Two Properties of SVD and Its Application in Data Hiding

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.

Block-wise reversible data hiding in encrypted domain using SVD

This paper concerns accurate computation of the singular value decomposition (SVD) of an $m\times n$ matrix $A$ . As is well known, cross-product matrix based SVD algorithms compute large singular values accurately but generally deliver poor small singular values. A new novel cross-product matrix based SVD method is proposed: (a) Use a backward stable algorithm to compute the eigenpairs of $A^{\rm T}A$ and take the square roots of the large eigenvalues of it as the large singular values of $A$ ; (b) form the Rayleigh quotient of $A^{\rm T}A$ with respect to the matrix consisting of the computed eigenvectors associated with the computed small eigenvalues of $A^{\rm T}A$ ; (c) compute the eigenvalues of the Rayleigh quotient and take the square roots of them as the small singular values of $A$ . A detailed quantitative error analysis is conducted on the method. It is proved that if small singular values are well separated from the large ones then the method can compute the small ones accurately up to the order of the unit roundoff $\epsilon$ . An algorithm is developed that is not only cheaper than the standard Golub–Reinsch and Chan SVD algorithms but also can update or downdate a new SVD by adding or deleting a row and compute certain refined Ritz vectors for large matrix eigenproblems at very low cost. Several variants of the algorithm are proposed that compute some or all parts of the SVD. Typical numerical examples confirm the high accuracy of our algorithm.

The security of information exchange is very important on the network. Authentication and information hiding have also become important issues. Information hiding techniques are acquiring an increasing importance due to the widespread diffusion of multimedia contents. The aim of this chapter is to focus on the Singular Value Decomposition (SVD) transform, with the aim of providing an exhaustive overview on those steganography, image cryptography and watermarking techniques leveraging on the important properties of such a transform. Despite the attention it has received in the last years, SVD in image processing and security is still in its infancy. Many SVD characteristics are still unutilized in image processing. In this chapter the author tries to highlight the basic properties of SVD and some of their applications in the field of security to encourage researchers to discover more about SVD properties which are not yet utilized.

In this article, we have improved the quantitative inversion performance of the cross-correlated contrast source inversion (CC-CSI) method by incorporating the subspace optimization strategy. The proposed method is called the cross-correlated subspace optimization method (CC-SOM). Meanwhile, multifrequency data are used to improve the inversion performance of high-contrast scatterers, where the L-curve method is introduced to select the regularization parameters of each frequency point without relying on experience. Finally, a fast algorithm is implemented by using the property of singular value decomposition (SVD) to simplify the large-scale matrix, and the fast Fourier transform (FFT) to accelerate the calculation. Synthetic and experimental inversion results demonstrate that both CC-SOM and CC-CSI show better robustness than SOM. In comparison to CC-CSI, CC-SOM is superior in terms of inversion accuracy when the regularization parameters have been appropriately selected. However, these advantages come at the cost of higher computational complexity.

Author profiling is a challenging task that consists of identifying a person’s relevant attributes based on the content he/she generates. In this article, we validate a classification method based on the reconstructive classification to identify two demographic attributes, age and gender, for users of social networks based on the text content they publish. For the problem, we consider balanced and unbalanced data, where a gender or age group has a larger presence than the others. The proposed method is based on using the reconstructive property of singular value decomposition (SVD), and its suitability to work with sparse data, to find a matrix with the main latent components to represent the information of specific gender or age classes. Afterward, we use such a matrix to project and reconstruct new users’ information to identify their demographic variables. We test our method with a set of datasets in several languages collected from Twitter and Pinterest users, and we use different evaluation metrics to compare their performance with the ones of several popular classifiers based on traditional machine learning, and on deep learning, and with some relevant works in the literature. The results show that the proposed classifier performs generally well in identifying the age and gender of users in social networks.

We propose a technique for video shot segmentation and classification based on singular value decomposition (SVD). For the input video sequence, we create a feature-frame matrix A, and perform the SVD on it. From this SVD, we are able to not only derive the refined feature space to better segment the video sequence along the time axis, but also define metrics to enable classifications of the detected video shots. Using these SVD properties, we achieve the two goals of accurate video shot segmentation, and visual content-based shot classification at the same time.

In view of the fact that the random noise interferes with the characteristic extraction of a rolling bearing fault signal, a new method of fault feature extraction is proposed based on the combination of the generalized S transform and singular value decomposition (SVD). Firstly, the 2D time–frequency spectrum bearing fault signal is obtained by applying the generalized S transform, and the time–frequency spectrum matrix is used as the objective matrix of SVD to solve the singular values. Then the K-means clustering algorithm is used to classify the singular value sequence, and the singular values for reconstruction are determined. Finally, the de-noised matrix is carried out the generalized S inversion transform to get the de-noised fault signal, and the power spectrum is calculated to finish the fault diagnosis. By analyzing the simulated signal and the actual bearing fault data, results show that the proposed method can effectively identify typical faults of rolling bearings and improve the diagnosis effect of rolling bearing faults. And it provides a new way to realize the fault diagnosis of rolling bearings under noise.

When seismic waves encounter abrupt points of stratum or lithology in the process of propagation, such as fault edges, pinch-out points, or the protrusion of unconformity surfaces, the Snell law will break down and many diffractions will be generated. However, the diffraction information is typically masked by strong reflections; thus, separating diffractions is one key issue for diffraction imaging. The traditional singular value decomposition (SVD) method with the ability for wavefield decomposition and reconstruction is useful in removing strong reflections of large singular values. However, the continuously changing characteristics of the singular value of steep-slope reflections make it difficult to choose a suitable parameter for separating diffractions. To solve the problem of singular value selection in diffractions reconstruction by the SVD method, we have developed a Cook-distance SVD method by mathematically least-squares measuring the contribution of every singular value. The Cook-distance SVD can amplify the difference between continuously changing singular values and easily find the singular values representing diffractions. Synthetic examples and field data applications demonstrate that our Cook-distance SVD method can avoid parameter testing and has good performance in diffraction separation and can highlight reservoir-involved small-scale geologic edges and scatterers.

Modern deep neural networks (DNNs) often require high memory consumption and large computational loads. In order to deploy DNN algorithms efficiently on edge or mobile devices, a series of DNN compression algorithms have been explored, including factorization methods. Factorization methods approximate the weight matrix of a DNN layer with the multiplication of two or multiple low-rank matrices. However, it is hard to measure the ranks of DNN layers during the training process. Previous works mainly induce low-rank through implicit approximations or via costly singular value decomposition (SVD) process on every training step. The former approach usually induces a high accuracy loss while the latter has a low efficiency. In this work, we propose SVD training, the first method to explicitly achieve low-rank DNNs during training without applying SVD on every step. SVD training first decomposes each layer into the form of its full-rank SVD, then performs training directly on the decomposed weights. We add orthogonality regularization to the singular vectors, which ensure the valid form of SVD and avoid gradient vanishing/exploding. Low-rank is encouraged by applying sparsity-inducing regularizers on the singular values of each layer. Singular value pruning is applied at the end to explicitly reach a low-rank model. We empirically show that SVD training can significantly reduce the rank of DNN layers and achieve higher reduction on computation load under the same accuracy, comparing to not only previous factorization methods but also state-of-the-art filter pruning methods.

We monitored the occupancy of a functionally important non-coordinated water molecule in the distal heme pocket of sperm whale myoglobin over the pH range 4.3-9.4. Water occupancy was assessed by using time-resolved spectroscopy to detect the perturbation of the heme visible band absorption spectrum caused by water entry after CO photodissociation ( Goldbeck, R. A., Bhaskaran, S., Ortega, C., Mendoza, J. L., Olson, J. S., Soman, J., Kliger, D. S., and Esquerra, R. M. (2006) Proc. Natl. Acad. Sci. U. S. A. 103, 1254-1259 ). We found that the water occupancy observed during the time interval between ligand photolysis and diffusive recombination decreased by nearly 20% as the pH was lowered below 6. This decrease accounted for most of the concomitant increase in the observed CO bimolecular recombination rate constant, as the lower water occupancy presented a smaller kinetic barrier to CO entry into the pocket at lower pH. These results were consistent with a model in which the distal histidine, which stabilizes the water molecule within the distal pocket by accepting a hydrogen bond, tends to swing out of the pocket upon protonation and destabilize the water occupancy at low pH. Extrapolation of this model to lower pH suggests that the additional increase in ligand association rate constant observed previously in stopped-flow studies at pH 3 may also be due in part to reduced distal water occupancy concomitant with further His64 protonation and coupled protein conformational change.

Matrix factorization plays an important role in scientific computation. The widely used one is singular value decomposition (SVD) which approximates the original data matrix with three lower rank matrices with orthogonality constraints. Recently nonnegative matrix factorization (NMF) considering the nonnegativity of data makes the results more interpretable than those of SVD. However NMF finds only two factor matrices and there is no significant index as singular values of SVD which can be used for sorting learned basis vectors. In this paper we take into account the nonnegativity for SVD and propose nonnegative SVD (NNSVD). The preliminary results on the microarray data of spermatogenesis show that NNSVD has advantages of both SVD and NMF.

Blood flow visualization is a challenging task in the presence of tissue motion. Conventional clutter filtering techniques perform poorly since blood and tissue clutter echoes share similar spectral characteristics. Thus, unsuppressed tissue clutter produces flashing artefacts in ultrasound color flow images. Eigen-based filtering was recently introduced and has shown good clutter rejection performance; however, there is yet no standard approach to robustly determine the eigen components corresponding to tissue clutter. To address this issue, we propose a novel 3D clustering based singular value decomposition (SVD) clutter filtering method. The proposed technique makes use of three key spatiotemporal statistics: singular value magnitude, spatial correlation and the mean Doppler frequency of singular vectors to adaptively determine the clutter and noise clusters and their corresponding eigen rank to achieve maximal clutter and noise suppression. To test the clutter rejection performance of the proposed filter, high frame rate plane wave data was acquired in-vivo from a subject’s common carotid artery and jugular vein region induced with extrinsic tissue motion (voluntary probe motion). The flow detection efficacy of the clustering based SVD filter was statistically evaluated and compared with current eigen rank estimation methods using the receiver operating characteristic (ROC) analysis. Results show that the clustering based SVD filter yielded the highest area under the ROC curve (0.9082) in comparison with other eigen rank estimation methods, signifying its improved flow detection capability.

One key aspect of local fault diagnosis is how to effectively extract abrupt features from the vibration signals. This paper proposes a method to automatically extract abrupt information based on singular value decomposition and higher-order statistics. In order to observe the distribution law of singular values, a numerical analysis to simulate the noise, periodic signal, abrupt signal and singular value distribution is conducted. Based on higher-order statistics and spectrum analysis, a method to automatically choose the upper and lower borders of the singular value interval reflecting the abrupt information is built. And the selected singular values derived from this method are used to reconstruct abrupt signals. It is proven that the method is able to obtain accurate results by processing the rub-impact fault signal measured from the experiments. The analytical and experimental results indicate that the proposed method is feasible for automatically extracting abrupt information caused by faults like the rotor–stator rub-impact.

A fast-convergence singular value decomposition (SVD) algorithm is developed for tracking time-varying channels in massive MIMO precoding/beamforming systems. Since only strong eigen-modes are selected for data transmission in these systems, our SVD algorithm exploits the properties of partial decomposition and temporal correlation. Besides, the proposed self-adjusting inverse power method can achieve fast convergence by modifying the shift according to the intermediate result during each iteration. Furthermore, the singular vectors and values of the desired eigenmodes can be computed simultaneously. Thus, parallel processing is possible to facilitate high-throughput implementation. Compared to the self-power method with super linear convergence, the self-adjusting inverse power method has better convergence and lower complexity. Good channel tracking capability is also demonstrated.