Image denoising by sparse 3-D transform-domain collaborative filtering.

We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2-D image fragments (e.g., blocks) into 3-D data arrays which we call "groups." Collaborative filtering is a special procedure developed to deal with these 3-D groups. We realize it using the three successive steps: 3-D transformation of a group, shrinkage of the transform spectrum, and inverse 3-D transformation. The result is a 3-D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.     

基于小波域Curvelet变换的湍流图像去噪算法

为了提高湍流图像的空间分辨率,提出了一种基于小波域Curvelet变换(wavelet domain Curvelet transform,WDCT)的湍流图像去噪算法。该算法根据湍流退化图像噪声的统计特性,结合贝叶斯萎缩方法优化阈值选择。首先,对含噪湍流图像进行单层二维离散小波变换,接着提取高频系数并对它作快速离散Curvelet变换,最后根据贝叶斯准则估计阈值T,改进阈值的自适应选取方法,获得最优阈值,最后给出湍流图像去噪实现过程。为验证本文算法,根据客观评价标准峰值信噪比(peak signal to noise ratio,PSNR)和均方根误差(mean square error,MSE),对模拟图像和实测湍流图像进行去噪实验。与DWT-NABayesShrink算法、UWT算法相比,视觉效果更好,PSNR值分别提高7.27%和4.92%,MSE值分别降低26.3%和23.1%。本文算法得到较清晰的目标图像,对湍流退化图像去噪有一定的应用价值。     

基于奇异性检测的信号去噪新方法

该文引进了一种基于奇异性检测的信号去噪方法,并对其在二维降噪中所需进行的复杂的线性内插作了进一步简化,使得整个二维降噪得以大大简化而达到快速运算和节省存储量的目的。文中详细描述了该算法的理论基础并给出其一维计算机仿真,同时也给出了进一步简化后的二维降噪仿真。这种去噪方法不需要信号或噪声的先验信息。仿真结果表明,相比其它小波去噪方法,该方法的主要优势在于:它在某一时刻的脉冲噪声的辨识和去除能力相当强,而且在去噪的同时能很好地保持信号边缘。     

瑞利BOTDA系统的2维提升小波降噪方法

为了解决基于瑞利散射的布里渊光时域分析系统（BOTDA）中传感信号受噪声干扰严重的问题,采用2维提升小波变换算法,将测量信号从1维空间转换到2维空间,进行阈值降噪处理。通过理论分析和实验验证,取得了传统小波与2维提升小波降噪数据。结果表明,2维提升小波变换比传统小波变换信噪比提高约10dB,运算量减少了1/3;2维提升小波充分利用测量信号时间上的相关性,变换结构简单、运算速度快、降噪效果优于传统小波,适用于瑞利BOTDA系统降噪。该结果对光纤传感系统中信号降噪的研究有一定参考价值。     

3-D discrete shearlet transform and video processing

In this paper, we introduce a digital implementation of the 3-D shearlet transform and illustrate its application to problems of video denoising and enhancement. The shearlet representation is a multiscale pyramid of well-localized waveforms defined at various locations and orientations, which was introduced to overcome the limitations of traditional multiscale systems in dealing with multidimensional data. While the shearlet approach shares the general philosophy of curvelets and surfacelets, it is based on a very different mathematical framework, which is derived from the theory of affine systems and uses shearing matrices rather than rotations. This allows a natural transition from the continuous setting to the digital setting and a more flexible mathematical structure. The 3-D digital shearlet transform algorithm presented in this paper consists in a cascade of a multiscale decomposition and a directional filtering stage. The filters employed in this decomposition are implemented as finite-length filters, and this ensures that the transform is local and numerically efficient. To illustrate its performance, the 3-D discrete shearlet transform is applied to problems of video denoising and enhancement, and compared against other state-of-the-art multiscale techniques, including curvelets and surfacelets.     

一种基于小波-Contourlet变换的图像去噪算法

提出了一种基于小波-Contourlet变换的图像去噪算法.实验证明,该算法相对于小波变换和Contourlet变换能更稀疏的表达图像,并利用此优越性进行图像去噪,可以达到更好的效果和更高的PSNR值.     

基于Contourlet变换的图像去噪方法

图像去噪是数字图像处理领域的一项重要技术.传统的基于小波变换的去噪方法,去噪效果不是很理想.为了解决这一问题,提出了一种基于Contourlet变换的图像去噪方法.实验结果表明,与传统小波去噪方法相比,该方法不但可以保留图像的边缘信息,而且能提高去噪后图像的信噪比.     

混沌信号的自适应阈值同步挤压小波变换消噪

针对同步挤压小波变换（SST）消噪过程中仅使用单一阈值的不足,对SST消噪时的幅度阈值进行了改进,提出了一种基于SST分层阈值的混沌信号消噪方法.首先,根据信号和噪声经SST分解后系数的分布模型,推导SST混沌去噪时幅度阈值权系数的均方误差计算公式;进而,根据均方误差最小准则,计算幅度阈值权系数的最优取值;最后,根据最优阈值权系数和噪声标准差,确定SST混沌去噪时的分层阈值.利用模拟混沌信号和实测月太阳黑子信号对所提方法进行了实验分析,实验结果表明,本文方法可较好地滤除混沌信号中的噪声,同时原始信号的内在混沌特性也能得到较大程度的恢复.与小波阈值法和集合经验模态分解（EEMD）消噪法相比,可获得更好的消噪效果.     

Moving window-based double Haar wavelet transform for image processing.

Image denoising is a lively research field. The classical nonlinear filters used for image denoising, such as median filter, are based on a local analysis of the pixels within a moving window. Recently, the research of image denoising has been focused on the wavelet domain. Compared to the classical nonlinear filters, it is based on a global multiscale analysis of images. Apparently, the wavelet transform can be embedded in a moving window. Thus, a moving window-based local multiscale analysis is obtained. In this paper, based on the Haar wavelet, a class of nonorthogonal multi-channel filter bank with its corresponding wavelet shrinkage called Lee shrinkage is derived. As a special case of this filter bank, the double Haar wavelet transform is introduced. Examples show that it is suitable for a moving window-based local multiscale analysis used for image denoising, edge detection, and edge enhancement.     

利用HSSIM和残差比阈值的3维激光扫描图像去噪

为了更好地实现3维激光扫描图像的去噪,提出一种融合直方图结构相似度(HSSIM)和残差比阈值的改进稀疏去噪算法。利用初始化过完备字典进行稀疏分解,以相似因子代替重构误差作为保真项,利用残差比阈值作为正交匹配追踪算法的迭代终止条件对图像进行去噪,获得了去噪后图像的峰值信噪比及HSSIM指标。结果表明,与基于db2小波变换、多尺度曲波变换和离散余弦变换的去噪方法相比,该算法能获得更好的峰值信噪比和HSSIM数据。在有效去除图像噪声的同时还能更有效地保留图像的细节特征。     

一种基于小波变换的自适应图像降噪法

提出了一种基于二进小波变换的图像降噪方法,通过对小波变换系数进行阈值处理实现降噪。该方法结合图像的自身邻域信息,具有一定的自适应性。实验结果证明能够产生较好的效果。     

基于Contourlet变换的红外图像梯度自适应去噪

对Contourlet变换图像去噪阈值的选择进行了研究.分析了可见光图像去噪和红外图像去噪的特点,提出了红外图像梯度能量自适应去噪算法.通过实验证明,与传统的几种去噪相比,这种方法更好的保留了图像的轮廓细节,提高了图像的PSNR值,增强了去噪后的视觉效果.     

小波变换及其在信号去噪中的应用

介绍了小波变换理论及基于小波变换去除信号噪声的基本原理和方法.研究利用小波变换技术对噪声进行阈值处理和去除非平稳信号的噪声,并应用Matlab软件实现了小波去噪的计算机仿真,仿真结果表明小波变换去除噪声的效果优于传统的Fourier变换.     

结合Contourlet变换的Bayes自适应图像去噪算法

提出了结合Contourlet变换的Bayes自适应图像去噪算法。充分利用Contourlet变换的局部性、多分辨率、各向异性等优点。通过Contourlet变换得到图像不同尺度不同方向上Contourlet系数矩阵,实现了建立在对图像多尺度几何分析基础上Bayes估计自适应图像去噪算法。实验表明,新算法能够获得良好的视觉效果并且有效地提高了去噪图像的PSNR值,同时有效的避免了“过扼杀”系数现象,更好地保留了图像的纹理和细节。     

IMAGE WAVELET DENOISING USING THE ROBUST LOCAL THRESHOLD

This paper suggests a scheme of image denoising based on two-dimensional discrete wavelet transform.The denoising algorithm is described with some operatiors.By thresholding the wavelet transform coefficients of noisy images, the original image can be reconstructed cor-rectly.Different threshold selections and thresholding methods are discussed.A new robust local threshold scheme is proposed.Quantifying the performance of image denoising schemes by using the mean square error, the performance of the robust local threshold scheme is demonstrated and is compared with the universal threshold scheme.The experiment shows that image denoising using the robust local threshold performs better than that using the universal threshold.     

Poisson inverse problems by the Plug-and-Play scheme

The easy-to-compute Anscombe transform offers a conversion of a Poisson random variable into a variance stabilized Gaussian one, thus becoming handy in various Poisson-noisy inverse problems. Solution to such problems can be done by applying this transform, then invoking a high-performance Gaussian-noise-oriented restoration algorithm, and finally using an inverse transform. This process works well for high-SNR images, but when the noise level is high, it loses much of its effectiveness. This work suggests a novel method for coupling Gaussian denoising algorithms to Poisson noisy inverse problems. This approach is based on a general approach termed “Plug-and-Play-Prior”. Deploying this to Poisson inverse-problems leads to an iterative scheme that repeats an easy treatable convex programming task, followed by a powerful Gaussian denoising This method, like the Anscombe transform, enables to plug Gaussian denoising algorithms for the Poisson-oriented problem, and yet, it is effective for all SNR ranges.     

基于正交小波变换的图像去噪算法研究

提出了一种基于正交小波变换的图像去噪方法,首先利用离散小波对图像信号按Mallat算法进行分解,然后采用软闽值与小波重构的算法进行去噪。深入研究了小波变换中的图像分解与重构的Mallat算法,详细介绍了正交小波变换中阈值的选取,并进行了实验研究。实验结果表明,该方法可以有效去除噪声,并保留了图像细节部分的有用信息。     

Denoising for 3-D Photon-Limited Imaging Data Using Nonseparable Filterbanks

In this paper, we present a novel frame-based denoising algorithm for photon-limited 3-D images. We first construct a new 3-D nonseparable filterbank by adding elements to an existing frame in a structurally stable way. In contrast with the traditional 3-D separable wavelet system, the new filterbank is capable of using edge information in multiple directions. We then propose a data-adaptive hysteresis thresholding algorithm based on this new 3-D nonseparable filterbank. In addition, we develop a new validation strategy for denoising of photon-limited images containing sparse structures, such as neurons (the structure of interest is less than 5% of total volume). The validation method, based on tubular neighborhoods around the structure, is used to determine the optimal threshold of the proposed denoising algorithm. We compare our method with other state-of-the-art methods and report very encouraging results on applications utilizing both synthetic and real data.      

3-D discrete analytical ridgelet transform.

In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.     

Study on Denoising Based on the Wavelet Transform

The wavelet transform has remarkable advantages and wide applications in denoising because of its characteristic of good time-frequency. Based on the analysis of traditional wavelet denoising methods, which are based on Fourier transform, an improved method is proposed. It overcomes the shortcomings of the traditional Fourier denoising method. In this paper, the denoising procedures are introduced respectively based on the wavelet transform and the method of connecting the wavelet threshold with the wavelet...