 to selectively remove the wavelet coefficients of the noise floor in the log MTS of the noisy speech. The wavelet coefficients that remained are then used to reconstruct a denoised MTS and in turn generate a smooth a-posteriori SNR function. To adapt to the enhanced a-posteriori SNR function, we further propose a new method to estimate the generalized likelihood ratio (GLR), which is an essential parameter for SPP estimation. Simulation results show that the new SPP estimator outperforms the traditional approaches and enables an improvement in both the quality and intelligibility of the enhanced speeches.     

邻域小波系数自适应的图像降噪

如何去除自然图像中的高斯白噪声是图像处理中的一个经典问题。基于小波收缩的NeighShrink降噪方法取得了很好的降噪效果,但是NeighShrink在所有小波子带上均使用了次优的universal阈值以及固定的邻域窗口尺寸,导致了较大的偏差,而且使得算法不健壮。为此,运用Stein的无偏风险估计改进了NeighShrink方法。该方法能够为每个小波子带确定最优的阈值和邻域窗口尺寸。实验结果显示,该方法取得了比NeighShrink更低的均方误差,也优于当前尖端的图像降噪算法—FeatShrink,其平均MSE大约低6%。     

基于改进小波阈值法的图像去噪算法

图像去噪是图像处理中最基本、最重要的前期工作,本文提出一种基于衰减法的Garrote阈值函数,并将基于该改进阈值函数的小波阈值法用于图像去噪过程,最后通过MATLAB仿真实验验证了本文所提出算法的有效性.本文在分析小波阈值法对图像去噪效果影响的基础上,针对该去噪算法在去除噪声的同时也损失了一定量的图像细节信息的问题,改进了传统阈值函数未考虑阈值以下的小波系数可能含有图像细节信息而对阈值以下小波系数盲目置零的缺点,对Garrote阈值函数阈值以下的小波系数采取衰减方法,以保留更多的图像细节信息,并加入三个调整因子以提高其性能和灵活度,实验表明本文提出的改进小波阈值去噪算法能够有效地去除噪声,且能够保留大量的图像边缘及细节信息.     

基于软门限去噪的图象压缩编码研究

在详细地分析了Donoho提出的子波域软限去噪方法的基础上,给出了含噪图象信号噪声水平的估计及门限值随尺度变化的规律。采用可分离的二维子波滤波器,方便地将Donoho的软门限去噪方法应用于图象信号处理,从而对含噪图象,在去除噪声的同时,又最大限度地进行了压缩。针对含噪的自然景物图象和合成孔径雷达图象的不同特点,分别提出了这在图象的压缩方案。对于SAR图象的压缩编码,通过一个自然对数变换,使得乘性噪声转变为适于软门限去噪的加性噪声。模拟结果显示,用软门限方法处理的解压缩图象比硬门限方法具有更好的视觉质量,因而该方法是解决含噪图象压缩编码的有效技术。     

基于改进阈值函数的分数阶小波图像去噪

为了消除噪声对图像的影响并较好地保留图像细节信息,提出一种基于改进阈值函数的分数阶小波图像去噪方法。该方法通过分数阶小波变换将含噪信号进行多尺度分解,采用改进的阈值函数对各层分数阶小波域系数进行处理,对处理后的系数进行重构得到去噪后的信号。仿真实验表明,相比已有的软阈值、硬阈值和均值加权法,本文方法去噪后的图像信噪比较大、均方误差较小,取得了满意的视觉效果,是一种实用的去噪方法。     

基于小波域加权阈值的图像去噪方法

针对小波全局阈值去噪的缺点，介绍了一种子带自适应的阈值加权算法。通过对图像小波分解系数统计特性的分析，提出了一种近指数模型作为分解层之间小波系数的先验分布。在此基础上，对比噪声图像和无噪图像在各尺度下统计特性，给出了一种子带自适应的加权阈值计算方法，避免了各层子带去噪的不平衡。实验表明，与全局阈值和其它子带自适应阈值去噪方法相比，基于加权阈值的图像去噪方法能获得更高的信噪比和更好的视觉效果。     

基于蜂群算法和带参阈值函数的图像去噪方法

针对小波阈值去噪方法中存在阈值选取困难和阈值函数量化效果差的缺陷,提出一种基于人工蜂群算法和带参阈值函数的图像去噪方法。首先,设计一个新的小波阈值函数,该函数具有连续性,高阶可微性和参数可调性,能够有效地解决硬阈值函数的不连续性和软阈值函数具有恒定偏差的问题。然后采用人工蜂群优化算法选取最优阈值,将其代入新小波阈值函数对带噪图像进行去噪处理。最后用MATLAB进行仿真实验,对比新阈值函数和传统阈值函数的去噪效果。实验结果表明：在图像去噪效果方面,提出的基于人工蜂群算法的新阈值函数明显优于传统阈值函数。     

基于离散小波阈值的偏微分图像去噪

小波方法和偏微分方程方法是图像去噪中的主要方法。该文提出基于离散小波变换对图像进行阈值去噪,得出了小波阈值的偏微分方程表示形式,在此基础上研究偏微分方程的解法,采用分数步的小波阈值方法对图像去噪,得到了较好的去噪效果,同时可以保护边缘。数值试验结果表明,该方法具有比小波方法更好的去噪效果,能获得较高的信噪比。     

改进的阈值图像去噪算法仿真研究

研究了图像优化识别问题,图像中噪声经常会影响图像的清晰度,造成图像模糊等。为了更好的去除图像中的噪声,特别是去除图像中细节丰富的区域中的噪声,通常传统的去噪方法难以完成。为了更好的去除图像噪声并较好的保留图像细节信息。在经典的小波软、硬阈值消噪方法的基础上,提出了一种小波包分析的改进方法。小波包变换是一种时频分析的方法,在分析中高频方面优于小波变换,将其应用于图像中噪声的消除。在Matlab上仿真结果表明,此法同时克服了传统阈值方法的缺点,有效提高了图像去除噪声能力,清晰度更高,为图像优化消噪提供了参考。     

Adaptive edge-preserving image denoising using wavelet transforms

Image denoising is a relevant issue found in diverse image processing and computer vision problems. It is a challenge to preserve important features, such as edges, corners and other sharp structures, during the denoising process. Wavelet transforms have been widely used for image denoising since they provide a suitable basis for separating noisy signal from the image signal. This paper describes a novel image denoising method based on wavelet transforms to preserve edges. The decomposition is performed by dividing the image into a set of blocks and transforming the data into the wavelet domain. An adaptive thresholding scheme based on edge strength is used to effectively reduce noise while preserving important features of the original image. Experimental results, compared to other approaches, demonstrate that the proposed method is suitable for different classes of images contaminated by Gaussian noise.     

基于小波变换和稀疏表示的图像去噪

传统小波阈值去噪在对图像进行去噪时,并不能很好地保留图像的细节纹理等边缘信息部分.针对这一不足,结合了稀疏表示相关的理论,提出了一种基于小波变换和正交匹配算法相结合的图像去噪算法.首先选取小波函数对含噪图像进行处理,分离出图像的高频和低频小波系数,然后对高频系数结合正交匹配追踪算法,通过多次反复迭代求得高频稀疏分量,再结合低频分量,用逆小波变换得到恢复图像.实验结果表明,在相同的噪声条件下,该算法能取得较好的峰值信噪比(PSNR),获得更好的视觉效果.     

基于改进阈值函数的小波变换图像去噪算法

针对传统硬阈值函数在阈值处的不连续、软阈值函数中小波系数与小波估计系数之间存在的恒定偏差问题,提出一种基于改进阈值函数的图像去噪算法。该算法结合改进阈值函数的优点,通过设置适当的调整参数动态选取固定阈值,增加调节因子来降低原小波系数和估计小波系数之间的恒定偏差,从而提高重构图像和原图像的逼近程度。改进后的阈值函数在阈值处满足连续性,同时满足函数的渐进性和高阶可导性。仿真结果表明,采用改进后的阈值函数进行图像去噪,视觉效果好,PSNR和SNR都提高了,MSE有所降低,去噪效果得到了优化。     

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。     

基于3次B样条小波变换的改进自适应阈值边缘检测算法

针对含噪声图像边缘提取问题,提出了一种改进NormalShrink自适应阈值去噪算法。该算法首先通过小波变换和局部模极大值法提取出可能包含图像边缘特征的小波系数,利用边缘像素之间特殊的空间关系以及噪声在各级小波分解尺度下的不同效应,构建适合各个尺度级的改进NormalShrink自适应阈值,并依此对提取出的小波系数进行筛选。实验结果表明,与改进的Candy算子和传统的NormalShrink自适应阈值相比,本方法提取出的图像边缘较为完整清晰,峰值信噪比提升约6 db。     

Image Thresholding by Maximizing the Index of Nonfuzziness of the 2-D Grayscale Histogram

Image segmentation plays an important role in various image processing applications including robot vision and document image analysis and understanding. In contrast to classical set theory, fuzzy set theory, which takes into account the uncertainty intrinsic to various images, has found great success in the area of image thresholding. In this paper, an image thresholding approach based on the index of nonfuzziness maximization of the 2-D grayscale histogram is proposed. The threshold vector (T, S), where T is a threshold for pixel intensity and S is another threshold for the local average of pixels, is obtained by an exhaustive searching algorithm. In this approach, the difference between these two components (T and S) is guaranteed to be within a relatively small range, which leads to reasonable results from the viewpoint of human vision perception. This cannot be achieved in certain entropy-based methods. Experimental results have shown that our proposed approach not only performs well and effectively but also is more robust when applied to noisy images.