Moore-Penrose Pseudo-inverse Matrix Research Articles

Restoration of Vector Magnetization Image from Vector Scanning-SQUID Microscope Measurement

Abstract A generalized mathematical framework to treat image data measured by the scanning superconducting quantum interference device (SQUID) microscope using a three-dimensional vector pickup coil is presented. The blurring of the images originating from the effects of diamagnetism due to the superconductivity of the sensor, the non-zero sensor size, and the finite sensor-to-sample separation are numerically reduced. We use a lattice model of the measurement system, and singular value decomposition and the Moore-Penrose pseudo-inverse matrix are employed to handle ill-conditioned matrices we encounter in the numerical processes. Based on a numerical model, measurement of the vector magnetization distributed on a sample surface, and the image restoration using the present procedure are demonstrated.

Current Signature Modeling of Surface-Mounted PMSM Drives With Current Sensors Faults

This paper presents the closed-form analytical determination of the current signature of a surface-mounted permanent magnet synchronous motor drive controlled by means of field oriented control strategy, when a fault occurs in one or more current sensors. Both DC offset and gain fault for all phase current sensors are considered. The proposed model includes the response of the control loop and related gains, eliminating the need for phase voltage sensors and complicated state estimation. However, the proposed approach requires the solution of an overdetermined system of equations. Then a new methodology of solution is proposed to save computing time, as an alternative to the classical one based on the Moore-Penrose pseudoinverse matrix. Experimental results and sensitivity analysis to parameter variations confirm the validity of the proposed model.

A Two-Step Continuous-Control-Set MPC for Modular Multilevel Converters Operating With Variable Output Voltage and Frequency

This paper presents a new enhanced single-stage two-step Continuous Control Set Model Predictive Control (CCS-MPC) algorithm, for Modular Multilevel Converters (MMCs) operating with variable output frequency at the AC port. The proposed two-step CCS-MPC allows the implementation of feed-forward compensation of the one-step ahead perturbations at the AC side, using an algorithm based on the Moore-Penrose pseudoinverse matrix. Limitations of the current and voltages in the MMC clusters are implemented to avoid overmodulation and overcurrents, being the solution of the constrained CCS-MPC online solved using the active-set method. Without losing generality, the experimental validation of the single-stage CCS-MPC is performed using an 18-cell MMC prototype, driving a 7.5 kW cage induction machine operating in a wide speed range. A dSPACE MicroLabBox platform is used to control the MMC-based drive by implementing the CCS-MPC algorithm, the modulation stage and the active-set method. It is experimentally demonstrated that the compensation of the low-frequency perturbations allows a considerable reduction in the required circulating currents at the low-frequency operation of the drive. Reduction in the capacitor voltage ripple, improved efficiency, and a smaller Total Harmonic Distortion (THD) in the output currents are also achieved with the proposed single-stage two-step CCS-MPC.

MOLASS: Software for automatic processing of matrix data obtained from small-angle X-ray scattering and UV-visible spectroscopy combined with size-exclusion chromatography.

Recent small-angle X-ray scattering (SAXS) for biological macromolecules (BioSAXS) is generally combined with size-exclusion chromatography (SEC-SAXS) at synchrotron facilities worldwide. For SEC-SAXS analysis, the final scattering profile for the target molecule is calculated from a large volume of continuously collected data. It would be ideal to automate this process; however, several complex problems exist regarding data measurement and analysis that have prevented automation. Here, we developed the analytical software MOLASS (Matrix Optimization with Low-rank factorization for Automated analysis of SEC-SAXS) to automatically calculate the final scattering profiles for solution structure analysis of target molecules. In this paper, the strategies for automatic analysis of SEC-SAXS data are described, including correction of baseline-drift using a low percentile method, optimization of peak decompositions composed of multiple scattering components using modified Gaussian fitting against the chromatogram, and rank determination for extrapolation to infinite dilution. In order to easily calculate each scattering component, the Moore-Penrose pseudo-inverse matrix is adopted as a basic calculation. Furthermore, this analysis method, in combination with UV-visible spectroscopy, led to better results in terms of accuracy in peak decomposition. Therefore, MOLASS will be able to smoothly suggest to users an accurate scattering profile for the subsequent structural analysis.

DETEKSI SEL DARAH SECARA OTOMATIS DENGAN EXTREME LEARNING MACHINE

Blood tests in humans play an important role not only to determine a person's blood type but also to detect diseases. Blood tests are carried out by composing blood preparations and checking them in the laboratory. With the development of technology in computer vision, the examination of blood preparations can be done through digital images of the microscope preparat. This study was conducted to detect blood cells automatically from digital images using the Extreme Learning Machine (ELM) method. The most obvious difference between ELM and other Neural Networks is in the number of its hidden layer. The ELM architecture only consists of 1 layer, while the hidden layer architecture in other Neural Networks may contain more than 1 layer. In the learning process, ELM utilizes the Moore Penrose Pseudoinverse matrix inverse theory which has the best generalization results with faster computation time. Experiments were carried out by digitizing the image of the blood cells. These images consisted of two types, the stained images and the unstained images. In the stained microscopic images, each component of the blood cells can be clearly seen and easily identified. Meanwhile, in the image of the unstained preparations, the components of the blood cells cannot be distinguished or seen directly by the human eye. The experimental results show that the developed method can achieve 95.83% accuracy for the stained image and 68.6% accuracy for the unstained image. Furthermore, the average testing accuracy of varied white blood cell types has an accuracy of 81.36%.

Development of a Solvability Map.

From time to time, it is necessary to determine whether there are sufficient measurements for the image reconstruction task especially when a non-standard scanning geometry is used. When the imaging system can be approximately modeled as a system of linear equations, the condition number of the system matrix indicates whether the entire system can be stably solved as a whole. When the system as a whole cannot be stably solved, the Moore-Penrose pseudo inverse matrix can be evaluated through the singular value decomposition (SVD) and then a generalized solution can be obtained. However, these methods are not practical because they require the computer memory to store the whole system matrix, which is often too large to store. Also, we do not know if the generalized solution is good enough for the application in mind. This paper proposes a practical image solvability map, which can be obtained for any practical image reconstruction algorithm. This image solvability map measures the reconstruction errors for each location using a large number of computer-simulated random phantoms. In other words, the map is generated by a Monte Carlo approach.

Nonequilibrium molecular dynamics method based on coarse-graining formalism: Application to a nonuniform temperature field system.

A nonequilibrium molecular dynamics method is proposed to produce nonequilibrium states flexibly. In this method, virtual points are set in a simulation box, and coarse-grained physical quantities at these points are constrained using Gauss's principle of least constraint. The coarse-grained physical quantities are evaluated by averaging microscopic quantities with an appropriate weight. To obtain the weight to evaluate the coarse-grained physical quantities, a shape function matrix is initially constructed from the particle configuration. This matrix expresses an interpolation of the physical quantities at particle positions from the coarse-grained quantities at the virtual points. Then, a matrix form of the weight is calculated as the Moore-Penrose pseudoinverse matrix for the shape function matrix. This method is applied to constrain the coarse-grained kinetic energy and produce a nonuniform temperature field in the system. The temperature profile at a nonequilibrium steady state depends on the method for constructing the shape function matrix. In particular, a local temperature coincides with the coarse-grained temperature when the shape function matrix is constructed based on a higher-order interpolation.

Statement of the problem of assessing instability of passive quantum frequency standards in the presence of an error from the interaction

Construction of modern measuring complexes of the coordinate-time support system of Ukraine is impossible without improving mathematical models of quantum standards of frequency (QSF) used in group standards. This work is devoted to the analysis of methods for the stable solution of direct and inverse problems (methods for solving ill-posed problems) in models of the interaction of passive QSF in the process of their comparisons. The priority task is to use these methods for the numerical solution of problems in the design of group QSF and parallel quantum generators of random numbers. Methods for solving such problems are in demand, since they make it possible to create mathematical models of group QSF interaction. These models will enable the design of efficient parallel quantum random number generation devices for high-tech areas of cybersecurity.
 Varieties of methods such as the method of least squares or the method of the Moore-Penrose pseudo-inverse matrix are used, as a rule when evaluating the metrological parameters of QSF.Robust methods of regularization or filtering, for example, the Kalman or Wiener filter method, are used in the algorithms of group standards, due to the instability of the solution.However, these methods do not work in the presence of an error from the interaction of QSF in the process of their functioning in a group standard or in comparisons.
 The aim of this work is to analyze and substantiate the formulation of the problem of assessing the potential accuracy characteristics of passive QSF in the presence of an error from the interaction. Regularization parameters when determining the state vector of the group standard are found using signals transmitted by global navigation satellite systems such as GPS\GLONASS in the local differential correction mode.

Adaptive Reinforcement Learning-Enhanced Motion/Force Control Strategy for Multirobot Systems

This paper presents an adaptive reinforcement learning- (ARL-) based motion/force tracking control scheme consisting of the optimal motion dynamic control law and force control scheme for multimanipulator systems. Specifically, a new additional term and appropriate state vector are employed in designing the ARL technique for time-varying dynamical systems with online actor/critic algorithm to be established by minimizing the squared Bellman error. Additionally, the force control law is designed after obtaining the computation of constraint force coefficient by the Moore–Penrose pseudo-inverse matrix. The tracking effectiveness of the ARL-based optimal control is verified in the closed-loop system by theoretical analysis. Finally, simulation studies are conducted on a system of three manipulators to validate the physical realization of the proposed optimal tracking control design.

Parallel versus cascaded logistic regression trained single-hidden feedforward neural network for medical data

ObjectiveAn important step towards a better healthcare system is fast and accurate diagnosis. In the last decade, the application of intelligent systems in healthcare has led to impressive results. The goal of this paper is to extend the LogSLFN (single-hidden layer feedforward neural network trained using logistic regression) algorithm, which has been deployed successfully in the past for the case of a two-class decision problem, to the case of multiple classes. We have considered and statistically analyzed two approaches: a parallel LogSLFN, and a cascaded LogSLFN. Materials and methodsAccording to the universal approximation theorem, a single-hidden layer feedforward neural network has the ability to approximate arbitrarily closely continuous functions of several real variables under certain reasonable assumptions. Essentially, a single hidden layer containing a finite fixed number of neurons is sufficient to provide an arbitrarily well approximation to a given training set of inputs and a desired target output represented by a continuous function. Parallel LogSLFN and cascaded LogSLFN are two novel approaches that can be applied to multiple-class decision problems. Both methods are extensions of the LogSLFN, which uses logistic regression to compute the weights between the input and hidden layer of a single-hidden layer feedforward network. No error correction is needed, the weights between the hidden and the output layer being computed using the Moore-Penrose pseudoinverse matrix. The proposed models have been tested on two medical datasets regarding cancer diagnosis and liver fibrosis staging. Experimental results and the subsequent statistical analysis have proved the robustness of the proposed models with other machine learning techniques reported in literature. Main findingsThe experimental results showed that the Parallel approach surpasses the Cascaded one. Still, both models are competitive to the other state-of-the-art techniques. ConclusionsThe LogSFLN algorithm can be successfully extended to multiple-class decision problems. By embedding knowledge extracted from the data into the architecture, we obtained a raise by 20% in accuracy when applied on the liver fibrosis dataset.

Design of a source-detector array for dual-slope diffuse optical imaging.

We recently proposed a dual-slope technique for diffuse optical spectroscopy and imaging of scattering media. This technique requires a special configuration of light sources and optical detectors to create dual-slope sets. Here, we present methods for designing, optimizing, and building an optical imaging array that features m dual-slope sets to image n voxels. After defining the m × n matrix (S) that describes the sensitivity of the m dual-slope measurements to absorption perturbations in each of the n voxels, we formulate the inverse imaging problem in terms of the Moore-Penrose pseudoinverse matrix of S (S+). This approach allows us to introduce several measures of imaging performance: reconstruction accuracy (correct spatial mapping), crosstalk (incorrect spatial mapping), resolution (point spread function), and localization (offset between actual and reconstructed point perturbations). Furthermore, by considering the singular value decomposition formulation, we show the significance of visualizing the first m right singular vectors of S, whose linear combination generates the reconstructed map. We also describe methods to build a physical array using a three-layer mesh structure (two polyethylene films and polypropylene hook-and-loop fabric) embedded in silicone (PDMS). Finally, we apply these methods to design two arrays and choose one to construct. The chosen array consists of 16 illumination fibers, 10 detection fibers, and 27 dual-slope sets for dual-slope imaging optimized for the size of field of view and localization of absorption perturbations. This particular array is aimed at functional near-infrared spectroscopy of the human brain, but the methods presented here are of general applicability to a variety of devices and imaging scenarios.

전기적 대형 물체 RCS 해석을 위한 근거리-원거리장 변환 알고리즘 연구

Preliminary analyses of radar cross section (RCS) in the design process of military weapon systems are very important. Recently, weapon systems such as missiles and fighter jets are adapted for large-size electrical objects in preparation for the wavelengths used in radar. Therefore, it is difficult to pre-analyze the RCS through commercial simulation programs unless a high-performance computing power is provided. To solve these problems, we propose a near to far field transformation algorithm that can be applied to domain decomposition analyses. First, we analyzed the theoretical equation and the physical meaning of the algorithm and matricized the integral equation to a constant part and a scattering part. Then, the Moore-Penrose pseudo-inverse matrix method was used to solve the scattering characteristics. We have also studied the possibility of extracting the far field RCS from near field data.

A Fast Neural Network Learning Algorithm with Approximate Singular Value Decomposition

Abstract The learning of neural networks is becoming more and more important. Researchers have constructed dozens of learning algorithms, but it is still necessary to develop faster, more flexible, or more accurate learning algorithms. With fast learning we can examine more learning scenarios for a given problem, especially in the case of meta-learning. In this article we focus on the construction of a much faster learning algorithm and its modifications, especially for nonlinear versions of neural networks. The main idea of this algorithm lies in the usage of fast approximation of the Moore–Penrose pseudo-inverse matrix. The complexity of the original singular value decomposition algorithm is O(mn2). We consider algorithms with a complexity of O(mnl),where l<n and l is often significantly smaller than n. Such learning algorithms can be applied to the learning of radial basis function networks, extreme learning machines or deep ELMs, principal component analysis or even missing data imputation.

On a regularization method for solving linear Noetherian boundary value problem for difference system

The article proposes unusual regularization conditions as well as a scheme for finding bounded solutions of the linear Noetherian boundary value problem for a system of difference equations in the critical case, significantly using the Moore-Penrose matrix pseudo-inversion technology. The problem posed in the article continues the study of the a sufficient condition for solvability and regularization conditions for linear Noetherian boundary value problems in the critical case given in the monographs by A.N. Tikhonov, V.Ya. Arsenin, S.G. Krein, A.M. Samoilenko, N.V. Azbelev, V.P. Maksimov, L.F. Rakhmatullina and A.A. Boichuk. The general case is studied in which a linear bounded operator corresponding to a homogeneous part of a linear Noetherian boundary value problem has no inverse. The noninvertibility of the operators corresponding to a homogeneous part of a linear Noetherian boundary value problem is a consequence of the fact that the number of boundary conditions does not coincide with the number of unknown variables of the difference equations. Using the theory of generalized inverse operators and Moore-Penrose pseudoinverse matrix in the article, a generalized Green operator is constructed and the type of a linear perturbation of a regularized linear Noether boundary value problem for a system of difference equations in the critical case is found. The proposed regularization conditions, as well as the scheme for finding of bounded solutions to linear Noetherian boundary value problems for a system of difference equations in the critical case, are illustrated in details with examples. In contrast to the earlier articles of the authors, the regularization problem for a linear Noether boundary value problem for a system of difference equations in the critical case has been resolved constructively, and sufficient conditions has been obtained for the existence of a bounded solution to the regularization problem.

A time-domain system identification numerical procedure for obtaining linear dynamical models of multibody mechanical systems

This paper is focused on the development of a numerical procedure for solving the system identification problem of linear dynamical models that mathematically describe multibody mechanical systems. To this end, an input–output representation of the time evolution of a general mechanical system based on a sequence of matrices referred to as Markov parameters is employed. The set of Markov parameters incorporate the state-space matrices that allow for describing the dynamic behavior of a general mechanical system considering the assumption of structural linearity. The system Markov parameters are defined by means of a discretization process applied to the analytical description of a mechanical system, and therefore, they are difficult to obtain directly from observable measurements. However, a state observer can be introduced in order to define a set of observer Markov parameters that can be readily recovered from input–output experimental data. The observer Markov parameters obtained by using a least-square approach allow for computing in a recursive manner the system Markov parameters as well as another discrete sequence of matrices referred to as observer gain Markov parameters. Subsequently, the system and observer gain Markov parameters identified from observable input–output data are used for constructing a sequence of generalized Hankel matrices from which a state-space model of the mechanical system of interest can be extracted. This fundamental step of the identification procedure is performed in the algorithm elaborated in this work employing a numerical procedure which relies on the use of the Moore–Penrose pseudoinverse matrix obtained by means of the singular value decomposition. In the paper, the principal analytical and numerical aspects of the proposed identification algorithm are described in detail. Furthermore, a numerical example based on a simple vehicle model is discussed in order to verify by means of numerical experiments the effectiveness of the identification procedure developed in this work.

Improvements in transaural synthesis with the Moore-Penrose pseudoinverse matrix

Transaural synthesis using loudspeakers is a powerful technique for conducting binaural hearing experiments while avoiding myriad problems caused by headphones. It is the most promising method to test binaural hearing for listeners using cochlear implants. Transaural synthesis is typically implemented using crosstalk cancellation, a technique whereby the left-channel signal and right-channel signal are adjusted so that reproduction by two synthesis loudspeakers results in near perfect transmission of the target left and right signals to the left and right ears (or processor microphones). Crosstalk cancellation has enabled precise experimental control over the stimulus delivered to each ear. Unfortunately, the 2×2 matrix inversion required for crosstalk cancellation can occasionally introduce spuriously large amplitudes for specific frequencies into the adjusted signals. These large amplitudes lead to perceptually salient tones. We demonstrate through simulation and experiment in a real room that adding a third loudspeaker and solving the resulting 2×3 problem using the Moore-Penrose pseudoinverse matrix yields dramatically fewer large amplitudes in the resulting adjusted waveforms. We have also conducted experiments to investigate the 2×3 system's robustness to inadvertent listener motions.

Representing Weighted Pseudoinverse Matrices with Mixed Weights in Terms of Other Pseudoinverses

The paper considers weighted pseudoinverse where both weighted matrices are symmetric and one of them is positive definite matrix and the other is nonsingular and indefinite. Formulas are obtained to represent these matrices in terms of the Moore–Penrose pseudoinverse matrix and other weighted pseudoinverses.

Study of spectral reflectance reconstruction based on regularization matrix R method

In order to solve the ill-posed problem in the process of reconstructing the spectral reflectance of the traditional matrix R method, a regularization matrix R method was proposed in this paper. Through analyzing the ill-posed equation of matrix R to reconstruct the spectral reflectance, the Tikhonov regularization method was researched to restrict the ill-posed problem to solve the Moore-Penrose pseudo inverse matrix. The L-curve method was used to obtain the optimal regularization parameter by training samples data in order to effectively restrict the ill-posed situation which was caused by the equation solving of spectral reconstruction. The experimental results verified that the proposed regularization matrix R method had higher spectral and chromatic accuracy of reconstructed spectrum than traditional matrix R method. At the same time, the proposed regularization matrix R method achieved good performance for color reproduction of real mural in practical application.

SPAM revisited for median filtering detection using higher‐order difference

AbstractIn this paper, we propose a robust median filtering detection scheme utilizing the conditional joint distribution of high‐order differences. The higher‐order differences provide additional information about the correlation between a pixel and its neighbors. The relationship between a pixel and its neighbors becomes more prominent in median‐filtered images as compared with non‐median filtered images. We evaluate the performance of our method and compare it with the state of the art median filtering detection techniques on multiple databases in various environments. We use a linear discriminant classifier based on Moore–Penrose pseudoinverse matrix for classifying the median and non‐median filtered images. Experimentally, we find that our method is more effective for all types of images including uncompressed and highly compressed JPEG low‐resolution images. We also evaluate the performance of our method on Gaussian‐filtered, averaging‐filtered, and median‐filtered images of the BOWS2 and UCID databases. Copyright © 2016 John Wiley & Sons, Ltd.

Tactile data processing method for the reconstruction of contact force distributions

The main task of robotic skin is recognition of tactile stimuli acting on the surface of a soft elastic layer through the outputs of embedded sensor arrays. The focus of this work is the development of an algorithm for estimating the spatial distribution of contact forces as well as their intensities and directions starting from sensor data. This requires the solution of an inverse problem where only incomplete information (e.g. normal stress on the sensors) is usually available. The proposed method discretizes external forces at the nodes of a grid. The more practical solution is fixing the node number equal to the number of sensors. In this case, the inverse problem of retrieving the force distribution from sensor data is trivially solved if normal forces are applied. For multi-component force distributions, on the other hand, the problem is in principle ill-posed. A solution is achieved through an optimization procedure accounting for the physical features of the problem by the use of the Moore–Penrose pseudo-inverse matrix and of a vector depending on two continuous and adjustable scalar parameters. The algorithm has been tested on simulated single-contact problems (both Hertzian and non-Hertzian normal force distributions) with encouraging results for both accuracy and robustness of the solution.