利用差分图像奇异值分解的置乱程度评价研究

提出了基于差分图像和奇异值分解相结合的图像置乱效果评价新方法。针对基于奇异值分解法的置乱程度评价法不能客观地反映图像置乱效果好坏的不足,首先对置乱前后图像进行差分运算并得到其相应的差分图像,其次对两差分图像进行奇异值分解,最后计算其奇异值差异程度的大小作为图像置乱效果评价的新准则。实验结果表明,提出的评价方法能够较好地刻画图像的置乱程度,反映了加密次数与置乱程度之间的关系,与人的视觉基本相符。对于不同的图像,该评价方法在一定程度上反映了所用的置乱变换在各置乱阶段的效果。     

Adaptive singular value decomposition in wavelet domain for image denoising

Image denoising is an important issue in image preprocessing. Two popular methods to the problem are singular value decomposition (SVD) and wavelet transform. Various denoising algorithms based on these two methods have been independently developed. This paper proposes an approach for image denoising by performing SVD filtering in detail subbands of wavelet domain, where SVD filtering is adaptive to the inhomogeneous nature of natural images. Comparisons were made with respect to both SVD-based filtering methods and wavelet transform-based methods.     

基于奇异值分解的伪光谱图像压缩算法

提出了一种光谱图像的快速获取和有效压缩算法。将一幅三原色图像转换为光谱图像,其像素被通过查找光谱调色板后所确定的相应的光谱反射因子取代,该反射因子的色度值与原像素最为接近。此时转换所得的图像并没有真实光谱数据而只有基于调色板的伪光谱值,它可用于模拟原始RGB图像在不同光源条件下的颜色外观。奇异值分解法对于光谱图像的压缩是非常有用的,人们可以对局部子块图像中经过重新排列后的36个像素×36个光谱波段的数据运用该方法,以能够充分利用矩阵数据在空间和光谱分布中的强相关性。实验结果表明,基于奇异值分解的光谱图像压缩算法在较高的压缩比下仍能取得很好的光谱重建效果。     

基于奇异值分解和Contourlet变换的图像压缩算法

随着互联网的飞速发展,产生大量的图像信息。为了减小存储并提高图像质量,故提出了一种基于奇异值分解和Contourlet变化结合的有损图像压缩算法。该算法先对图像进行奇异值分解,根据奇异值对图像信号的贡献,选取适当的奇异值,来实现图像压缩,再对图像进行Contourlet 变换和量化,实现图像二级压缩。将该算法和图像奇异值分解直接压缩算法、Contourlet变换压缩算法进行实验比较,试验结果表明,该算法比图像奇异值分解直接压缩算法、Contourlet变换压缩算法有更好的性能,在同样的压缩比的情况下能获得更高的峰值信噪比和SSIM。     

Video summarization and retrieval using singular value decomposition

In this paper, we propose novel video summarization and retrieval systems based on unique properties from singular value decomposition (SVD). Through mathematical analysis, we derive the SVD properties that capture both the temporal and spatial characteristics of the input video in the singular vector space. Using these SVD properties, we are able to summarize a video by outputting a motion video summary with the user-specified length. The motion video summary aims to eliminate visual redundancies while assigning equal show time to equal amounts of visual content for the original video program. On the other hand, the same SVD properties can also be used to categorize and retrieve video shots based on their temporal and spatial characteristics. As an extended application of the derived SVD properties, we propose a system that is able to retrieve video shots according to their degrees of visual changes, color distribution uniformities, and visual similarities.     

A new robust and secure digital image watermarking scheme based on the integer wavelet transform and singular value decomposition

In this paper, a new robust and secure digital image watermarking scheme that can be used for copyright protection is proposed. The scheme uses the integer wavelet transform (IWT) and singular value decomposition (SVD). The grey image watermark pixels values are embedded directly into the singular values of the 1-level IWT decomposed sub-bands. Experimental results demonstrate the effectiveness of the proposed scheme in terms of robustness, imperceptibility and capacity due to the IWT and SVD properties. A challenge due to the false positive problem which may be faced by most of SVD-based watermarking schemes has been solved in this work by adopting a digital signature into the watermarked image. The proposed digital signature mechanism is applied to generate and embed a digital signature after embedding the watermarks; the ownership is then authenticated before extracting watermarks. Thus, the proposed scheme achieved the security issue where the false positive problem is solved, in addition to that, the scheme is considered as a blind scheme. A computer simulation is used to verify the feasibility of the proposed scheme and its robustness against various types of attacks and to compare it with some previous schemes. Furthermore, the statistical Wilcoxon signed rank test is employed to certify the effectiveness of the proposed scheme.     

奇异值分解用于图像置乱程度评价研究

提出了基于奇异值分解的图像置乱程度评价新方法。首先求置乱前后两图像灰度值差的绝对值矩阵;其次计算灰度差绝对值矩阵与其转置矩阵之积并进行奇异值分解;最后根据所得奇异值构造一个离散概率分布并计算其信息熵作为图像置乱程度评价函数。实验结果表明,所提出的评价方法能够较好地刻画图像的置乱程度,反映了加密次数与置乱程度之间的关系,与人的视觉基本相符。而且对于不同的图像,该评价方法能在一定程度上反映所用的置乱变换在各置乱阶段的效果。     

A content-based image authentication scheme based on singular value decomposition

In this paper, we propose an image authentication scheme in which image features are embedded for copyright protection and content-tampering detection. The features are based on the invariance of the relationship among SVD coefficients. The proposed method is sensitive to malicious manipulations and robust to lossy compressions or regular image operations, such as brightening, shifting, averaging, rotation, and so on. Several experiments demonstrated that the proposed scheme could efficiently detect locations which have been tampered with and effectively resist several types of attacks. Moreover, stego images based on our proposed method have high visual quality. The text was submitted by the authors in English. Tzu-Chuen Lu received the B.M. degree (1999) and MSIM degree (2001) in information management from Chaoyang University of Technology, Taiwan. She received her Ph.D. degree (2006) in computer engineering from National Chung Cheng University. Her current title is an Assistant Professor in Departament of Information Management from Chaoyang University of Technology. Her current research interests include data mining, image retrieval, image authentication, information hiding, and knowledge management. Chin-Chen Chang received his B.S. degree in applied mathematics in 1977 and the M.S. degree in computer and decision sciences in 1979, both from the National Tsing Hua University, Hsinchu, Taiwan. He received his Ph.D. in computer engineering in 1982 from the National Chiao Tung University, Hsinchu, Taiwan. From August 1995 to October 1997, he was the provost at the National Chung Cheng University. From September 1996 to October 1997, Dr. Chang was the Acting President at the Nationa Chung Cheng University. From July 1998 to June 2000, he was a director of the Ministry of Education of China. In addition, he has served as a consultant to several research institutes and government departments. His current research interests include database design, computer cryptography, image compression and data structures. Yi-Long Liu received the B.S. degree (2002) in the Department of Mathematics (Applied Mathematics Section) from the College of Science and Engineering at Fu-Jen Catholic University, Taiwan. Liu is now a Master student in National Chung Cheng University and is studying in the domain of image processing. His current research interests include data hiding, data compression, and progressive image transmission.     

Adding and subtracting eigenspaces with eigenvalue decomposition and singular value decomposition

This paper provides algorithms for adding and subtracting eigenspaces, thus allowing for incremental updating and downdating of data models. Importantly, and unlike previous work, we keep an accurate track of the mean of the data, which allows our methods to be used in classification applications. The result of adding eigenspaces, each made from a set of data, is an approximation to that which would obtain were the sets of data taken together. Subtracting eigenspaces yields a result approximating that which would obtain were a subset of data used. Using our algorithms, it is possible to perform ‘arithmetic’ on eigenspaces without reference to the original data. Eigenspaces can be constructed using either eigenvalue decomposition (EVD) or singular value decomposition (SVD). We provide addition operators for both methods, but subtraction for EVD only, arguing there is no closed-form solution for SVD. The methods and discussion surrounding SVD provide the principle novelty in this paper. We illustrate the use of our algorithms in three generic applications, including the dynamic construction of Gaussian mixture models.     

基于奇异值分解的彩色图像水印算法

针对基于量化的嵌入方法不能抵抗亮度增强等攻击而基于关系的嵌入方法抵抗常见的攻击能力较弱等缺点, 提出了一种混合量化和关系嵌入方法的彩色图像水印算法。该算法先对彩色图像的每一分量进行互不重叠的大小为8×8的分块, 借助密钥选取待嵌入水印的分块并对选取的分块进行1级离散小波变换和分别对低频子带与高频子带进行奇异值分解, 在低频和高频子带奇异值分解后的奇异值矩阵分别采用量化和关系的嵌入策略嵌入预处理后的水印。实验表明, 该算法实现简单, 具有较好的不可见性。与其他算法相比, 该算法具有更好的鲁棒性能。     

基于复小波域奇异值分解的自适应图像水印

将双树复小波分解的多方向性扣冗余性与奇异值稳定性结合,提出一种新的盲检测数字水印方案.该方案将水印嵌入图像双树复小波分解后各子带系数的分块奇异值中,块长可动态调整.为避免产生块状效应.使用统计学模型来自适应调整量化参数,改善了水印图像的不可感知性和安全性.实验表明,该方案对于通常的几何攻击具有鲁棒性,对JPEG压缩攻击性能较稳定,并有效提高了水印的容量.     

一种基于四叉树分解的图像压缩方法

在信息社会高度发展的今天,图像成为可以传递信息的重要载体之一。由于未经处理的图像信息量非常大,大力研究和开发图像压缩编码技术就非常重要。论文主要探讨对于存在连续阴影或者大量连续相同像素的图像压缩,通过分析RLE算法的不足,提出了一种基于四叉树分解的图像压缩方法,实验表明运用这种方法实现静态图像压缩可以使压缩效率得到进一步的提高,该方法为实现静态图像压缩开辟了新的思路和途径。     

Network traffic analysis using singular value decomposition and multiscale transforms

The present work integrates the multiscale transform provided by the wavelets and singular value decomposition (SVD) for the detection of anomaly in self-similar network data. The algorithm proposed in this paper uses the properties of singular value decomposition (SVD) of a matrix whose elements are local energies of wavelet coefficients at different scales. Unlike existing techniques, our method determines both the presence (i.e., the time intervals in which anomaly occurs) and the nature of anomaly (i.e., anomaly of bursty type, long or short duration, etc.) in network data. It uses the diagonal, left and right singular matrices obtained in SVD to determine the number of scales of self-similarity, location and scales of anomaly in data, respectively. Our simulation work on different data sets demonstrates that the method performs better than the existing anomaly detection methods proposed for self-similar data.     

Approximate factorization of multivariate polynomials using singular value decomposition

We describe the design, implementation and experimental evaluation of new algorithms for computing the approximate factorization of multivariate polynomials with complex coefficients that contain numerical noise. Our algorithms are based on a generalization of the differential forms introduced by W. Ruppert and S. Gao to many variables, and use singular value decomposition or structured total least squares approximation and Gauss–Newton optimization to numerically compute the approximate multivariate factors. We demonstrate on a large set of benchmark polynomials that our algorithms efficiently yield approximate factorizations within the coefficient noise even when the relative error in the input is substantial (10⁻³).     

Rapid distributed model predictive control design using singular value decomposition for linear systems

The issue of model predictive control design of distribution systems using a popular singular value decomposition (SVD) technique is addressed. Namely, projection to a set of conjugate structure is dealt with in this paper. The structure of the resulting predictive model is decomposed into small sets of subsystems. The optimal inputs can be separately designed at each subsystem in parallel without any interaction problems. The optimal inputs can be directly obtained and the communication among the subsystems can be significantly reduced. In addition, the design of distribution model predictive control (DMPC) with constraints using the SVD framework is also presented. The unconstraint inputs are checked in parallel in the conjugate space. Without solving the QP problem of each subsystem, the suboptimal solution can be quickly obtained by selecting the bigger singular values and discarding the small singular values in the singular value space. The convergence condition of the proposed algorithm is also proved. Two case studies are used to illustrate the distribution control systems using the suggested approach. Comparisons between the centralized model predictive control method and the proposed DMPC method are carried out to show the advantages of the newly proposed method.     

双正交提升小波和奇异值分解的彩色水印算法研究

在现有彩色图像水印提取技术基础上, 提出一种结合9/7双正交提升小波和图像矩阵奇异值分解的彩色图像水印加密算法。首先将彩色原始图像和彩色水印图像R、G、B分离, 将图像相应分量进行提升小波三级分解得到低频部分, 并将该低频信息进行奇异值分解, 把水印信息视做扰动矩阵按一定的量加在低频信息的对角阵上, 其中彩色水印图像预处理结合了骑士巡游变换和Arnold置乱算法。实验结果表明算法在确保水印不可见性的基础上有效地增强了水印的强度和鲁棒性, 实现了水印图像的盲检验。     

Updating the partial singular value decomposition in latent semantic indexing

Latent semantic indexing (LSI) is a method of information retrieval (IR) that relies heavily on the partial singular value decomposition (PSVD) of the term-document matrix representation of a data set. Calculating the PSVD of large term-document matrices is computationally expensive; hence in the case where terms or documents are merely added to an existing data set, it is extremely beneficial to update the previously calculated PSVD to reflect the changes. It is shown how updating can be used in LSI to significantly reduce the computational cost of finding the PSVD without significantly impacting performance. Moreover, it is shown how the computational cost can be reduced further, again without impacting performance, through a combination of updating and folding-in.     

基于DWT和Tucker分解的超光谱图像压缩技术研究

由于超光谱图像（HSI）的大数据量,HSI压缩技术的研究近年来越来越受到关注。鉴于此,提出了一种基于离散小波变换（DWT）和Tucker分解的HSI压缩方法。充分利用HSI频域和空域的信息,对HSI频带的小波变换系数进行Tucker分解,先利用小波变换将HSI分解为不同的子图像,然后利用Tucker分解实现子图像的压缩;最后用实际的HSI对算法的有效性进行评估。与其他算法的比较结果表明该算法具有更好的性能;实验还显示了压缩HSI在监督分类方法中的作用。     

Context-based embedded image compression using binary wavelet transform

Binary wavelet transform (BWT) has several distinct advantages over the real wavelet transform (RWT), such as the conservation of alphabet size of wavelet coefficients, no quantization introduced during the transform and the simple Boolean operations involved. Thus, less coding passes are engaged and no sign bits are required in the compression of transformed coefficients. However, the use of BWT for the embedded grayscale image compression is not well established. This paper proposes a novel Context-based Binary Wavelet Transform Coding approach (CBWTC) that combines the BWT with a high-order context-based arithmetic coding scheme to embedded compression of grayscale images. In our CBWTC algorithm, BWT is applied to decorrelate the linear correlations among image coefficients without expansion of the alphabet size of symbols. In order to match up with the CBWTC algorithm, we employ the gray code representation (GCR) to remove the statistical dependencies among bi-level bitplane images and develop a combined arithmetic coding scheme. In the proposed combined arithmetic coding scheme, three highpass BWT coefficients at the same location are combined to form an octave symbol and then encoded with a ternary arithmetic coder. In this way, the compression performance of our CBWTC algorithm is improved in that it not only alleviate the degradation of predictability caused by the BWT, but also eliminate the correlation of BWT coefficients in the same level subbands. The conditional context of the CBWTC is properly modeled by exploiting the characteristics of the BWT as well as taking advantages of non-causal adaptive context modeling. Experimental results show that the average coding performance of the CBWTC is superior to that of the state-of-the-art grayscale image coders, and always outperforms the JBIG2 algorithm and other BWT-based binary coding technique for a set of test images with different characteristics and resolutions.     

An HVS-based adaptive coder for perceptually lossy image compression

In this paper a locally adaptive wavelet image coder is presented. It is based on an embedded human visual system model that exploits the space- and frequency-localization properties of wavelet decompositions for tuning the quantization step for each discrete wavelet transforms coefficient, according to the local properties of the image. A coarser quantization is performed in the areas of the image where the visibility of errors is reduced, thus decreasing the total bit rate without affecting the resulting visual quality. The size of the quantization step for each DWT coefficient is computed by taking into account the multiresolution structure of wavelet decompositions, so that there is no need for any side information to be sent to the decoder or for prediction mechanisms.Perceptually lossless as well as perceptually lossy compression is supported: the desired visual quality of the compressed image is set by means of a quality factor. Moreover, the technique for tuning the target visual quality allows the user to define arbitrarily shaped regions of interest and to set for each one a different quality factor.