Use Of Singular Value Decomposition Research Articles

Multiscale SVD entropy for the analysis of gait dynamics

This work explores the use of singular value decomposition (SVD) entropy to characterize the complexity of stride interval sequences from gait dynamics. The computation of the approximate (ApEn) and sample (SampEn) entropies require the specification of the length of the scrutinized patterns (m) and the pattern similarity tolerance (r). In contrast, the SVD entropy estimation does not require these parameters since the computations are based on the inspection of similarities among lagged vectors. In this regard, the present work aims to assess the SVD entropy to characterize gait dynamics. The gait maturation and the neurodegenerative disease (NDD) datasets from Physionet were considered. The SVDEn of the gait dynamics decreased with the age to normalized values of about 0.2. In contrast, the SampEn, which was used for comparison, decreased to values close to zero. For the gait NDD dataset, it was found that the gait dynamics of Parkinson, ASL and Huntington pathologies exhibit increased SVDEn relative to a control group, with normalized values of about 0.2 and 0.4, respectively. However, the SVDEn and the SampEn were unable to distinguish between the control and neurodisease groups (p < 0.05). Overall, the results indicated that the gait dynamics of the NDD are less regular than that of the control group. Although the SVDEn and other entropy metrics (e.g., SampEn) showed similar results, the SVDEn offers the advantage that the computation require the specification of only the scale parameter.

Uncertainty qualification in evaluating dynamic and static stress intensity factors using SBFEM based on model order reduction

This paper presents a novel framework for Monte Carlo simulation (MCs) of dynamic and static fracture problems. The stress intensity factors can be directly extracted by using polygon scaled boundary finite element method (SBFEM) to analyze dynamic and static fracture problems. Uncertainty qualification analysis focuses on the output uncertainty caused by the uncertainty of system input. MCs is considered as a general tool to solve complex multi-dimensional uncertainty problems because of its simplicity and directness. However, its applicability is hindered due to the huge calculating cost. The use of singular value decomposition (SVD) and radial basis function (RBF) can reduce the computational cost, improve the computational efficiency, and realize the rapid uncertainty qualification analysis based on MCs. Considering the influence of uncertainty of structural material property parameters and structural shape parameters on the calculation results, MCs is used to analyze the statistical characteristics of structural response under random variables. Finally, several examples are given to verify the correctness and effectiveness of the algorithm.

Adaptive noise reduction for power Doppler imaging using SVD filtering in the channel domain and coherence weighting of pixels

Objective. Ultrafast power Doppler (UPD) is an ultrasound method that can image blood flow at several thousands of frames per second. In particular, the high number of data provided by UPD enables the use of singular value decomposition (SVD) as a clutter filter for suppressing tissue signal. Notably, is has been demonstrated in various applications that SVD filtering increases significantly the sensitivity of UPD to microvascular flows. However, UPD is subjected to significant depth-dependent electronic noise and an optimal denoising approach is still being sought. Approach. In this study, we propose a new denoising method for UPD imaging: the Coherence Factor Mask (CFM). This filter is first based on filtering the ultrasound time-delayed data using SVD in the channel domain to remove clutter signal. Then, a spatiotemporal coherence mask that exploits coherence information between channels for identifying noisy pixels is computed. The mask is finally applied to beamformed images to decrease electronic noise before forming the power Doppler image. We describe theoretically how to filter channel data using a single SVD. Then, we evaluate the efficiency of the CFM filter for denoising in vitro and in vivo images and compare its performances with standard UPD and with three existing denoising approaches. Main results. The CFM filter gives gains in signal-to-noise ratio and contrast-to-noise ratio of up to 22 dB and 20 dB, respectively, compared to standard UPD and globally outperforms existing methods for reducing electronic noise. Furthermore, the CFM filter has the advantage over existing approaches of being adaptive and highly efficient while not requiring a cut-off for discriminating noise and blood signals nor for determining an optimal coherence lag. Significance. The CFM filter has the potential to help establish UPD as a powerful modality for imaging microvascular flows.

On the use of singular value decomposition for QRS detection and ECG denoising

Abstract QRS detection is a pre-processing step to detect the heartbeat in an electrocardiogram (ECG) for subsequent rhythm classification. However, measured ECG waveforms may differ as a result of intrinsic variability or due to artefacts or noise. If the signals are distorted, then this often leads to difficulties in QRS detection. Of course, a high QRS detection performance is an important part of an ECG analysis algorithm, and furthermore, it must work even for highly noisy signals. Singular value decompositon (SVD) is the factorization of a matrix into the product three matrices. SVD allows us to find important components of data and, thus, can be used for dimension reduction or denoising. We introduce SVD based methods for QRS detection and ECG denoising, especially for short unknown signal segments, and show application results.

Array Gain Analyses of Single User MIMO in 5G NR PDSCH

In the last decade, Multiple-Input Multiple-Output (MIMO) algorithms have been developed for mobile communications networks to increase spectrum efficiency and reduce the transmitted power, which are also two of the main Key Performance Indicators of Fifth Generation New Radio (5G NR). Therefore, various MIMO algorithm are being researched for their suitability in 5G NR specifications. The objective of this study is to examine the performance gains achieved through the use of multiple transmit antennas and multiple receive antennas in 5G NR Physical Shared Downlink Channel (PDSCH). The study examines separately the array gains of Single-Input Multiple Output (SIMO) and Multiple-Input Single Output (MISO) then combines the transmitter and the receiver diversities in a MIMO system for 5G PDSCH. The array gains are achieved through precoding and combining vectors obtained by the use of Singular Value Decomposition (SVD). The results show that theoretical array gains are achieved in simulation environment.

Innovative Reactive Distillation Process for the Sustainable Purification of Lactic Acid

Lactic acid is commonly used in a wide range of fields, such as cosmetics, pharmaceutical products, chemistry, and food. During recent years, its use for new applications, such as the production of biodegradable and biocompatible polymers, green solvents, and oxygenated chemicals, have received considerable attention. However, the relatively high production cost of lactic acid hinders many large-scale applications. It is necessary to develop more efficient methods of separation and purification to cheapen lactic acid production processes. The main objective of this study is to investigate the use of process intensification, particularly the reactive distillation process, for a sustainable purification of lactic acid. To do so, there have been proposed, on the one hand, four intensified alternatives in which synthesis and design are based on thermal couplings and, on the other hand, three alternatives looking for water mass integration. Design and optimization of those modified configurations are carried out employing a stochastic optimization method, using as objective functions some metrics associated with the concept of sustainability (economics, environmental, and inherent safety indexes). A study on the dynamic performance of the configurations through the use of singular value decomposition is carried out in a complementary way. The results in the first redesign stage show improvements in all performance indexes. However, a great difference between the implementation of a thermal coupling that substitutes a condenser instead of a reboiler has been identified. The best scheme, based on a sustainability framework, resulted in a modified process, including a dividing wall column-based scheme.

Theoretical and computational improvements to the algebraic method for discovering cooperative rigid-unit modes

A linear-algebraic algorithm for identifying rigid-unit modes in networks of interconnected rigid units has recently been demonstrated. This article presents a series of enhancements to the original algorithm, which greatly improve its conceptual simplicity, numerical robustness, computational efficiency and interpretability. The improvements include the efficient isolation of constraints, the observation of variable-block separability, the use of singular value decomposition and a quantitative measure of solution inexactness.

On the denoising of structural vibration response records from low-cost sensors: a critical comparison and assessment

Due to the increasing quest of adopting low-cost sensors in structural health monitoring (SHM) processes, which may lead to detecting signals contaminated by significant levels of noise, the need to devise appropriate and effective denoising strategies, at the post-processing stage, is becoming more and more essential. Among several approaches proposed in the literature, it has been demonstrated that the employment of discrete wavelet transform (DWT) as a multi-rate filter bank, as well as the use of singular value decomposition (SVD), may result to be quite effective in signal denoising within various research fields, as biological, acoustic and mechanical. Here, DWT- and SVD-based denoising techniques are first independently reconsidered and reimplemented, aiming at exploring their optimal calibration in purifying noise-corrupted vibration response signals encountered in civil engineering applications. Then, a systematic performance evaluation is provided within a comparative framework, developed at an increasing level of noise affecting the measurements, in terms of noise-to-signal (N/S) ratio. In the study, two specific classes of synthetic response signals are first considered, namely earthquake and ambient vibration signals, since they may be assumed as representative of more general non-stationary and stationary signal typologies, respectively. To achieve a complete description of the clarified signal, strengths and weaknesses of the two denoising approaches are explored, in both time and frequency domains. The results prove the effectiveness of the analyzed implementations, especially in purifying seismic response signals, while some limitations may arise concerning the treatment of ambient vibration signals, in particular for the DWT-based denoising technique. Finally, a real case study is analyzed, where both denoising approaches are adapted and employed for clarifying acceleration signals detected on a modern short-span railway bridge, with rather satisfactory results, for both techniques.

Singular Value Decomposition (SVD) Berdasarkan Intensitas Pencahayaannya Untuk Pengenal Wajah

Singular Value Decomposition (SVD) is a method that can be used for biometric systems, where the biometric system is a system for identification by using physical features or human limbs such as fingerprints, eye retina, face, and others. This writing aims to recognize faces based on the intensity of their lighting using SVD. The use of SVD is done by forming the basis of a matrix (where this matrix is a collection of database faces (db)), then this base is used to transform the inputted image / face / db file and database files, then the results of this transformation the norm is calculated, if the minimum norm (db files and input files) is still within a certain tolerance the input file will be categorized as face / db file / ith person. The simulation results show that SVD can classify an image as a face or not with an accuracy of 94.7231% and a period of 35.2020 seconds for the recognition of 900 image files, a face image is a database or not of 68.4616% within 7.5480 seconds for the recognition of 650 face files, a The face images that are in the database are 90.7692% of the people in the 3,7340 seconds period for the introduction of 325 database files.

Improved anti-noise attack ability of image encryption algorithm using de-noising technique

Information security is considered as one of the important issues in the information age used to preserve the secret information through out transmissions in practical applications. With regard to image encryption, a lot of schemes related to information security were applied. Such approaches might be categorized into 2 domains; domain frequency and domain spatial. The presented work develops an encryption technique on the basis of conventional watermarking system with the use of singular value decomposition (SVD), discrete cosine transform (DCT), and discrete wavelet transform (DWT) together, the suggested DWT-DCT-SVD method has high robustness in comparison to the other conventional approaches and enhanced approach for having high robustness against Gaussian noise attacks with using denoising approach according to DWT. MSE in addition to the peak signal-to-noise ratio (PSNR) specified the performance measures which are the base of this study’s results, as they are showing that the algorithm utilized in this study has high robustness against Gaussian noise attacks.

Reorientation-induced relaxation of free OH at the air/water interface revealed by ultrafast heterodyne-detected nonlinear spectroscopy

The uniqueness of water originates from its three-dimensional hydrogen-bond network, but this hydrogen-bond network is suddenly truncated at the interface and non-hydrogen-bonded OH (free OH) appears. Although this free OH is the most characteristic feature of interfacial water, the molecular-level understanding of its dynamic property is still limited due to the technical difficulty. We study ultrafast vibrational relaxation dynamics of the free OH at the air/water interface using time-resolved heterodyne-detected vibrational sum frequency generation (TR-HD-VSFG) spectroscopy. With the use of singular value decomposition (SVD) analysis, the vibrational relaxation (T1) times of the free OH at the neat H2O and isotopically-diluted water interfaces are determined to be 0.87 ± 0.06 ps (neat H2O), 0.84 ± 0.09 ps (H2O/HOD/D2O = 1/2/1), and 0.88 ± 0.16 ps (H2O/HOD/D2O = 1/8/16). The absence of the isotope effect on the T1 time indicates that the main mechanism of the vibrational relaxation of the free OH is reorientation of the topmost water molecules. The determined sub-picosecond T1 time also suggests that the free OH reorients diffusively without the switching of the hydrogen-bond partner by the topmost water molecule.

A Hybrid Method of Textile Defect Detection using GLCM, LBP, SVD and Wavelet Transform

A roll of fabric with defects can have a depreciation of 45 to 65% with respect to the original price. While some commercial solutions exist, automatic fabric defect detection remains an active field of development and research. The goal is to extract the characteristics of the texture of the fabric to detect defects contained using image processing techniques. To date, there is no standard method which ensures the detection of texture defects in fabrics with high precision. In the following work, the use of Singular Value Decomposition (SVD), Local Binary Pattern (LBP) and Gray-Level Co-Occurrence Matrix (GLCM) features of images for the identification of defects in textiles is presented, where the application of techniques for pre-processing is presented, and for the analysis of texture LBP and the GLCM in order to extract features and segmentation is done using SVD approach. This model makes it possible to obtain compact and precise detection of the faulty texture structures. Our method is capable of achieving very precise detection and localization of texture defects in the images of the Fabric-Defect-Inspection-GLSR database, while ensuring a reasonable processing time.

An improved SVD-based blind color image watermarking algorithm with mixed modulation incorporated

This study systematically investigated the use of singular value decomposition (SVD) for the blind watermarking of color images. The proposed algorithm overcomes most of the problems typically encountered when using existing SVD-based schemes, while concurrently enhancing performance in terms of imperceptibility and robustness. After applying SVD to non-overlapping 4 × 4 image blocks, level shifting is used to control the embedding strength in accordance with the intensity of pixels in each block. The proposed watermark embedding process helps to preserve orthonormality in the unitary matrix and compensate for the resulting distortion. Iterative regulation ensures the accurate retrieval of the embedded watermark, while mixed modulation helps to improve robustness without compromising image quality. Experiment results demonstrate that the proposed watermarking algorithm is highly resistant to a variety of image processing attacks and error-free in the absence of attack. The proposed method outperforms existing SVD-based schemes in terms of imperceptibility and robustness at a payload capacity of 1/16 bit per pixel.

Experimental investigation of transonic and supersonic flow over a sphere for Reynolds numbers of 103–105 by free-flight tests with schlieren visualization

In this study, free-flight tests of a sphere for Reynolds numbers between 3.9 × 103 and 3.8 × 105 and free-flight Mach numbers between 0.9 and 1.6 were conducted using a ballistic range, and compressible low-Reynolds-number flows over an isolated sphere were investigated with the schlieren technique. The flow visualization was carried out under low-pressure conditions with a small sphere (minimum diameter of 1.5 mm) to produce compressible low-Reynolds-number flow. Also, time-averaged images of the flow near the sphere were obtained and compared to previous numerical results for Reynolds numbers between 50 and 1000. The experimental results clarified the structure of shock waves, recirculation region, and wake structures at the Reynolds number of 103–105 under transonic and supersonic flows. As a result, the following characteristics were clarified: (1) the amplitude of the wake oscillation was attenuated as the free-flight Mach number increased; (2) use of singular value decomposition permitted extraction of the mode of the wake structure even when schlieren images were unclear due to severe condition, and different modes in the wake structure were identified; (3) the Reynolds number had little effect on the separation point, but the length of the recirculation region increased as the Reynolds number decreased; and (4) the wake diameter at the end of the recirculation region decreased as the Mach number increased.

Singular Value Decomposition Approaches in A Correspondence Analysis with The Use of R

Abstract The aim of a correspondence analysis is the graphical representation of the categories of variables in one frame of reference. This visualization is possible due to the decomposition of the basic matrix with the use of Singular Value Decomposition (SVD). There are three matrices used in the process of decomposition: right singular vectors, left singular vectors, and a singular value diagonal matrix. The aim of this paper is to compare four different approaches and algorithms of SVD methods used in a correspondence analysis. In the literature, four approaches are known to singular value decomposition, defined by: R.A. Fisher (1940), M.J. Greenacre (1984), E.B. Anderson (1991), and J.D. Jobson (1992). Those computational procedures will be presented and compared in this paper. Also, methods of determining the coordinates of the category column and line matrix, as well as the values of inertia will be defined for these approaches. A key problem is to compare the well-known approaches, since in the literature only one approach ‒ proposed by Greenacre ‒ is used for singular value decomposition. The reason of the superiority of this algorithm over the others may be the simplicity and ease of the mathematical calculations. Greenacre’s algorithm is also used in R statistical software, making its availability and popularity growing, however, other algorithms are worth presenting and focusing on.

Signal separation from X-ray image sequence using singular value decomposition

Abstract This work proposes singular value decomposition (SVD) to separate the signal from a noisy X-ray image sequence without any prior knowledge of the noise. SVD is based on the theory that the noise is always uncorrelated to the signal in a noisy image, and SVD, which belongs to Blind Source Separation (BSS), can decorrelate the signal from the noise components. To apply this proposed denoising method, two groups of X-ray images produced at 25 kV & 20 mAs and 34 kV & 20 mAs are sampled. To measure the proposed denoising method, ROIs with differing glandularity are selected. This work supports the use of SVD in X-ray image denoising. Normally, the separated signal will be less noisy when more noisy images are included for separating signals. Compared with other classical denoising methods, SVD is superior in reducing noise and improving CNR or SNR.

Correlation of spacecraft thermal mathematical models to reference data

Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data.In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.

Using SVD-FRFT Filtering to Suppress First-Order Sea Clutter in HFSWR

This letter presents a novel signal processing method for HF surface wave radar that offers a solution to suppress significant sea clutter interference. Conventional clutter rejection methods, when the target signal and first-order sea clutter are mixed in the Doppler spectrum, tend to eliminate both the target signal and clutter without distinction. To address this problem, the frequency-modulated difference between the target signal and clutter is considered. Target echoes can be characterized as a linear-frequency modulation signal in long coherent time, while first-order sea clutter can be regarded as a superposition of several single-frequency signals. Based on the hybrid use of singular value decomposition (SVD) and the fractional Fourier transform (FRFT), SVD-FRFT filtering is conducted to suppress the components of the first-order sea clutter without impairing the target signals. The effectiveness of this method is illustrated by simulation and experimental results. It is further demonstrated that SVD-FRFT filtering can improve the signal-to-clutter ratio (SCR) to up to 40 dB for different SCRs.

Image Watermarking using Singular Value Decomposition with integration of Particle Swarm Optimization in Discrete wavelet transform

This paper proposes an additive watermarking method by using an optimization technique which make use of singular value decomposition (SVD) and makes use of Particle swarm optimization in discrete wavelet domain to enhance the watermarking scheme.SVD based watermarking Is done to provide high capacity. In order to improve the quality of images and to achieve the imperceptibility without losing robustness, an optimal scheme for embedding the secret message derived from PSO. Meanwhile PSO as a popular optimization technique and has been used as a method to balance the imperceptibility and robustness it is because PSO serves the weighting factor inside of embedding process. The proposed technique takes an advantage of Arnold transformations that provide security after successful watermark extraction.DWT is applied on the original image and the value of scaling factors to insert the watermark are obtained using PSO. Result comparisons shows that this algorithm proposed outperforms the additive work as compared to the existing algorithm.

Informed Group-Sparse Representation for Singing Voice Separation

Singing voice separation attempts to separate the vocal and instrumental parts of a music recording, which is a fundamental problem in music information retrieval. Recent work on singing voice separation has shown that the low-rank representation and informed separation approaches are both able to improve separation quality. However, low-rank optimizations are computationally inefficient due to the use of singular value decompositions. Therefore, in this paper, we propose a new linear-time algorithm called informed group-sparse representation, and use it to separate the vocals from music using pitch annotations as side information. Experimental results on the iKala dataset confirm the efficacy of our approach, suggesting that the music accompaniment follows a group-sparse structure given a pre-trained instrumental dictionary. We also show how our work can be easily extended to accommodate multiple dictionaries using the DSD100 dataset.