Solution Of Inverse Problem Research Articles

Thunderstorm Ground Enhancements Measured on Aragats and Progress of High-Energy Physics in the Atmosphere

High-energy physics in the atmosphere (HEPA) has undergone an intense reformation in the last decade. Correlated measurements of particle fluxes modulated by strong atmospheric electric fields, simultaneous measurements of the disturbances of the near-surface electric fields and lightning location, and registration of various meteorological parameters on the Earth have led to a better understanding of the complex processes in the terrestrial atmosphere. The cooperation of cosmic rays and atmospheric physics has led to the development of models for the origin of particle bursts recorded on the Earth’s surface, estimation of vertical and horizontal profiles of electric fields in the lower atmosphere, recovery of electron and gamma ray energy spectra, the muon deceleration effect, etc. The main goal of this review is to demonstrate how the measurements performed at the Aragats cosmic ray observatory led to new results in atmospheric physics. We monitored particle fluxes around the clock using synchronized networks of advanced sensors that recorded and stored multidimensional data in databases with open, fast, and reliable access. Visualization and statistical analysis of particle data from hundreds of measurement channels disclosed the structure and strength of the atmospheric electric fields and explained observed particle bursts. Consequent solving of direct and inverse problems of cosmic rays revealed the modulation effects that the atmospheric electric field has on cosmic ray fluxes.

Estimating the chemical composition of municipal solid waste using the inverse method

This research aims to perform and implement an inverse solution method in waste-to-energy power plants for carrying out solid waste analysis without sampling. For this purpose, a simple simulated experiment is defined to evaluate the stability and accuracy of the method, which is investigated by adding random errors to the results of the direct problem conducted by the Monte Carlo method. The inverse problem solution procedure is solved by obtaining data categories for measuring parameters. In addition, the coefficient matrix is created and the linearization method is employed. By assuming a 0.5 percent nitrogen content in municipal solid waste, the number of unknown parameters is reduced, and the problem is solvable. The regularization method is applied to obtain the stability of the answer. The procedure is done for a municipal solid waste analysis with different regularization parameters. The mean value error and variance of the obtained solution from each analysis are evaluated and the acceptable range for regularization parameters is determined. Also, the identified matrix parameters between 1 and 100 are examined in the constant regularization parameter, and the acceptable parameters are determined. The error in validation by simulated experiment for carbon, oxygen, hydrogen, sulfur, moisture, and ash content of municipal solid waste is 1.47, 3.81, 0.91, 0.22, 7.32, and 1.57 percent, respectively. In the next step, the developed procedure is applied to the Aradkooh waste-to-energy power plant in Tehran, Iran. The operating data are gathered from the power plant, and the municipal solid waste composition is estimated. Results indicate the feasibility of the proposed method, and the municipal solid waste composition and mass flow rate can be predicted indirectly by the flue gas analysis and some other measurements without needing to sample the municipal solid waste. According to the results, the carbon, oxygen, hydrogen, sulfur, moisture, and ash content of municipal solid waste in the Aradkooh power plant is 21.13, 41.96, 5.70, 0.01, 25.06, and 5.63 percent, respectively. Further, the mass flow rate of municipal solid waste and air are 0.53 and 2.5 kg per second. Finally, the sensitivity of the estimated municipal solid waste composition to errors is evaluated by error analysis.

Application of the Model of Spots for Inverse Problems.

This article proposes the application of a new mathematical model of spots for solving inverse problems using a learning method, which is similar to using deep learning. In general, the spots represent vague figures in abstract "information spaces" or crisp figures with a lack of information about their shapes. However, crisp figures are regarded as a special and limiting case of spots. A basic mathematical apparatus, based on L4 numbers, has been developed for the representation and processing of qualitative information of elementary spatial relations between spots. Moreover, we defined L4 vectors, L4 matrices, and mathematical operations on them. The developed apparatus can be used in Artificial Intelligence, in particular, for knowledge representation and for modeling qualitative reasoning and learning. Another application area is the solution of inverse problems by learning. For example, this can be applied to image reconstruction using ultrasound, X-ray, magnetic resonance, or radar scan data. The introduced apparatus was verified by solving problems of reconstruction of images, utilizing only qualitative data of its elementary relations with some scanning figures. This article also demonstrates the application of a spot-based inverse Radon algorithm for binary image reconstruction. In both cases, the spot-based algorithms have demonstrated an effective denoising property.

ANALYSIS ON CAPSULE NETWORKS TO DETECT FORGED IMAGES AND VIDEOS

Modern day computer vision tasks requires efficient solution to problems such as image recognition, natural language processing, object detection, object segmentation and language translation. Symbolic Artificial Intelligence with its hard coding rules is incapable of solving these complex problems resulting in the introduction of Deep Learning (DL) models such as Recurrent Neural Networks and Convolutional Neural Networks (CNN). However, CNNs require lots of training data and are incapable of recognizing pose and deformation of objects leading to the introduction of Capsule Networks. And these are the new sensation in Deep Learning. They have lived to this expectation as their performance in relation to the above problems has been better than Convolutional Neural Networks. Even with this promise in performance, lack of architectural knowledge and inner workings of Capsules serves as a hindrance for researchers to take full advantage of this breakthrough. In this paper, we provide a comprehensive review of the state of the art architectures, tools and methodologies in existing implementations of capsule networks. We highlight the successes, failures and opportunities for further research to serve as a motivation to researchers and industry players to exploit the full potential of this new field. The main contribution of this survey article is that it explains and summarizes significant current state of the art Capsule Network architectures and implementations. The method introduced in this paper uses a capsule network to detect various kinds of spoofs, from replay attacks using printed images or recorded videos to computer generated videos using deep convolutional neural networks. It extends the application of capsule networks beyond their original intention to the solving of inverse graphics problems.

Full Waveform Inversion Based on an Asymptotic Solution of Helmholtz Equation

This study considers the full waveform inversion (FWI) method based on the asymptotic solution of the Helmholtz equation. We provide frequency-dependent ray tracing to obtain the wave field used to compute the FWI gradient and calculate the modeled data. With a comparable quality of the inverse problem solution as applied to the standard finite difference approach, the speed of the calculations in the asymptotic method is an order of magnitude higher. A series of numerical experiments demonstrate the approach’s effectiveness in reconstructing the macro velocity structure of complex media for low frequencies.

Algorytmy konstrukcji obrazów w systemach tomografii procesowej

Tomography is one of the methods used to obtain cross-sectional images of the analysed object. This imaging technique has been used for many years in medicine, providing significantly higher efficiency of patient’s diagnosis. In recent years, the imaging method has also found application for visualization of industrial processes. The article describes the tomographic image construction methods used in the modules of monitoring of dynamic industrial processes. Introduction to methods of the inverse problems solutions in tomography systems, from a practical point of view, was presented, with particular emphasis on the electrical capacitance tomography. It was shown how based on the mathematical theorems and knowledge about physics rules, concerning the behaviour of measurement signal in tomography sensor, is possible to construct cross-sectional image of industrial process. In article the image construction steps were explained and discussion on the impact of various factors on the quality and speed of imaging was conducted.

The Sparsity of Cycle Spinning for Wavelet-Based Solutions of Linear Inverse Problems

The usual explanation of the efficacy of wavelet-based methods hinges on the sparsity of many real-world objects in the wavelet domain. Yet, standard wavelet-shrinkage techniques for sparse reconstruction are not competitive in practice, one reason being that the lack of shift-invariance of the wavelet transform produces blocky artifacts. The standard remedy is cycle spinning, which results in a substantial reduction of these artifacts. In this letter, we propose a theoretical investigation of the sparsity of solutions to the cycle-spinning variant of wavelet-based resolutions of linear inverse problems. We derive a representer theorem that provides a complete characterization of the solution set. Our theorem indicates that the solutions are typically not sparse, where sparsity is measured with respect to the wavelet dictionary. This exposes that the role of sparsity in the success of wavelet-based solutions of linear inverse problems requires further investigation. We corroborate our theoretical results with numerical examples for the problem of image denoising.

Machine Learning Assisted Hybrid Electromagnetic Modeling Framework and Its Applications to UWB MIMO Antennas

Machine learning (ML) has gained recognition as an efficient and robust technique to realize the solution of electromagnetic forward and inverse problems. This article introduces a hybrid ML framework that simultaneously acts as a forward and inverse model based on a mode input. Multivariate relevance vector regression (MVRVR) is adopted for implementing the hybrid ML model. MVRVR models for forward and inverse modeling are also presented. In addition, three hybrid ML models based on support vector regression (SVR), Gaussian process regression (GPR), and artificial neural network (ANN) are also implemented and a thorough comparative analysis between these ML models with the proposed MVRVR model is investigated to verify its accuracy. The proposed hybrid framework can be used to replace the requirements of the two separate models for solving forward and inverse problems. Two examples of ultra-wideband (UWB) MIMO antennas are employed to validate the effectiveness of the proposed modeling framework.

АЛГОРИТМЫ ВЫЧИСЛЕНИЯ СОБСТВЕННЫХ ЗНАЧЕНИЙ ДИСКРЕТНЫХ ПОЛУОГРАНИЧЕННЫХ ОПЕРАТОРОВ, ЗАДАННЫХ НА КВАНТОВЫХ ГРАФАХ

Spectral problems for differential operators defined on quantum graphs are of great scientific interest related to problems in quantum mechanics, computer network modeling, image processing, ranking algorithms, modeling of electrical, and mechanical and acoustic processes, in networks of a diverse nature, in designing nano systems with prescribed properties and in other areas. Theoretical solutions of direct and inverse spectral problems on quantum graphs have been developed, but computational algorithms based on these methods are computationally inefficient. We have not seen any published works that consider examples of numerical solutions of spectral problems on finite connected graphs with a large number of vertices and edges. Therefore, the development of new computationally effective algorithms for numerical solution of spectral problems given on finite connected graphs is urgent. This paper develops a technique for finding the eigenvalues of boundary value problems on finite connected graphs with a required number of vertices and edges. To use this technique, it is necessary to know the eigenvalues and vectors of the eigenfunctions of corresponding unperturbed vector operators which are usually self-adjoint. Finding them manually, if the graph has a large number of vertices and edges, is difficult. This led to writing a package of programs in the mathematical environment Maple to find transcendental equations in the symbolic mode to calculate eigenvalues and find the eigenfunctions of unperturbed boundary value problems. Examples of calculating eigenvalues for a quantum graph which models an anthracene aromatic compound molecule are presented.

Experimental estimation of the local heat transfer coefficient for thin liquid film evaporation in a capillary tube

• Local heat transfer coefficient was estimated for thin liquid film evaporation in a capillary tube. • Temperature infrared measurements were employed as input data of the inverse heat conduction problem. • A robust estimation procedure was adopted. • Procedure validation through the application to both synthetic and experimental data. • Original insight of thin liquid film evaporation was given. Two-phase heat transfer devices consisting of mini and microtubes represent a powerful solution to the continuous reduction of electronic components' dimensions and to the increase of the power to dissipate. Despite many studies on the two-phase heat transfer phenomenon in minitubes, most provided outcomes regarding the average heat transfer coefficient or Nusselt number. A technique to assess the local convective wall heat flux and heat transfer coefficient is proposed, validated, and then applied to the experimental case of thin-film evaporation in a heated capillary tube. The evaporation of the thin film of liquid plays a vital part in the two-phase heat transfer phenomenon inside mini/microtubes. Our study investigated this phenomenon by examining a semi-infinite slug flow. The estimation method used is represented by the inverse heat conduction problem solution in the tube wall, applying the Tikhonov regularisation method. The temperature distributions on the outer surface of the channel measured by an infrared camera were employed as input data for the inverse problem. The estimated heat transfer coefficient distributions confirm the available correlations in average values and provide insight into these complex phenomena in local and instantaneous quantities.

Experimental analysis of shock smoothing design strategy for reducing cavitation erosion aggressiveness

This article presents the experimental analysis of cavitation erosion for two cascade hydrofoil profiles. The aim is to evaluate the change in erosive intensity between a conventional smooth blade surface and one generated by the means of inverse design specifically to reduce cavitation aggressiveness. The applied design strategy consists in imposing a reduced amplitude and gradient at the cavity closure pressure jump in order to bring down the potential energy contained in the vapor sheet. The result is a unique geometry that presents a surface kink located at cavity closure, which successfully smoothes the pressure jump according to computational fluid dynamics (CFD) verification analysis. Here, an experimental rig is constructed and equipped with a pressure sensing system and high-speed imaging to capture the flow field. The measurements for both geometries are first compared against a set of steady-state CFD solutions, which demonstrate the reliability of the inverse design solver for generating targeted flow characteristics in non-cavitating and cavitating conditions. Visual recordings also reveal significant changes in the aspect of the vapor sheet between the two blades indicating a shift in its dynamic behavior. Erosion intensity levels are then measured by paint method at identical conditions. The outcome of the experiment is highly conclusive as a marked reduction in paint erosion is observed for the design geometry. The measured data also serve as a benchmark test for predictive cavitation erosion models by comparing the measured erosion distributions for each blade to those obtained numerically from unsteady CFD.

Statistical Temporal Variations in the Auroral Electrojet Estimated With Ground Magnetometers in Fennoscandia

AbstractWe present the implementation of an improved technique to coherently model the high‐latitude ionospheric equivalent current. Using a fixed selection of 20 ground magnetometers in Fennoscandia, we present a method based on Spherical Elementary Current Systems (SECS) to model the currents coherently during 2000–2020. Due to the north‐south extent of the magnetometers, we focus on the model output along the 105° magnetic meridian. Our improvements involve fixed data locations and SECS analysis grid and using a priori knowledge of the large‐scale currents improving the robustness of the inverse problem solution. We account for contributions from ground induced currents assuming so‐called mirror currents. This study produces a new data set of divergence‐free (DF) currents and magnetic field perturbations along the 105° magnetic meridian with 1‐min resolution. By comparing averages of the data set with an empirical model of the ionosphere we demonstrate the validity of the data set. We show how our data set, in particular its temporal nature, is distinct from empirical models and other studies. Not only can the temporal evolution of the DF currents and magnetic field perturbations be investigated, but the time derivative of said quantities can be analyzed. For application in ground induced currents, we present the statistical properties of where (in magnetic latitude and local time) and at what rate (∂Br/∂t) the radial magnetic field component fluctuates, a temporal derivative that has received very little attention. We show that ∂Br/∂t is dependent on latitude, local time, and solar cycle. We present other applications such as Ultra Low Frequency Waves monitoring.

A Solution to TMR-EMT Blind Spots Based on Biaxial TMR

Electromagnetic tomography based on tunneling magnetoresistance (TMR-EMT) is a new type of electrical tomography technology. In contrast to the traditional EMT that uses the magnetic flux obtained from the coil to reconstruct the electrical conductivity distribution in the region of interest (ROI), the TMR-EMT reconstructs the magnetic permeability distribution in the ROI by the boundary magnetic induction intensity in the direction of the sensitive axis of the uniaxial TMR (Uni-TMR). However, the Uni-TMR measurements are influenced by the direction of boundary magnetic induction intensity at the Uni-TMR location, when the direction is orthogonal to the sensitive axis direction, the Uni-TMR cannot measure the boundary magnetic induction intensity, and such locations are named TMR-EMT blind spots in this paper. The blind spots will exacerbate the ill-condition of inverse problem solving of TMR-EMT, and even lead to failure of imaging. Aiming at the problem of TMR-EMT blind spots, this paper proposes a solution to measure the boundary magnetic induction intensity using biaxial TMR (Bi-TMR). The Bi-TMR consists of two Uni-TMRs whose sensitive axis directions are orthogonal to each other. The Bi-TMR measurement is obtained by squaring the sum of the squares of these two Uni-TMR measurements, which is unaffected by the boundary magnetic induction intensity direction. Simulation and experimental results show that this solution does not have the blind spots, and can obtain complete boundary magnetic induction intensity in plane.

Full Wave Inversion and Inverse Scattering in Ultrasound Tomography/Volography.

Ultrasound breast tomography has been around for more than 40years. Early approaches to reconstruction focused on simple algebraic reconstructions and bent ray techniques. These approaches were not able to provide high-quality and high spatial-resolution images. The advent of inverse scattering approaches resulted in a shift in image reconstruction approaches for breast tomography and a subsequent improvement in image quality. Full wave inverse solvers were developed to improve the reconstruction times without sacrificing image quality. The development of GPUs has markedly decreased the time for reconstruction using inverse scatting approaches. The development of fully 3D image solvers and hardware capable of capturing out of plane scattering have resulted in further improvement in breast tomography. This chapter discusses the state-of-the-art in ultrasound breast tomography, its history, the theory behind inverse scattering, approximations that are included to improve convergence, 3D image reconstruction, and hardware implementation of the constructions.

Effect of Segmentation Uncertainty on the ECGI Inverse Problem Solution and Source Localization.

Electrocardiographic Imaging (ECGI) is a promising tool to non-invasively map the electrical activity of the heart using body surface potentials (BSPs) and the patient specific anatomical data. One of the first steps of ECGI is the segmentation of the heart and torso geometries. In the clinical practice, the segmentation procedure is not fully-automated yet and is in consequence operator-dependent. We expect that the inter-operator variation in cardiac segmentation would influence the ECGI solution. This effect remains however non quantified. In the present work, we study the effect of segmentation variability on the ECGI estimation of the cardiac activity with 262 shape models generated from fifteen different segmentations. Therefore, we designed two test cases: with and without shape model uncertainty. Moreover, we used four cases for ectopic ventricular excitation and compared the ECGI results in terms of reconstructed activation times and excitation origins. The preliminary results indicate that a small variation of the activation maps can be observed with a model uncertainty but no significant effect on the source localization is observed.

Two inverse non-stationary problems of axially symmetric deformation of a finite-length elastic cylindrical shell

Among the many problems of the solid mechanics, there is a whole class of problems that are related to inverse problems. In turn, among the inverse problems, many problems are ill-posed. Obtaining an exact analytical solution of such problems is related to certain mathematical difficulties and requires using special methods. Goal. The goal of the study is to obtain analytical solutions for inverse problems of the identification of non-stationary load and the control of non-stationary vibrations of a cylindrical shell with asymmetric boundary conditions. Methodology. In this investigation, a refined theory of medium-thickness shells was used. Fourier series expansion, the theory of integral equations and the Laplace transform were used to obtain the solution of the direct problem. Tikhonov’s regularization method was used to solve inverse problems. Results. As a result of the investigation, the solutions of two inverse problems of the solid mechanics were obtained. The first task is to identify a fixed and moving concentrated axisymmetric non-stationary force acting on a cylindrical shell, based on the displacement values at any point of the shell; identification of two fixed concentrated forces. The second task is to control vibrations at any point of the cylindrical shell by introducing an auxiliary concentrated force. Numerical results obtained demonstrate the fulfillment of the control criterion as a result of the action of the given and auxiliary force. Originality. Analytical solutions of the inverse problems of the solid mechanics for a cylindrical shell of medium thickness with asymmetric boundary support conditions are obtained. Practical value. The technique received allows effective identification of an unknown non-stationary load. It’s important for the rational design of reliable cylindrical shell structures. Its use also makes possible to create a theoretical basis to control the deflected mode parameters of cylindrical shell structural elements

QUASI-ANALYTIC METHOD OF LINEAR DYNAMIC SYSTEMS INVERSION

The problem of inversion of dynamic systems has become widespread while solving the problems of control, identification, and measurement problems arising during the design and research of electrical and mechanical dynamic systems. Inverting is an effective way of implementing disturbance control processes, as well as in combined control systems with a predictive model. The analysis of information sources showed that in the practical solution of most inversion problems, a number of difficulties arise, which are associated with the high sensitivity of the results in relation to the accuracy of the parameters of the mathematical model of the control object, the instability of the inverse model of non-minimum-phase objects, and the violation of the conditions of physical feasibility. The work offers an effective method of inverting linear stationary dynamic systems, free from the mentioned shortcomings in many respects. The basis of the method is the presentation of input and output signals in the form of infinite linear combinations of their derivatives. A method of determining the sequence of matrix coefficients of linear representations of input and output signals is proposed. The main theoretical result is obtaining relationships between matrix coefficients of input and output signals. The work considers mathematical models of linear dynamic systems in the form of differential equations in the state space and in the equivalent "input-output" form. The considered systems must meet the conditions of asymptotic stability, as well as the condition of equal dimensions of the input and output vectors. Requirements for mathematical models of input and output signals are given, the fulfillment of which allows, instead of infinite sums representing signals, to be limited to a finite number of terms.

Polluted aquifer inverse problem solution using artificial neural networks

The problem of identifying an unknown pollution source in polluted aquifers, based on known contaminant concentrations measurement in the studied areas, is part of the broader group of issues, called inverse problems. This paper investigates the feasibility of using Artificial Neural Networks (ANNs) for solving the inverse problem of locating in time and space the source of a contamination event in a homogeneous and isotropic two dimensional domain. ANNs are trained in order to implement an input-output relationship which associates the position. Once the output of the system is known, the input is reconstructed by inverting the trained ANNs. The approach is applied for studying a theoretical test case where the inverse problem is solved on the basis of measurements of contaminant concentrations in monitoring wells located in the studied area. Groundwater pollution sources are characterized by varying spatial location and duration of activity. To identify these unknown pollution sources, concentration measurements data of monitoring wells are used. If concentration observations are missing over a length of time after an unknown source has become active, it is more difficult to correctly identify the unknown pollution source. In this work, a missing data scenario has been taken into consideration. In particular, a case where only one measurement has been made after the pollutant source interrupted its activity has been considered.

Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems

We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible. Then, we restrict this forward operator to finite-dimensional spaces so that the inverse is Lipschitz continuous. For the inverse operator, we demonstrate that there exists a neural network which is a robust-to-noise approximation of the operator. In addition, we show that these neural networks can be learned from appropriately perturbed training data. We demonstrate the admissibility of this approach to a wide range of inverse problems of practical interest. Numerical examples are given that support the theoretical findings.

Convergence rates for the joint solution of inverse problems with compressed sensing data

Compressed sensing (CS) is a powerful tool for reducing the amount of data to be collected while maintaining high spatial resolution. Such techniques work well in practice and at the same time are supported by solid theory. Standard CS results assume measurements to be made directly on the targeted signal. In many practical applications, however, CS information can only be taken from indirect data related to the original signal by an additional forward operator. If inverting the forward operator is ill-posed, then existing CS theory is not applicable. In this paper, we address this issue and present two joint reconstruction approaches, namely relaxed co-regularization and strict co-regularization, for CS from indirect data. As main results, we derive error estimates for recovering and . In particular, we derive a linear convergence rate in the norm for the latter. To obtain these results, solutions are required to satisfy a source condition and the CS measurement operator is required to satisfy a restricted injectivity condition. We further show that these conditions are not only sufficient but even necessary to obtain linear convergence.