Properties Of Singular Value Decomposition Research Articles

Robust blind image watermarking scheme based on Redundant Discrete Wavelet Transform and Singular Value Decomposition

Copyright protection and proof of ownership are two of the main important applications of the digital image watermarking. The challenges faced by researchers interested in digital image watermarking applications lie in the creation of new algorithms to serve those applications and to be resistant to most types of attacks, especially the geometrical attacks. Robustness, high imperceptibility, security, and large capacity are four essential requirements in any watermarking scheme. This paper presents a new image watermarking scheme based on the Redundant Discrete Wavelet Transform (RDWT) and the Singular Value Decomposition (SVD). The gray scale image watermark was embedded directly in the singular values of the RDWT sub-bands of the host image. The scheme achieved a large capacity due to the redundancy in the RDWT domain and at the same time preserved high imperceptibility due to SVD properties. Embedding the watermarking pixel's values without any modification inside the wavelet coefficient of the host image overcomes the security issue. Furthermore, the experimental results of the proposed scheme showed a high level of robustness not only against the image processing attacks but also against the geometrical attacks which are considered as difficult attacks to resist.

Digital Watermark Based on W-SVD Method in Copyright Protection of E-Service

Abstract In order to solve digital products copyright problem, this paper uses the good mathematical properties of singular value decomposition and combines with two-dimensional wavelet decomposition, chaotic Logistic sequence and template scrambling to product a high security digital watermark. The statistic analysis indicates this method has good security and robust, which can be used widely in the e-service area.

SVD Based Image Processing Applications: State of The Art, Contributions and Research Challenges

Singular Value Decomposition (SVD) has recently emerged as a new paradigm for processing different types of images. SVD is an attractive algebraic transform for image processing applications. The paper proposes an experimental survey for the SVD as an efficient transform in image processing applications. Despite the well known fact that SVD offers attractive properties in imaging, the exploring of using its properties in various image applications is currently at its infancy. Since the SVD has many attractive properties have not been utilized, this paper contributes in using these generous properties in newly image applications and gives a highly recommendation for more research challenges. In this paper, the SVD properties for images are experimentally presented to be utilized in developing new SVD-based image processing applications. The paper offers survey on the developed SVD based image applications. The paper also proposes some new contributions that were originated from SVD properties analysis in different image processing. The aim of this paper is to provide a better understanding of the SVD in image processing and identify important various applications and open research directions in this increasingly important area; SVD based image processing in the future research.

A New Singular Value Decomposition Based Robust Graphical Clustering Technique and Its Application in Climatic Data

An attempt is made to study mathematical properties of singular value decomposition (SVD) and its data exploring capacity and to apply them to make exploratory type clustering for 10 climatic variables and thirty weather stations in Bangladesh using a newly developed graphical technique. Findings in SVD and Robust singular value decomposition (RSVD) based graphs are compared with that of classical K-means cluster analysis, its robust version, partition by medoids (PAM) and classical factor analysis, and the comparison clearly demonstrates the advantage of SVD over its competitors. Lastly the method is tested on well known Hawkins-Bradu-Kass (1984) data.

SVD properties of orthogonal two-channel filter banks

We study the Singular Value Decomposition (SVD) of the three building blocks of the matrix representation of two-channel orthogonal filter banks. We show the highly structured decomposition of these blocks and derive their mutual relations. We give examples to exploit the SVD properties in the implementation and design of orthogonal filter banks and wavelets.

A digital watermarking scheme based on singular value decomposition and tiny genetic algorithm

A robust digital image watermarking scheme based on singular value decomposition (SVD) and a tiny genetic algorithm (Tiny-GA) is proposed in this paper. Previous works have shown that both one-way and non-symmetric properties of SVD make it desirable for watermarking techniques. The produced singular values are very stable and vary very little under various image processing operations or attacks. In the proposed scheme, the singular values of a cover image are modified by multiple scale factors to embed the watermark image. Since the values of scale factors determine the watermark strength; therefore, we use the Tiny-GA to search the proper values in order to improve the visual quality of the watermarked image and the robustness of the watermark. Experimental results demonstrate that our scheme is able to withstand a variety of image processing attacks.

Contrast enhancement of x-ray image based on singular value selection

Low-contrast profile images are frequently encountered in medical practice, and the correct interpretation of these images is of vital importance. This study introduces a contrast enhancement technique based on singular value decomposition (SVD) to enhance low-contrast fracture x-ray images. We propose a development of the traditional singular value solution by applying a feature selection process on the extracted singular values. The proposal calls for the establishment of a feature space in which the interpretability or perception of information in images for human viewers is enhanced, while noise and blurring are reduced. In this approach, the area of interest is manually cropped, and histogram equalization (HE) and singular value selection procedures are then conducted for comparative study. This approach exploits the spectral property of SVD, and the singular value selection algorithm is developed based on the corresponding Fourier domain technique for high frequency enhancement. The proposed method can generate more enhanced views of the target images than HE processing. Ten physicians confirm the performance of the proposed model using the visual analog scale (VAS). The average VAS score improves from 2.5 with HE to 8.3 using the proposed method. Experimental results indicate that the proposed method is helpful in fracture x-ray image processing.

Applications of singular value decomposition in structural optimisation

AbstractThe usage of the singular value decomposition (SVD) in scope of structural optimisation is motivated. We briefly outline several applications of SVD from different scientific fields to point out their similarities with structural optimisation. Here, our focus is on model reduction, on numerical defects and on their quantitative description using SVD. In this context we address the singular value decomposition of matrices which appear in an optimisation algorithm, i.e. the pseudo load matrix and the sensitivity matrix. In this contribution on the example of topology optimisation we would like to clarify all the properties of SVD. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

Real-time classification of variable length multi-attribute motions

Multi-attribute motion data can be generated in many applications/ devices, such as motion capture devices and animations. It can have dozens of attributes, thousands of rows, and even similar motions can have different durations and different speeds at corresponding parts. There are no row-to-row correspondences between data matrices of two motions. To be classified and recognized, multi-attribute motion data of different lengths are reduced to feature vectors by using the properties of singular value decomposition (SVD) of motion data. The reduced feature vectors of similar motions are close to each other, while reduced feature vectors are different from each other if their motions are different. By applying support vector machines (SVM) to the feature vectors, we efficiently classify and recognize real-world multi-attribute motion data. With our data set of more than 300 motions with different lengths and variations, SVM outperforms classification by related similarity measures, in terms of accuracy and CPU time. The performance of our approach shows its feasibility of real-time applications to real-world data.

COMBINING EXTREMAL OPTIMIZATION WITH SINGULAR VALUE DECOMPOSITION FOR EFFECTIVE POINT MATCHING

Feature point matching is a key step for most problems in computer vision. It is an ill-posed problem and suffers from combinatorial complexity which becomes even more critical with the increase in data and the presence of outliers. The work covered in this paper describes a new framework to solve this problem in order to achieve robust registration of two feature point sets assumed to be available. This framework combines the use of extremal optimization heuristic with a clever startup routine which exploits some properties of singular value decomposition. The role of the latter is to produce an interesting matching configuration whereas the role of the former is to refine the initial matching by generating hypothetical matches and outliers using a far-from-equilibrium based stochastic rule. Experiments on a wide range of real data have shown the effectiveness of the proposed method and its ability to achieve reliable feature point matching.

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.

Singular value decomposition analysis of protein sequence alignment score data.

One of the standard tools for the analysis of data arranged in matrix form is singular value decomposition (SVD). Few applications to genomic data have been reported to date mainly for the analysis of gene expression microarray data. We review SVD properties, examine mathematical terms and assumptions implicit in the SVD formalism, and show that SVD can be applied to the analysis of matrices representing pairwise alignment scores between large sets of protein sequences. In particular, we illustrate SVD capabilities for data dimension reduction and for clustering protein sequences. A comparison is performed between SVD-generated clusters of proteins and annotation reported in the SWISS-PROT Database for a set of protein sequences forming the calycin superfamily, entailing all entries corresponding to the lipocalin, cytosolic fatty acid-binding protein, and avidin-streptavidin Prosite patterns.

Some properties of singular value decomposition and their applications to digital signal processing

Singular value decomposition (SVD), one of the most basic and important tools of numerical linear algebra, is finding increasing applications in digital signal processing. In this paper, we first review some basic properties of SVD for matrices and then for linear operators between two Hilbert spaces. While SVD results for matrices are quite well known, applications of SVD on operators are less well known. Specifically, we propose the use of a representation for a stochastic linear system from the point of view of a stochastic SVD and show its relationship to the classical Karhunen-Loève expansion. Furthermore, issues related to practical use of time-averaging of realizations of random processes from the SVD point of view are also considered. Then algorithms for performing SVD are briefly discussed. These include the well known QR method, the modified Jacobi method of Nash, and an extension of the modified Jacobi method applicable to SVD of linear operators. Finally, we review various applications of finite rank approximation properties of SVD to digital signal processing problems in least-squares estimations, complexity reduction of FIR digital filters, matrix rank and system order determinations, and digital image processing.

Improvement of Lesion Detection in Scintigraphic Images by SVD Techniques for Resolution Recovery

The properties of singular value decomposition (SVD) are used to implement an SVD spatial domain pseudoinverse restoration filter. This type of filter is attractive for poor imaging conditions (low spatial resolution, high image noise) and is thus appealing for nuclear medicine images. The method might offer some advantages over more traditional frequency domain filter techniques since the restoration is performed on a local rather than global basis. High-contrast thyroid phantom images collected at different count densities and low-contrast liver phantom images were processed with the SVD filter. Restored images yielded improved spatial resolution, lesion contrast, and signal-to-noise ratio. The SVD pseudoinverse restoration filter implemented as an interactive process permits the operator to terminate filtering at a stage where the visually "best" image is obtained compared to the original data. Processed images suggest that the technique may have potential for improving lesion detection in nuclear medicine.