Singular Value Decomposition Method Research Articles

A novel lidar signal denoising method based on variational mode decomposition optimized using whale algorithm

Original lidar return signals are covered by high levels of noise that seriously affect the accuracy of subsequent data processing and inversion. Therefore, it is important to separate the effective signal from the returned signal with noise interference. In this paper, an efficient denoising method based on the variational mode decomposition (VMD) algorithm optimized using the global search strategy-based whale algorithm and the total variational stationary wavelet transform (GSWOA-VMD-SWTTV) is proposed, and this method is applied to denoising of lidar return signals. First, the global search strategy-based whale optimization algorithm (GSWOA) is used to acquire the optimal parameters of the VMD algorithm adaptively, and the lidar return signal is then decomposed by global search strategy-based whale optimization algorithm (GSWOA)-VMD. The effective modal components are then determined using the cross-correlation coefficient method from the decomposed modal components, and total variation stationary wavelet denoising is performed on each effective mode. Finally, the effective modes are reconstructed to obtain a clean lidar return signal. Moreover, to provide further verification of the effectiveness of the proposed method, it is compared with the ensemble empirical mode decomposition (EEMD) method, the complete EEMD with adaptive noise (CEEMDAN) method, the singular value decomposition (SVD) method, and the wavelet threshold method under sunny, cloudy, and dusty weather conditions. The experimental results demonstrate the superior noise reduction performance of the proposed algorithm, which can filter out strong noise from the signal while retaining the complete signal details without distortion; additionally, the proposed method has the highest signal-to-noise ratio and lowest mean square error.

Digital Image Watermarking

Digital watermarking has become an essential method for encrypting multimedia files by adding undetectable data. In this work, we present a novel approach to digital watermarking that makes use of the Singular Value Decomposition (SVD) and Discrete Wavelet Transform (DWT) methods. By combining these methods, robustness against different types of attacks can be achieved while preserving excellent perceptual quality. Our approach ensures resilience and invisibility by embedding the watermark in the singular values that are obtained from the decomposition of DWT subbands. The outcomes of the experiments show that the suggested strategy is more efficient and effective than the current techniques when it comes to maintaining image quality and being resistant to common image processing threats.

Iterative removal of sources to model the turbulent electromotive force

ABSTRACT We describe a novel method to compute the components of dynamo tensors from direct magnetohydrodynamic (MHD) simulations. Our method relies upon an extension and generalization of the standard Högbom CLEAN algorithm widely used in radio astronomy to systematically remove the impact of the strongest beams on to the corresponding image. This generalization, called the Iterative Removal of Sources (IROS) method, has been adopted here to model the turbulent electromotive force (EMF) in terms of the mean magnetic fields and currents. Analogous to the CLEAN algorithm, IROS treats the time series of the mean magnetic field and current as beams that convolve with the dynamo coefficients which are treated as (clean) images to produce the EMF time series (the dirty image). We apply this method to MHD simulations of galactic dynamos, to which we have previously employed other methods of computing dynamo coefficients such as the test-field method, the regression method, as well as local and non-local versions of the singular value decomposition (SVD) method. We show that our new method reliably recovers the dynamo coefficients from the MHD simulations. It also allows priors on the dynamo coefficients to be incorporated easily during the inversion, unlike in earlier methods. Moreover, using synthetic data, we demonstrate that it may serve as a viable post-processing tool in determining the dynamo coefficients, even when the power of additive noise to the EMF is twice as much the actual EMF.

Convex set-oriented singular value decomposition with bounded uncertainties

Singular value decomposition (SVD) has played a crucial role in mathematics and applied mathematics, particularly in the field of practical engineering technology, which is almost indispensable in these fields. However, incomplete information caused by uncertainties from multiple sources and fluctuations in inherent properties during engineering practice can seriously interfere with obtaining singular values. Based on the convex set uncertainty theory, a novel convex set-oriented singular value decomposition (CSSVD) is proposed to overcome the limitations of using the nominal SVD method. The CSSVD aims to accurately and efficiently calculate the uncertainty bounds of singular values and vectors through the bounds and correlations of initial uncertainty parameters. Traditional probability methods rely on a sufficient sample size, and when the sample size is insufficient, accurate results cannot be obtained. However, the CSSVD method is based on set theory and can still demonstrate excellent performance in scenarios with small samples. This study investigates the detailed derivation steps of the proposed CSSVD method, taking into consideration properties such as normalization, orthogonality, and Monte Carlo simulation (MCS) to verify the accurate bounds of convex sets. The proposed method is finally applied to several numerical examples to demonstrate its superiority. This includes verifying singular values and vectors, handling high-order matrices, matrices with close singular values, and rectangular matrices. An application of image denoising is also used to evaluate the effectiveness of the proposed method.

Communication signal detection based on high-order cumulants time-frequency analysis: on the application of deep learning YOLOV5 network

The detection of communication signals in heterogeneous electromagnetic environments currently relies primarily on a one-dimensional statistical feature threshold method. However, this approach is highly sensitive to dynamic changes in the environment, fluctuations in signal-to-noise ratios, and complex noise. To address these limitations, this paper proposes a novel time-frequency diagram based on high-order accumulation for signal detection. Traditional time-frequency diagrams suffer from poor noise suppression ability and unclear features. However, higher-order cumulants can effectively overcome these shortcomings. Currently, methods based on higher-order cumulants are typically limited to one-dimensional signals. Yet, two-dimensional time-frequency signal diagrams can represent a broader array of features. This paper employs higher-order accumulation to extract time-frequency features from the received signal, thereby transforming the conventional radio detection problem into an image recognition challenge. By merging the advantages of higher-order accumulations and time-frequency diagrams, we propose the use of higher-order accumulation time-frequency diagrams for signal detection. Extensive experimental simulations demonstrate that the proposed time-frequency diagram exhibits strong anti-noise performance and effectively suppresses frequency bias from multiple perspectives. The performance of the Higher-Order Cumulant-Time Frequency (HOC-TF) indicated lower Root Mean Square Error (RMSE) compared with the Short-Time Fourier Transform-Time Frequency (STFT-TF) and Wavelet Transform-Time Frequency (WT-TF). Additionally, compared to the STFT-TF and WT-TF methodologies, the novel time-frequency diagram introduced demonstrates superior stability using the Singular Value Decomposition (SVD) method. Moreover, by combining the new time-frequency diagram with the deep learning YOLOV5 network, signal detection and modulation identification of communication signals can be achieved.

Self-Equilibrium Analysis and Minimal Mass Design of Tensegrity Prism Units

Abstract This paper provides a specific analysis strategy for tensegrity prism units with different complexities and connectivity. Through the nodal coordinate matrix and connectivity matrix, we can establish the equilibrium equation of the structure in the self-equilibrium state, and the equilibrium matrix can be obtained. The Singular Value Decomposition (SVD) method can find the self-equilibrium configuration. The torsional angle formula between the upper and bottom surfaces of the prismatic tensegrity structure, which includes complexity and connectivity, can be obtained through the SVD form-finding method. According to the torsional angle formula of the self-equilibrium configuration, we carry out the mechanical analysis of the single node, and the force density relationship between elements is gained. As one of the standards, the mass is used to evaluate the light structure. This paper also studied the minimal mass of the self-equilibrium tensegrity structure with the same complexity in different connectivity and got the minimal mass calculation formula. A six-bar tensegrity prism unit is investigated in this paper, which shows the feasibility of systematic analysis of prismatic structures. This paper provides a theoretical reference for prismatic tensegrity units.

Three-dimensional deformation measurement techniques in space multi-physical fields based on digital image correlation

Aiming at the three-dimensional deformation measurement requirement of the high-stability structure of spacecraft in space multi-physical fields, a comprehensive instrument protection device in a vacuum high-low temperature environment is developed using ultra-low temperature anti-condensation and vacuum heat insulation technology. This ensures that the digital image correlation (DIC) measurement camera always remains in a constant temperature and pressure environment and can stably exert its original efficiency in space multi-physical field environments. Subsequently, a path-dependent DIC method based on a graphics processing unit computing parallel acceleration is proposed by combining a pre-interpolation strategy and integrated image technology, which realizes high-precision matching of digital images before and after deformation in a spatial multi-physical field environment and improves the computing efficiency. To address the problem that a common reference point may deform significantly in a space environment with a large temperature change, which leads to inaccurate system accuracy, combined with a random sampling consistency algorithm and singular value decomposition method, the optimal registration of the coordinate system and the solution of deformation were realized by setting the threshold of the reference point margin screening. Finally, a three-dimensional deformation measurement system in high- and low-temperature vacuum environments was built, and the three-dimensional deformation measurement of the satellite antenna in high- and low-temperature vacuum environments was verified, which proves the effectiveness and accuracy of the above method.

An Abnormal Account Identification Method by Topology Feature Analysis for Blockchain-Based Transaction Network

Cryptocurrency, as one of the most successful applications of blockchain technology, has played a vital role in promoting the development of the digital economy. However, its anonymity, large scale of cryptographic transactions, and decentralization have also brought new challenges in identifying abnormal accounts and preventing abnormal transaction behaviors, such as money laundering, extortion, and market manipulation. Recently, some researchers have proposed efficient and accurate abnormal transaction detection based on machine learning. However, in reality, abnormal accounts and transactions are far less common than normal accounts and transactions, so it is difficult for the previous methods to detect abnormal accounts by training with such an imbalance in abnormal/normal accounts. To address the issues, in this paper, we propose a method for identifying abnormal accounts using topology analysis of cryptographic transactions. We consider the accounts and transactions in the blockchain as graph nodes and edges. Since the abnormal accounts may have special topology features, we extract topology features from the transaction graph. By analyzing the topology features of transactions, we discover that the high-dimensional sparse topology features can be compressed by using the singular value decomposition method for feature dimension reduction. Subsequently, we use the generative adversarial network to generate samples like abnormal accounts, which will be sent to the training dataset to produce an equilibrium of abnormal/normal accounts. Finally, we utilize several machine learning techniques to detect abnormal accounts in the blockchain. Our experimental results demonstrate that our method significantly improves the accuracy and recall rate for detecting abnormal accounts in blockchain compared with the state-of-the-art methods.

Innovative K-Means based machine learning method for determination of non-uniform image coordinate system in panoramic imaging: a case study with Ladybug2 camera.

Currently, the practical implementations of panoramic cameras range from vehicle navigation to space studies due to their 360-degree imaging capability in particular. In this variety of uses, it is possible to calculate three-dimensional coordinates from a panoramic image, especially using the Direct Linear Transformation (DLT) method. There are several types of omnidirectional cameras which can be classified mainly as central and non-central cameras for 360-degree imaging. The central omnidirectional cameras are those which satisfy the single-viewpoint characteristic. Multi-camera systems are usually developed for applications for which two-image stereo vision is not flexible enough to capture the environment surrounding a moving platform. Although the technology based on multi-view geometry is inexpensive, accessible, and highly customizable, multi-camera panoramic imaging systems pose a difficulty in obtaining a single projection center for the cameras. In this study, not only a defining method of the non-uniform image coordinate system is suggested by means of the K-Means algorithm for a single panoramic image, captured with a Ladybug2 panoramic camera in the panoramic calibration room but also the use of an elliptical panoramic projection coordinate system definition by Singular Value Decomposition (SVD) method in panoramic view. The results of the suggested method have been compared with the DLT algorithm for a single panoramic image which defined a conventional photogrammetric image coordinate system.

A novel approach to predictor selection among large-scale climate indices for seasonal rainfall forecasting in small catchments

ABSTRACT Utilizing identical climate indices as predictors for all climate divisions within large basins may result in unreliable rainfall forecasts at the sub-basin scale. This study aimed to develop a new approach to identify the most effective predictors among large-scale climate indices for seasonal rainfall forecasting in small areas. The proposed approach combines a selective singular value decomposition method (SSVD) with a non-linear sequential forward selection method (NLSFS). Applying the new algorithm for seasonal rainfall forecasting within two climate divisions in Karkheh basin, Iran, indicated that the climate indices identified by the SSVD differed between the study areas. The combination of these indices exhibited a correlation with seasonal rainfall approximately 11% higher than those derived from the SVD method. Moreover, NLSFS significantly enhanced the forecast accuracy compared to the frequently employed linear sequential forward selection (SFS) method, and the optimal predictors chosen by the two methods differed across all seasons.

Two‐Dimensional Hybrid Simulation of the Second‐Harmonic Generation of EMIC Waves in the Inner Magnetosphere

AbstractTwo‐dimensional (2‐D) hybrid model is developed to investigate the second harmonic (SH) generation of electromagnetic ion cyclotron (EMIC) waves. Applying the singular value decomposition method to simulated fields, we show that the SH exhibits wave properties analogous to typical EMIC waves generated by ion cyclotron instabilities, that is, left‐hand polarization and small wave normal angle. However, the bicoherence index inferred from simulated fields reflects a strong phase coupling between the fundamental wave (FW) and the SH, illustrating the nonlinear generation of the SH by the FW. The necessary conditions, especially for the wave vector relation, are further verified from a 2‐D perspective. The simulated amplitude ratios well meet the theoretical results only in the SH saturation stage, while the necessary conditions remain satisfied almost throughout the simulation. This study provides a comprehensive analysis of the SH excitation in a 2‐D simulation domain, contributing to a deeper understanding of EMIC wave nonlinear generation.

Reduced‐order observer‐based finite‐time control for one‐sided Lipschitz nonlinear switched singular systems

SummaryThe reduced‐order observer‐based finite‐time control problem for one‐sided Lipschitz nonlinear switched singular systems is addressed in this paper. First, the design method of the reduced‐order observer is given via state transformation. Then, based on the average dwell time (ADT) approach, some new sufficient conditions for regularity, impulse‐freeness, have a unique solution and finite‐time boundedness (FTB) of the dynamic augmented systems are obtained by exploring the reduced‐order observer‐based controller. Further, the lower finite‐time bound can be obtained by using singular value decomposition method. And the state feedback gain and the observer gain are computed by solving linear matrix inequalities (LMIs). Finally, the validity of the obtained method is illustrated by means of a numerical example and a DC motor system.

Singular Value Decomposition-Driven Non-negative Matrix Factorization with Application to Identify the Association Patterns of Sarcoma Recurrence.

Sarcomas are malignant tumors from mesenchymal tissue and are characterized by their complexity and diversity. The high recurrence rate making it important to understand the mechanisms behind their recurrence and to develop personalized treatments and drugs. However, previous studies on the association patterns of multi-modal data on sarcoma recurrence have overlooked the fact that genes do not act independently, but rather function within signaling pathways. Therefore, this study collected 290 whole solid images, 869 gene and 1387 pathway data of over 260 sarcoma samples from UCSC and TCGA to identify the association patterns of gene-pathway-cell related to sarcoma recurrences. Meanwhile, considering that most multi-modal data fusion methods based on the joint non-negative matrix factorization (NMF) model led to poor experimental repeatability due to random initialization of factorization parameters, the study proposed the singular value decomposition (SVD)-driven joint NMF model by applying the SVD method to calculate initialized weight and coefficient matrices to achieve the reproducibility of the results. The results of the experimental comparison indicated that the SVD algorithm enhances the performance of the joint NMF algorithm. Furthermore, the representative module indicated a significant relationship between genes in pathways and image features. Multi-level analysis provided valuable insights into the connections between biological processes, cellular features, and sarcoma recurrence. In addition, potential biomarkers were uncovered, while various mechanisms of sarcoma recurrence were identified from an imaging genetic perspective. Overall, the SVD-NMF model affords a novel perspective on combining multi-omics data to explore the association related to sarcoma recurrence.

Minimum norm partial eigenstructure assignment approach for vibration system with time delay

AbstractIn this paper, the minimum norm partial eigenstructure assignment problems (PESAPs) in vibration system with time delay is studied via acceleration‐velocity‐displacement active control. A new explicit solution is given for solving PESAPs using orthogonality relations of symmetric vibration system. A new constructive technique is presented to solve the PESAPs in vibration system with time delay by singular value decomposition method. An optimization algorithm is proposed to solve the minimum norm PESAPs by a quasi‐Newton optimization method. The proposed algorithm works without using the knowledge of receptance matrices and without solving the Sylvester equation. The effectiveness of the proposed algorithm is verified by the results of two numerical examples.

Sedimentation of two circular particles with different sizes in a vertical channel at low Reynolds numbers

In this study, the generalized finite-difference with singular value decomposition method for fluid–structure interaction problems is used to simulate the sedimentation of the two circular particles with different sizes in a vertical channel. The effects of the Reynolds number (8 ≤ Re ≤ 70) and the size difference (0 ≤ β ≤ 0.1) on the final motions of the two particles are analyzed. Over the ranges of the parameters investigated, three modes in the final state of the two-particle system are identified, i.e., the steady state, the periodic oscillation state, and the period-doubling bifurcation (PDB) state. Depending on the importance of the inertial force, the steady state can be classified as the steady state I and the steady state II. Similarly, the periodic oscillation state can be categorized into the periodic motion I (PMI) and the periodic motion II (PMII) based on the influence of the wake between the two particles. The directions of the limit cycles corresponding to PMI and PMII are counterclockwise and clockwise, respectively. In PMI, the limit cycle at 8 ≤ Re ≤ 9 decreases in size with increasing β, while the limit cycle at 12 ≤ Re < 70 behaves oppositely. The limit cycle in PMII always increases in size with β. PDB, characterized by the limit cycle with two branches, mainly appears at 14 ≤ Re ≤ 30.

Evaluating the Usefulness of Least Squares Regression in Petrophysics Interpretation

This paper is to update the information provided in the author’s previous papers on evaluating the uncertainty in least squares results. It is prompted by new information that shows that the usefulness of any least squares result cannot be guaranteed by conventional statistics (such as R-squared, F-statistic, or standard error of the regression, sigma). A new method based on the singular value decomposition (SVD) of a matrix, when accompanied by a Relative Error Bound (REB) on the estimated parameters, provides the user with a tool that can better assess the usefulness of any least squares result. Another important aspect of the REB is that it provides the user of the SVD method with a powerful tool for judging which is the best among several candidate solutions. In addition, it provides the user with a numerically stable method of computing the data ordinarily provided by principal component regression by eliminating the need to perform an eigenvector-eigenvalue analysis of an ATA matrix. This is of particular interest because forming the ATA matrix is often accompanied by a loss of data. The new method also provides the user with an improved method for selection of which principal components should be retained for a given problem.

Geometrical decomposition of nonadiabatic interactions to collective coordinates in many-dimensional and many-state mixed fast-slow dynamics.

In general, for many-dimensional and many-state nonadiabatic dynamics composed of slow and fast modes, we geometrically decompose the nonadiabatic interactions by means of the method of singular value decomposition. Each pair of the left and right singular vectors connecting the slow (nuclear) and fast (electronic) modes gives rise to a one-dimensional collective coordinate, and the sum of them amounts to the total nonadiabatic interaction. The analysis identifies how efficiently the slow modes, thus decomposed, can induce a transition in their fast counterparts. We discuss the notions of nonadiabatic resonance and nonadiabatic chaos in terms of the decomposition.

Referenceless Nyquist ghost correction outperforms standard navigator-based method and improves efficiency of in vivo diffusion tensor cardiovascular magnetic resonance.

The study aims to assess the potential of referenceless methods of EPI ghost correction to accelerate the acquisition of in vivo diffusion tensor cardiovascular magnetic resonance (DT-CMR) data using both computational simulations and data from in vivo experiments. Three referenceless EPI ghost correction methods were evaluated on mid-ventricular short axis DT-CMR spin echo and STEAM datasets from 20 healthy subjects at 3T. The reduced field of view excitation technique was used to automatically quantify the Nyquist ghosts, and DT-CMR images were fit to a linear ghost model for correction. Numerical simulation showed the singular value decomposition (SVD) method is the least sensitive to noise, followed by Ghost/Object method and entropy-based method. In vivo experiments showed significant ghost reduction for all correction methods, with referenceless methods outperforming navigator methods for both spin echo and STEAM sequences at b = 32, 150, 450, and 600 . It is worth noting that as the strength of the diffusion encoding increases, the performance gap between the referenceless method and the navigator-based method diminishes. Referenceless ghost correction effectively reduces Nyquist ghost in DT-CMR data, showing promise for enhancing the accuracy and efficiency of measurements in clinical practice without the need for any additional reference scans.

Analysis of force-free fields in the solar corona at flare sites

Force-free magnetic fields can be used to compute the magnetic structure above active regions where the field strength is large. Using vector magnetograms for two active regions that gave rise to solar flares, the force-free fields are obtained for times before and after the flare. The current density in the upper atmosphere obtained from nonlinear force-free fields is analyzed using Singular Value Decomposition (SVD) methods to determine how it is distributed around the times of flare occurrence. Regions of localized and relatively intense currents are sought at the different scales since these are usually linked to magnetic reconnection. It is found that the probability distribution functions (PDF) for small scales exhibit long tails and they are compared for times before and after the flare. Previous to the flare they seem to be slightly wider but not significant enough to draw a definite conclusion. This is likely due to break down of the applicability of the Force-Free fields after the flare. The effect of having long-tailed PDFs is equivalent to the one found in temperature fluctuations about the flare occurrence (1) which could point to a correlation between electrical currents and temperature. It is also obtained that the energy content in the middle scales of the currents is larger before than after the flare which would point to a magnetic dissipation at those scales during the flare.

Denoising four-dimensional flow magnetic resonance imaging data using a split-and-overlap approach via singular value decomposition

Four-dimensional flow magnetic resonance imaging (4D flow MRI) offers a powerful tool for visualizing fluid flows, critical for both diagnosing cardiovascular diseases and analyzing engineering fluid dynamics. Despite its potential in medical research, the clinical applicability of 4D flow MRI often faces challenges due to inherent noise. To mitigate this, we introduce the split-and-overlap singular value decomposition (SOSVD) filter, a distinctive noise reduction approach. Unlike traditional singular value decomposition methods, the SOSVD filter partitions the primary data matrix into overlapping subdomains and then applies singular value decomposition to each subdomain, preserving only the dominant mode for noise attenuation. Evaluations on simulated and experimental flow data within a square duct revealed a significant decrease in root mean square noise metrics. Moreover, when applied to in vivo aortic data, the SOSVD filter enhanced various flow determinants, including divergence, velocity gradients, streamlines, and velocity coherence. Thus, the SOSVD method presents a promising avenue for augmenting noise reduction in 4D flow MRI, potentially elevating diagnostic accuracy and enriching cardiovascular disease research.