Two-dimensional Singular Value Decomposition Research Articles

Eigenwave analysis of vortex-induced vibrations on long cylinders in sheared flows

The vortex-induced vibration of long cylinders in sheared flows is usually a mixture of standing and traveling waves. Understanding how the waveform is developed is of significant scientific and engineering interest. However, the interference between the traveling wave components makes the response patterns hard to interpret. Therefore, a spatial–temporal domain decomposition may offer a new perspective for the problem. This paper presents an eigenwave analysis method based on two-dimensional singular value decomposition, aiming to discover the hidden spatial–temporal modes. The application to experimental data shows its capability to separate the traveling and standing wave components, revealing the alternating dominance of these two waveforms along the span. It can also decompose the motion into two intrinsic traveling waves propagating in opposite directions, evolving and interacting in space and time. Based on the amplitude profiles of these waves, we locate the power-in/out regions and evaluate the lock-in range of reduced velocity as 4.73 to 7.68. It also reveals that the varying phase difference between multi-frequency modes, instead of the mode transition, is the main reason for the envelope fluctuation. The findings suggest that the proposed method is a useful data-driven technique extending the current toolkit for research on related topics.

Unsupervised anomaly detection via two-dimensional singular value decomposition and subspace reconstruction for multivariate time series

Unsupervised anomaly detection via two-dimensional singular value decomposition and subspace reconstruction for multivariate time series

A secure dual-color image watermarking scheme based 2D DWT, SVD and Chaotic map

A secure dual-color image watermarking scheme based 2D DWT, SVD and Chaotic map

Pattern recognition in multilinear space and its applications: mathematics, computational algorithms and numerical validations

We clarify the mathematical equivalence between low-dimensional singular value decomposition and low-order tensor principal component analysis for two- and three-dimensional images. Furthermore, we show that the two- and three-dimensional discrete cosine transforms are, respectively, acceptable approximations to two- and three-dimensional singular value decomposition and classical principal component analysis. Moreover, for the practical computation in two-dimensional singular value decomposition, we introduce the marginal eigenvector method, which was proposed for image compression. For three-dimensional singular value decomposition, we also show an iterative algorithm. To evaluate the performances of the marginal eigenvector method and two-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for six datasets of two-dimensional image patterns. To evaluate the performances of the iterative algorithm and three-dimensional discrete cosine transform for dimension reduction, we compute recognition rates for datasets of gait patterns and human organs. For two- and three-dimensional images, the two- and three-dimensional discrete cosine transforms give almost the same recognition rates as the marginal eigenvector method and iterative algorithm, respectively.

A Survey on Low-Complexity Video Coding Methods and Architectures

Traditional video coding methods are able to achieve wonderful performance improvements in data compression. However, these methods have high computational complexity and hardware resource consumption, which are not suitable for some applications, such as wireless multi-media sensor network (WMSN) where low complexity video coding (LCVC) methods are modern technologies. In this survey, some typical LCVC methods are explored, including the cropping and improving of the traditional video encoder, Distributed Video Coding (DVC), Compressive Sensing (CS) video encoder, Underdetermined Blind Signal Separation (UBSS) and Two-Dimensional Singular Value Decomposition (2-D SVD) based video encoder. These technologies could obtain better trade-off between high compression ratio and well reconstructed video quality with lower encoding complexity. Moreover, some known architectures of the mentioned LCVC methods are analyzed, as well as the brief performance analysis and comparison. Finally, some applications of low complexity video coding are described, such as wireless video surveillance system and mobile video equipment. Keywords: Applications, compressive sensing, distributed video coding, low complexity, modification of traditional video coding methods, underdetermined blind signal separation, video coding, 2-D singular value decomposition.

Low-Complexity Video Coding Based on Two-Dimensional Singular Value Decomposition

In this paper, we propose a low-complexity video coding scheme based upon 2-D singular value decomposition (2-D SVD), which exploits basic temporal correlation in visual signals without resorting to motion estimation (ME). By exploring the energy compaction property of 2-D SVD coefficient matrices, high coding efficiency is achieved. The proposed scheme is for the better compromise of computational complexity and temporal redundancy reduction, i.e., compared with the existing video coding methods. In addition, the problems caused by frame decoding dependence in hybrid video coding, such as unavailability of random access, are avoided. The comparison of the proposed 2-D SVD coding scheme with the existing relevant non-ME-based low-complexity codecs shows its advantages and potential in applications.

145 Right ventricular function assessment in PAH patients: a two-dimensional strain and three-dimensional echocardiographic study

Right ventricular (RV) function has major prognostic implications for pulmonary arterial hypertension (PAH). RV function assessment by echocardiography is challenging in PAH patients. New techniques such as two-dimensional strain (2DS) and three dimension (3D) echocardiography may allow assessment of RV function. We sought to determine among echocardiographic techniques – those widely used, 2DS and 3D – which one was the best correlated to magnetic resonance imaging (MRI) measurements. Fourteen patients with PAH (mean age 58 +/- 17 yr, 7 women) were evaluated. RV fractional area change (RVFAC), Tei index, peak systolic velocity (S), Tricuspid Annular Plane Systolic Excursion (TAPSE) were measured. Global and segmental RV longitudinal deformations were recorded by 2DS echocardiography from 4 apical-chamber views using 6 segments RV model. Echocardiographic system designed for 3D was Tomtec. TAPSE, peak S and RVFAC were lower in PAH patients than control and correlated to MRI (p < 0.005). Global and free wall strain measured by 2DS and ejection fraction VD (FEVD) by MRI (r = 0.73; p< 0.005) were inversely correlated. The 3D volume and 3D FEVD were strongly correlated to corresponding measurements obtained by MRI (volume: r = 0.88; p < 0.005) (FE: r = 0.85; p<0.005). Both 2DS and 3D echocardiography techniques are strongly correlated to MRI. Simple and reliable 2DS could be preferred to 3D.

Classification of multivariate time series using two-dimensional singular value decomposition

Multivariate time series (MTS) are used in very broad areas such as multimedia, medicine, finance and speech recognition. A new approach for MTS classification using two-dimensional singular value decomposition (2dSVD) is proposed. 2dSVD is an extension of standard SVD, it captures explicitly the two-dimensional nature of MTS samples. The eigenvectors of row–row and column–column covariance matrices of MTS samples are computed for feature extraction. After the feature matrix is obtained for each MTS sample, one-nearest-neighbor classifier is used for MTS classification. Experimental results performed on five real-world datasets demonstrate the effectiveness of our proposed approach.