Singular Value Decomposition Approach Research Articles

A Robust and Secure Watermarking Approach Based on Hermite Transform and SVD-DCT

Currently, algorithms to embed watermarks into digital images are increasing exponentially, for example in image copyright protection. However, when a watermarking algorithm is applied, the preservation of the image’s quality is of utmost importance, for example in medical images, where improper embedding of the watermark could change the patient’s diagnosis. On the other hand, in digital images distributed over the Internet, the owner of the images must also be protected. In this work, an imperceptible, robust, secure, and hybrid watermarking algorithm is presented for copyright protection. It is based on the Hermite Transform (HT) and the Discrete Cosine Transform (DCT) as a spatial–frequency representation of a grayscale image. Besides, it uses a block-based strategy and a perfectibility analysis of the best embedding regions inspired by the Human Vision System (HVS), giving the imperceptibility of the watermark, and a Singular-Value Decomposition (SVD) approach improved robustness against attacks. In addition, the proposed method can embed two watermarks, a digital binary image (LOGO) and information about the owner and the technical data of the original image in text format (MetaData). To secure both watermarks, the proposed method uses the Jigsaw Transform (JST) and the Elementary Cellular Automaton (ECA) to encrypt the image LOGO and a random sequence generator and the XOR operation to encrypt the image MetaData. On the other hand, the proposed method was tested using a public dataset of 49 grayscale images to assess the effectiveness of the watermark embedding and extraction procedures. Furthermore, the proposed watermarking algorithm was evaluated under several processing and geometric algorithms to demonstrate its robustness to the majority, intentional or unintentional, attacks, and a comparison was made with several state-of-the-art techniques. The proposed method obtained average values of PSNR = 40.2051 dB, NCC = 0.9987, SSIM = 0.9999, and MSSIM = 0.9994 for the watermarked image. In the case of the extraction of the LOGO, the proposal gave MSE = 0, PSNR ≫ 60 dB, NCC = 1, SSIM = 1, and MSSIM = 1, whereas, for the image MetaData extracted, it gave BER = 0% and Berror=0. Finally, the proposed encryption method presented a large key space (K=1.2689×1089) for the LOGO image.

Attitude filtering with uncertain process and measurement noise covariance using SVD‐aided adaptive UKF

AbstractIt is presented in this article how to simultaneously alter the process and measurement noise covariance matrices for nontraditional attitude filtering technique. The unscented Kalman filter (UKF) and singular value decomposition (SVD) methods are integrated in the nontraditional attitude filtering algorithm to estimate a nanosatellite's attitude with an inherent robustness feature. The SVD approach determines the attitude of the nanosatellite and provides one estimate at a single frame utilizing measurements from the magnetometer and Sun sensor as the initial stage of the algorithm. These attitude terms are subsequently fed into the UKF with their error covariances, which makes the filter robust inherently. The attitude estimations of the satellite are compared between the filters presented. The Q (process noise covariance) adaption approach with multiple scale factors is specifically suggested for differences in between the process channels. Performance of the multiple scale factors‐based adaptive SVD‐aided UKF is examined in the event of process noise increase, which may result from changes in the environment or satellite dynamics.

Synchrophasor network-based detection and classification of power system events: A singular value decomposition approach

Timely detection and classification of power system events are essential for situation awareness and reliable electricity grid operation. It is also a crucial step with regard to synchrophasor network data management and archiving. In this paper, an event detection and classification method based on the singular value decomposition (SVD) of synchrophasor data is proposed. The detection algorithm exploits the low-dimensionality characteristics of synchrophasor data and identifies the changes in the dimensionality of a sliding data matrix. The SVD-based method assigns several detection flags indicating events and outliers in voltage magnitude, phase angle and frequency data. The proposed classification algorithm comprises a decision tree employing detection flags and singular values to classify events into several categories, e.g., fault, voltage magnitude and phase angle events, and generation-load mismatch events. Moreover, the proposed algorithm identifies whether events are spatially correlated. Field synchrophasor data collected from a smart grid are used to evaluate the performance of the proposed method. The numerical results show that the proposed method can successfully detect and classify different types of events even in the presence of measurement uncertainty.

Complementary waveforms for range sidelobe suppression based on a singular value decomposition approach

AbstractWhile Doppler resilient complementary waveforms (DRCWs) have previously been considered to suppress range sidelobes within a Doppler interval of interest in radar systems, their ability to provide Doppler resilience can be further improved. A new singular value decomposition (SVD)‐based DRCW construction is proposed, in which both transmit pulse trains (made up of complementary pairs) and receive pulse weights are jointly considered. Besides, using the proposed SVD‐based method, a theoretical bound is derived for the range sidelobes within the Doppler interval of interest. Moreover, based on the SVD solutions, a challenging non‐convex optimization problem is formulated and solved to maximise the signal‐to‐noise ratio (SNR) with the constraint of low range sidelobes. It is shown that, compared with existing DRCWs, the proposed SVD‐based DRCW has better Doppler resilience. Further, the new optimised SVD‐based DRCW has a higher SNR while maintaining the same Doppler resilience.

Fast online implementation of covariance-driven stochastic subspace identification

Fast online system identification is critical for the timeliness of downstream applications such anomaly detection, condition assessment and decision making. Although some very efficient algorithms, such as the fast Fourier transform (FFT), exist, they are unable to identify damping ratios or mode shapes. The stochastic subspace identification (SSI) method is currently a widely used system identification algorithm. However, its time-consuming operation prevents downstream applications from running online in (near) real time. This paper aims to develop a fast online implementation of covariance-driven SSI (COV-SSI). Time complexity is utilized to analyze the computational cost of COV-SSI. Two steps of COV-SSI are determined to be time-consuming and are accelerated. They are (i) the computation of the covariance matrix (accelerated through incremental aggregation in the dataflow model) and (ii) the singular value decomposition (SVD) of the Toeplitz matrix (accelerated through a fast truncated SVD approach). These strategies do not require any additional parameters; the error between the proposed method and the original COV-SSI method is negligible, but the method is significantly accelerated. Finally, some numerical examples are used to validate the speed and accuracy of the fast online strategies.

APPLICATION OF BIPLOT ANALYSIS WITH ROBUST SINGULAR VALUE DECOMPOSITION TO POVERTY DATA IN SULAWESI ISLAND

Poverty is defined as an inability of the individual to meet basic needs for a decent life. According to BPS data in2020, Sulawesi Island ranks fifth as the poorest island in Indonesia. This study aims to find out the mapping of areas and indicators of poverty in Sulawesi Island using Biplot Analysis with Robust Singular Value Decomposition approach for outlier research data. Based on the results of the study, there are five objects that are outlier and the information provided by the biplot amounted 98.45%. District/city that have similar characteristics are divided into 4 groups. The indicator of poverty that has the most diversity is the School Old Expectations Numbers (Var 4) and the one with the least diversity is Poor Households Using Clean Water (Var 8). Indicators of poverty that are positively correlated are Literacy Numbers (Var 1) and Non-Working Poor Population (Var 5), while the negative correlated are The Non-Working Poor Population (Var 5) and Poor Households Using Clean Water (Var 8). There are 19 districts/cities that have literacy values above the average of all districts/cities and 11 districts/cities that have a per capita expenditure value below the average of all districts/cities.

A fuzzy observer synthesis to state and fault estimation for Takagi-Sugeno implicit systems

<p>The present paper inquire a fuzzy observer design issue for continuous time Takagi-Sugeno aiming at estimating both of fault and state in case of unmeasurable premise variables. Thanks to singular value decomposition (SVD) approach, the fuzzy observer is synthesized in explicit form. The developed method is based on augmented structure that assemble state and actuator fault, sensor fault as well as their sequential derivatives is enjoined to institute the destined observer. The Lyapunov function is analyzed to assume the exponential stability of the studied observer, furthermore convergence conditions are expressed as linear matrix inequalities (LMIs) form. The applicability of the nominated theoritical result is elucidated and confiremed through numerical simulation using an example of an implicit fuzzy model.</p>

Multimodal Movie Recommendation System Using Deep Learning

Recommendation systems, the best way to deal with information overload, are widely utilized to provide users with personalized content and services with high efficiency. Many recommendation algorithms have been researched and deployed extensively in various e-commerce applications, including the movie streaming services over the last decade. However, sparse data cold-start problems are often encountered in many movie recommendation systems. In this paper, we reported a personalized multimodal movie recommendation system based on multimodal data analysis and deep learning. The real-world MovieLens datasets were selected to test the effectiveness of our new recommendation algorithm. With the input information, the hidden features of the movies and the users were mined using deep learning to build a deep-learning network algorithm model for training to further predict movie scores. With a learning rate of 0.001, the root mean squared error (RMSE) scores achieved 0.9908 and 0.9096 for test sets of MovieLens 100 K and 1 M datasets, respectively. The scoring prediction results show improved accuracy after incorporating the potential features and connections in multimodal data with deep-learning technology. Compared with the traditional collaborative filtering algorithms, such as user-based collaborative filtering (User-CF), item-based content-based filtering (Item-CF), and singular-value decomposition (SVD) approaches, the multimodal movie recommendation system using deep learning could provide better personalized recommendation results. Meanwhile, the sparse data problem was alleviated to a certain degree. We suggest that the recommendation system can be improved through the combination of the deep-learning technology and the multimodal data analysis.

A singular value decomposition approach for detecting and delineating harmful algal blooms in the Red Sea

Harmful algal blooms (HABs) have adverse effects on marine ecosystems. An effective approach for detecting, monitoring, and eventually predicting the occurrences of such events is required. By combining a singular value decomposition (SVD) approach and satellite remote sensing observations, we propose a remote sensing algorithm to detect and delineate species-specific HABs. We implemented and tested the proposed SVD algorithm to detect HABs associated with the mixed assemblages of different phytoplankton functional type (PFT) groupings in the Red Sea. The results were validated with concurrent in-situ data from surface samples, demonstrating that the SVD-model performs remarkably well at detecting and distinguishing HAB species in the Red Sea basin. The proposed SVD-model offers a cost-effective tool for implementing an automated remote-sensing monitoring system for detecting HAB species in the basin. Such a monitoring system could be used for predicting HAB outbreaks based on near real-time measurements, essential to support aquaculture industries, desalination plants, tourism, and public health.

Region-based SVD processing of high-frequency ultrafast ultrasound to visualize cutaneous vascular networks

Observing alterations in cutaneous vasculature in response to any disease or pathology is considered as a potential diagnostic marker in the progression and cure of a disease. To observe skin morphologies and tissue conditions, high-frequency ultrasound (HFUS) has been used in dermatology, although its ability to selectively visualize micro-vessels is limited due to insufficient Doppler sensitivity to peripheral slow-speed blood flow. In recent studies, this issue has been improved by increasing the sensitivity of Doppler imaging to slow flow, leveraging advanced cutter filtering approaches based on singular value decomposition (SVD) techniques that aid to effectively extract flow signals overlapped with tissue echo signals. Nevertheless, in skin imaging, variations in flow speed, diameter, and depth of the blood vessels at different skin layers can make clutter filtering challenging because these variations are problematic in selecting the optimal cut-off value for the SVD filtering. In this study, we aimed to devise a novel region-based SVD filtering approach for ultrafast HFUS data to visualize cutaneous vascular networks. The proposed method divides the acquired high-framerate data into two regions based on B-mode cutaneous morphological identification (dermis layer and subcutaneous tissue). Singular value decomposition processing was performed on each region to effectively extract the desired flow signal, and the processed regions were merged to generate a single power Doppler image, thereby highlighting the appearance of a complete cutaneous vascular network. Finally, top-hat transform was applied to the power Doppler image to further suppress the background noises and enhances the visibility of the micro-vessels. Experimental observations of the human cutaneous circulation showed that the image quality (contrast-to-noise ratio) through the region-based SVD filtering was measured to be 4.1 dB (before top-hat filtering) and 5.2 dB (after top-hat filtering), which were improved from 3.4 dB and 4.0 dB obtained using the global SVD approach with and without top-hat filtering, respectively. We envisioned that this approach would provide diverse applications in the diagnosis of cutaneous disorders.

Surrogate models for plasma displacement and current in 3D perturbed magnetohydrodynamic equilibria in tokamaks

A numerical database of over one thousand perturbed three-dimensional (3D) equilibria has been generated, constructed based on the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) computed plasma response to the externally applied 3D field sources in multiple tokamak devices. Perturbed 3D equilibria with the n = 1–4 (n is the toroidal mode number) toroidal periodicity are computed. Surrogate models are created for the computed perturbed 3D equilibrium utilizing model order reduction (MOR) techniques. In particular, retaining the first few eigenstates from the singular value decomposition (SVD) of the data is found to produce reasonably accurate MOR-representations for the key perturbed quantities, such as the perturbed parallel plasma current density and the plasma radial displacement. SVD also helps to reveal the core versus edge plasma response to the applied 3D field. For the database covering the conventional aspect ratio devices, about 95% of data can be represented by the truncated SVD-series with inclusion of only the first five eigenstates, achieving a relative error (RE) below 20%. The MOR-data is further utilized to train neural networks (NNs) to enable fast reconstruction of perturbed 3D equilibria, based on the two-dimensional equilibrium input and the 3D source field. The best NN-training is achieved for the MOR-data obtained with a global SVD approach, where the full set of samples used for NN training and testing are stretched and form a large matrix which is then subject to SVD. The fully connected multi-layer perceptron, with one or two hidden layers, can be trained to predict the MOR-data with less than 10% RE. As a key insight, a better strategy is to train separate NNs for the plasma response fields with different toroidal mode numbers. It is also better to apply MOR and to subsequently train NNs separately for conventional and low aspect ratio devices, due to enhanced toroidal coupling of Fourier spectra in the plasma response in the latter case.

Solution of the Radiative Transfer Equation for Vertically Inhomogeneous Media by Numerical Integration Solvers: Comparative Analysis

An efficiency of the singular value decomposition (SVD) method and ordinary differential equation (ODE) solvers in finding the reflection matrix are compared. A reflection matrix can be found by solving the one-dimensional radiative transfer equation. The latter’s solution based on the discrete ordinate method leads to the singular value decomposition (SVD) method. Alternative approach consists in transforming the original problem into a matrix Riccati equation written specifically for the reflection matrix. The matrix Riccati equation is solved using numerical integration techniques for ordinary differential equations (ODEs). It is found that for a single layer case, the SVD approach is faster than the ODE solvers by an order of magnitude. Yet as the number of layers increases, the ODE solvers become more efficient than the SVD approach. In addition, they outperform the SVD method when a solution for a set of optical thicknesses of the medium should be found or when retrieval of optical thickness should be performed. The comparison between different ODE solvers is performed, as well.

Machine learning-based fault diagnosis for research nuclear reactor medium voltage power cables in fraction Fourier domain

Fault diagnosis of Medium Voltage power Cables (MVCs) research nuclear reactor, incredibly inaccessible/remote ones, has to be carefully identified, located, and fixed within a short time. Therefore, this paper proposes a perfect simultaneous fault diagnosis scheme based on Multiclass Support-Vector Machine (MCSVM) in the fractional Fourier domain. First, the three-phase sending currents are simulated under different conditions then their features are extracted using Discrete Fractional Fourier Transform (DFRFT). Afterward, the features reduction process occurs via the Singular Value Decomposition (SVD) approach. MCSVM scheme is used to diagnose faults (i.e., discover, categorize, and trace) using reduced features outcome from DFRFT and SVD stages. Alternating Transient Program/Electromagnetic Transient Program (ATP/EMTP) simulations have been carried out for 22 kV unreachable MVC. Different kernels of SVM, i.e., linear, quadratic, or polynomial, and diverse factors of DFRFT, i.e., α, are investigated in simulations to obtain the optimum performance (i.e., best α and kernel pair). Hence, performance analysis of the proposed diagnosis method under different conditions (i.e., various fault resistances, locations, and inception angles) concluded two highest accuracy and lowest time settings, which were found at α = 0.5 (for both) quadratic kernel, and linear kernel, respectively. Moreover, the linear kernel achieves 99.8% accuracy rate, the lowest execution time (10 ms), and fault tracing error rate of 0.525789%, which is proper for real-time applications. Besides, our proposed method is more reliable and accurate against variable operating conditions (fault resistances, distances, and inception angles), leading to more reliable power production systems.

Multiresolution-Based Singular Value Decomposition Approach for Breast Cancer Image Classification.

Breast cancer is the most prevalent form of cancer that can strike at any age; the higher the age, the greater the risk. The presence of malignant tissue has become more frequent in women. Although medical therapy has improved breast cancer diagnostic and treatment methods, still the death rate remains high due to failure of diagnosing breast cancer in its early stages. A classification approach for mammography images based on nonsubsampled contourlet transform (NSCT) is proposed in order to investigate it. The proposed method uses multiresolution NSCT decomposition to the region of interest (ROI) of mammography images and then uses Z-moments for extracting features from the NSCT-decomposed images. The matrix is formed by the components that are extracted from the region of interest and are then subjected to singular value decomposition (SVD) in order to remove the essential features that can generalize globally. The method employs a support vector machine (SVM) classification algorithm to categorize mammography pictures into normal, benign, and malignant and to identify and classify the breast lesions. The accuracy of the proposed model is 96.76 percent, and the training time is greatly decreased, as evident from the experiments performed. The paper also focuses on conducting the feature extraction experiments using morphological spectroscopy. The experiment combines 16 different algorithms with 4 classification methods for achieving exceptional accuracy and time efficiency outcomes as compared to other existing state-of-the-art approaches.

Clutter Suppression and Rotor Blade Feature Extraction of a Helicopter Based on Time–Frequency Flash Shifts in a Passive Bistatic Radar

This paper presents a passive bistatic radar (PBR) configuration using a global navigation satellite system as an illuminator of opportunity for the rotor blade feature extraction of a helicopter. Aiming at the strong fixed clutter in the surveillance channel of the PBR, a novel iteration clutter elimination method-based singular-value decomposition approach is proposed. Instead of the range elimination method used in the classic extended cancellation algorithm, the proposed clutter elimination method distinguishes the clutter using the largest singular value and by remove this value. At the same time, the fuselage echo of the hovering helicopter can also be suppressed along with the ground clutter, then the rotor echo of this can be obtained. In the micro-motion feature extraction, the mathematic principle of the flash generation process in the time–frequency distribution (TFD) is derived first. Next, the phase compensation method is applied to achieve the time–frequency flash shift in the TFD. After this, the center frequencies of the standard flashes in the TFD are compared with the standard frequency dictionary. The mean l1 norm is utilized to estimate the feature parameters of the helicopter rotor. In the experiments, the scattering point model and the physical optics facet model demonstrate that the proposed method can obtain more accurate parameter estimation results than some classic algorithms.

Performance optimisation of a holographic Fourier domain diffuse correlation spectroscopy instrument.

We have previously demonstrated a novel interferometric multispeckle Fourier domain diffuse correlation spectroscopy system that makes use of holographic camera-based detection, and which is capable of making in vivo pulsatile flow measurements. In this work, we report on a systematic characterisation of the signal-to-noise ratio performance of our system. This includes demonstration and elimination of laser mode hopping, and correction for the instrument’s modulation transfer function to ensure faithful reconstruction of measured intensity profiles. We also demonstrate a singular value decomposition approach to ensure that spatiotemporally correlated experimental noise sources do not limit optimal signal-to-noise ratio performance. Finally, we present a novel multispeckle denoising algorithm that allows our instrument to achieve a signal-to-noise ratio gain that is equal to the square root of the number of detected speckles, whilst detecting up to ∼1290 speckles in parallel. The signal-to-noise ratio gain of 36 that we report is a significant step toward mitigating the trade-off that exists between signal-to-noise ratio and imaging depth in diffuse correlation spectroscopy.

Modification of the SVD Unfolding Regularization Method

Unfolding is currently an important stage of processing experimental data, reducing the effect of errors and reconstructing approximately real distributions of quantities. Numerous approaches exist to solve this problem; in particular, they are widely used in the modern physics of atomic nuclei and elementary particles, space physics, and other related areas. However, many algorithms are not designed or are poorly adapted to reconstruct multidimensional distributions corresponding to, e.g., several characteristics of particles measured simultaneously. In this work, a method has been proposed to adapt the singular value decomposition (SVD) unfolding algorithm to the multidimensional case. The proposed modified method has been tested in application to simulation data for the cosmic ray spectrum measured in the PAMELA space experiment. This method not only makes it possible to estimate the real distribution of a multidimensional quantity (momentum and two angles specifying the direction of entering a particle into an instrument) but also provides a better result compared to the classical SVD approach in the one-dimensional case (only the momentum of the p-article).

Finite-time [formula omitted] and [formula omitted] boundedness for nonlinear singular switched positive systems with D-perturbations

The article studies the positivity, finite-time L1 boundedness and finite-time L∞ boundedness for nonlinear singular switched positive systems(NSSPSs) with D-perturbations. Firstly, a necessary and sufficient positivity condition is presented for NSSPSs by singular value decomposition approach. Then, considering the disturbance signal in the form of norm bounded integrable signal, based on average dwell time and co-positive Lyapunov function approach, a sufficient condition of finite-time boundedness is derived for NSSPSs, and further considering the disturbance attenuation L1-gain performance, the result of finite-time L1 boundedness is presented for the considered system. In addition, considering the disturbance signal in the form of uniformly bounded signal, a sufficient condition of finite-time boundedness is derived for NSSPSs, and further considering the disturbance attenuation L∞-gain performance, the result of finite-time L∞ boundedness is presented for the considered system. Finally, the correctness and effectiveness of the results are verified with four given examples.

Robust fusion filter for multisensor descriptor system with uncertain‐variance noises and packet dropout

AbstractFor the multisensor linear stochastic descriptor system with uncertain‐variance noises and packet dropout, the standard state space model of the new reduced‐order augmented state is obtained based on the singular value decomposition (SVD) approach and augmented state approach. By applying the min‐max robust estimation principle and Kalman filtering theory, the local robust time‐varying Kalman filters of the reduced‐order augmented state and fictitious process noise are proposed. Then, the local robust time‐varying filters of the original descriptor system are presented according to the relation of the reduced‐order augmented state and the original state. And the distributed and covariance intersection (CI) fusion robust time‐varying filters are presented, and the actual and conservative filtering error variances are obtained. Further, the robustness of the local and fused robust filters are proved by applying Lyapunov equation approach, and the accuracy relation between them is analyzed. A simulation example applied to a circuit system shows its effectiveness and applicability.

Prediction of Heart Failure in Children with Congenital Heart Disease Based on Multichannel LSTM

Heart failure (HF) is a complicated clinical illness caused by a variety of primary and secondary causes, as well as increased infection pathways, that are associated with higher risk, illness, and costs. The overall incidence of congenital heart disease is approximately high and is the leading cause of death in infants and children. In this study, we present a novel computational model based on ECNN-LSTM for detecting congenital heart disease in real time and assessing its developing course objectively. The proposed model is a multiresolution singular value decomposition for congenital heart disease prediction in infants and children. Firstly, in the whole-life vibration time-domain signal of newborns and toddlers, the multiresolution singular value decomposition approach is employed to create approximation and detailed signals with different resolutions. Secondly, the health phases are split into the smooth running stage of newborns and toddlers, as well as the standard deviation of the earliest moments. Thirdly, the two-layer one-dimensional convolutional neural network structure divides the quick degradation stage, which can offer degradation information. Finally, the prediction of congenital heart disease is finished on LSTM utilizing the MSE loss function to unify the assessment scale. Validation with lifespan data demonstrates the feasibility and effectiveness of the proposed model. Moreover, the existing models have the insufficient ability for life span feature characterization in congenital heart disease prediction in infants and children.