Robust polarimetric dehazing algorithm based on low-rank approximation and multiple virtual-exposure fusion

Polarimetric dehazing is an effective way to enhance the quality of images captured in foggy weather.However,images of essential polarization parameters are vulnerable to noise,and the brightness of dehazed images is usually unstable due to different environmental illuminations.These two weaknesses reveal that current polarimetric dehazing algorithms are not robust enough to deal with different scenarios.This paper proposes a novel,to our knowledge,and robust polarimetric dehazing algorithm to enhance the quality of hazy images,where a low-rank approximation method is used to obtain low-noise polarization parameter images.Besides,in order to improve the brightness stability of the dehazed image and thus keep the image have more details within the standard dynamic range,this study proposes a multiple virtual-exposure fusion(MVEF)scheme to process the dehazed image(usually having a high dynamic range)obtained through polarimetric dehazing.Comparative experiments show that the proposed dehazing algorithm is robust and effective,which can significantly improve overall quality of hazy images captured under different environments.

Evolutionary Safe Padé Approximation Scheme for Dynamical Study of Nonlinear Cervical Human Papilloma Virus Infection Model

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic(CCE)model.The underlying CCE model lacks a closed-form exact solution.Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model’s necessary properties,such as positivity,boundedness,and feasibility.Therefore,the development of structure-preserving semi-analytical approaches is always necessary.This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model’s physical properties by formulating an equivalent unconstrained optimization problem.Singularity-free safe Padérational functions approximate the mathematical shape of state variables,while the model’s physical requirements are treated as problem constraints.The primary model of the governing differential equations is imposed to minimize the error between approximate solutions.An evolutionary algorithm,the Genetic Algorithm with Multi-Parent Crossover(GA-MPC),executes the optimization task.The resulting method is the Evolutionary Safe PadéApproximation(ESPA)scheme.The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations.The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padéapproximants.

Determining Hubbard U of VO_(2) by the quasi-harmonic approximation

Vanadium dioxide VO_(2) is a strongly correlated material that undergoes a metal-to-insulator transition around 340 K.In order to describe the electron correlation effects in VO_(2), the DFT+U method is commonly employed in calculations.However, the choice of the Hubbard U parameter has been a subject of debate and its value has been reported over a wide range. In this paper, taking focus on the phase transition behavior of VO_(2), the Hubbard U parameter for vanadium oxide is determined by using the quasi-harmonic approximation(QHA). First-principles calculations demonstrate that the phase transition temperature can be modulated by varying the U values. The phase transition temperature can be well reproduced by the calculations using the Perdew–Burke–Ernzerhof functional combined with the U parameter of 1.5eV. Additionally,the calculated band structure, insulating or metallic properties, and phonon dispersion with this U value are in line with experimental observations. By employing the QHA to determine the Hubbard U parameter, this study provides valuable insights into the phase transition behavior of VO_(2). The findings highlight the importance of electron correlation effects in accurately describing the properties of this material. The agreement between the calculated results and experimental observations further validates the chosen U value and supports the use of the DFT+U method in studying VO_(2).

Saddlepoint Approximation Method in Reliability Analysis:A Review

The escalating need for reliability analysis(RA)and reliability-based design optimization(RBDO)within engineering challenges has prompted the advancement of saddlepoint approximationmethods(SAM)tailored for such problems.This article offers a detailed overview of the general SAM and summarizes the method characteristics first.Subsequently,recent enhancements in the SAM theoretical framework are assessed.Notably,the mean value first-order saddlepoint approximation(MVFOSA)bears resemblance to the conceptual framework of the mean value second-order saddlepoint approximation(MVSOSA);the latter serves as an auxiliary approach to the former.Their distinction is rooted in the varying expansion orders of the performance function as implemented through the Taylor method.Both the saddlepoint approximation and third-moment(SATM)and saddlepoint approximation and fourth-moment(SAFM)strategies model the cumulant generating function(CGF)by leveraging the initial random moments of the function.Although their optimal application domains diverge,each method consistently ensures superior relative precision,enhanced efficiency,and sustained stability.Every method elucidated is exemplified through pertinent RA or RBDO scenarios.By juxtaposing them against alternative strategies,the efficacy of these methods becomes evident.The outcomes proffered are subsequently employed as a foundation for contemplating prospective theoretical and practical research endeavors concerning SAMs.The main purpose and value of this article is to review the SAM and reliability-related issues,which can provide some reference and inspiration for future research scholars in this field.

Gamma Approximation Based Multi-Antenna Covert Communication Detection

Covert communication technology makes wireless communication more secure,but it also provides more opportunities for illegal users to transmit harmful information.In order to detect the illegal covert communication of the lawbreakers in real time for subsequent processing,this paper proposes a Gamma approximation-based detection method for multi-antenna covert communication systems.Specifically,the Gamma approximation property is used to calculate the miss detection rate and false alarm rate of the monitor firstly.Then the optimization problem to minimize the sum of the missed detection rate and the false alarm rate is proposed.The optimal detection threshold and the minimum error detection probability are solved according to the properties of the Lambert W function.Finally,simulation results are given to demonstrate the effectiveness of the proposed method.

Relaxed Stability Criteria for Time-Delay Systems:A Novel Quadratic Function Convex Approximation Approach

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays.By introducing two adjustable parameters and two free variables,a novel convex function greater than or equal to the quadratic function is constructed,regardless of the sign of the coefficient in the quadratic term.The developed lemma can also be degenerated into the existing quadratic function negative-determination(QFND)lemma and relaxed QFND lemma respectively,by setting two adjustable parameters and two free variables as some particular values.Moreover,for a linear system with time-varying delays,a relaxed stability criterion is established via our developed lemma,together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality.As a result,the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems.Finally,the superiority of our results is illustrated through three numerical examples.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Nonlinear Filtering With Sample-Based Approximation Under Constrained Communication:Progress, Insights and Trends

The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance.The main objective of nonlinear filtering is to infer the states of a nonlinear dynamical system of interest based on the available noisy measurements. In recent years, the advance of network communication technology has not only popularized the networked systems with apparent advantages in terms of installation,cost and maintenance, but also brought about a series of challenges to the design of nonlinear filtering algorithms, among which the communication constraint has been recognized as a dominating concern. In this context, a great number of investigations have been launched towards the networked nonlinear filtering problem with communication constraints, and many samplebased nonlinear filters have been developed to deal with the highly nonlinear and/or non-Gaussian scenarios. The aim of this paper is to provide a timely survey about the recent advances on the sample-based networked nonlinear filtering problem from the perspective of communication constraints. More specifically, we first review three important families of sample-based filtering methods known as the unscented Kalman filter, particle filter,and maximum correntropy filter. Then, the latest developments are surveyed with stress on the topics regarding incomplete/imperfect information, limited resources and cyber security.Finally, several challenges and open problems are highlighted to shed some lights on the possible trends of future research in this realm.

The Low-Rank Approximation of Fourth-Order Partial-Symmetric and Conjugate Partial-Symmetric Tensor

We present an orthogonal matrix outer product decomposition for the fourth-order conjugate partial-symmetric(CPS)tensor and show that the greedy successive rank-one approximation(SROA)algorithm can recover this decomposition exactly.Based on this matrix decomposition,the CP rank of CPS tensor can be bounded by the matrix rank,which can be applied to low-rank tensor completion.Additionally,we give the rank-one equivalence property for the CPS tensor based on the SVD of matrix,which can be applied to the rank-one approximation for CPS tensors.

Linear low-rank approximation and nonlinear dimensionality reduction

We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of columnpartitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.

Fast nonnegative tensor ring decomposition based on the modulus method and low-rank approximation

Nonnegative tensor ring(NTR) decomposition is a powerful tool for capturing the significant features of tensor objects while preserving the multi-linear structure of tensor data. The existing algorithms rely on frequent reshaping and permutation operations in the optimization process and use a shrinking step size or projection techniques to ensure core tensor nonnegativity, which leads to a slow convergence rate, especially for large-scale problems. In this paper, we first propose an NTR algorithm based on the modulus method(NTR-MM), which constrains core tensor nonnegativity by modulus transformation. Second, a low-rank approximation(LRA) is introduced to NTR-MM(named LRA-NTR-MM), which not only reduces the computational complexity of NTR-MM significantly but also suppresses the noise. The simulation results demonstrate that the proposed LRA-NTR-MM algorithm achieves higher computational efficiency than the state-of-the-art algorithms while preserving the effectiveness of feature extraction.

Integrating a novel irrigation approximation method with a process-based remote sensing model to estimate multi-years'winter wheat yield over the North China Plain

Accurate estimation of regional winter wheat yields is essential for understanding the food production status and ensuring national food security.However,using the existing remote sensing-based crop yield models to accurately reproduce the inter-annual and spatial variations in winter wheat yields remains challenging due to the limited ability to acquire irrigation information in water-limited regions.Thus,we proposed a new approach to approximating irrigations of winter wheat over the North China Plain(NCP),where irrigation occurs extensively during the winter wheat growing season.This approach used irrigation pattern parameters(IPPs)to define the irrigation frequency and timing.Then,they were incorporated into a newly-developed process-based and remote sensing-driven crop yield model for winter wheat(PRYM–Wheat),to improve the regional estimates of winter wheat over the NCP.The IPPs were determined using statistical yield data of reference years(2010–2015)over the NCP.Our findings showed that PRYM–Wheat with the optimal IPPs could improve the regional estimate of winter wheat yield,with an increase and decrease in the correlation coefficient(R)and root mean square error(RMSE)of 0.15(about 37%)and 0.90 t ha–1(about 41%),respectively.The data in validation years(2001–2009 and 2016–2019)were used to validate PRYM–Wheat.In addition,our findings also showed R(RMSE)of 0.80(0.62 t ha–1)on a site level,0.61(0.91 t ha–1)for Hebei Province on a county level,0.73(0.97 t ha–1)for Henan Province on a county level,and 0.55(0.75 t ha–1)for Shandong Province on a city level.Overall,PRYM–Wheat can offer a stable and robust approach to estimating regional winter wheat yield across multiple years,providing a scientific basis for ensuring regional food security.

Formalism of rotating-wave approximation in high-spin system with quadrupole interaction

We investigate the rotating wave approximation applied in the high-spin quantum system driven by a linearly polarized alternating magnetic field in the presence of quadrupole interactions.The conventional way to apply the rotating wave approximation in a driven high-spin system is to assume the dynamics being restricted in the reduced Hilbert space.However,when the driving strength is relatively strong or the driving is off resonant,the leakage from the target resonance subspace cannot be neglected for a multi-level quantum system.We propose the correct formalism to apply the rotating wave approximation in the full Hilbert space by taking this leakage into account.By estimating the operator fidelity of the time propagator,our formalism applied in the full Hilbert space unambiguously manifests great advantages over the conventional method applied in the reduced Hilbert space.

A novel method for simulating nuclear explosion with chemical explosion to form an approximate plane wave: Field test and numerical simulation

A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.

Cyclic Solution and Optimal Approximation of the Quaternion Stein Equation

In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .

MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE

We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.

Radial Basis Approximations Based BEMD for Enhancement of Non-Uniform Illumination Images

An image can be degraded due to many environmental factors like foggy or hazy weather,low light conditions,extra light conditions etc.Image captured under the poor light conditions is generally known as non-uniform illumination image.Non-uniform illumination hides some important information present in an image during the image capture Also,it degrades the visual quality of image which generates the need for enhancement of such images.Various techniques have been present in literature for the enhancement of such type of images.In this paper,a novel architecture has been proposed for enhancement of poor illumination images which uses radial basis approximations based BEMD(Bi-dimensional Empirical Mode Decomposition).The enhancement algorithm is applied on intensity and saturation components of image.Firstly,intensity component has been decomposed into various bi-dimensional intrinsic mode function and residue by using sifting algorithm.Secondly,some linear transformations techniques have been applied on various bidimensional intrinsic modes obtained and residue and further on joining the transformed modes with residue,enhanced intensity component is obtained.Saturation part of an image is then enhanced in accordance to the enhanced intensity component.Final enhanced image can be obtained by joining the hue,enhanced intensity and enhanced saturation parts of the given image.The proposed algorithm will not only give the visual pleasant image but maintains the naturalness of image also.

Approximations by Ideal Minimal Structure with Chemical Application

The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information.It can be characterized by two crisp sets,named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset.This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J.The novel approach(indicated by JMSAS)modifies the approximation space to diminish the bound-ary region and enhance the measure of accuracy.The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques.Via illustrated examples,several remarkable results using these notions are obtained and some of their properties are established.Several sorts of near open(resp.closed)sets based on JMSAS are studied.Furthermore,the connections between these assorted kinds of near-open sets in JMSAS are deduced.The advantages and disadvan-tages of the proposed approach compared to previous ones are examined.An algorithm using MATLAB and a framework for decision-making problems are verified.Finally,the chemical application for the classification of amino acids(AAs)is treated to highlight the significance of applying the suggested approximation.

THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

An Uncertainty Analysis and Reliability-Based Multidisciplinary Design Optimization Method Using Fourth-Moment Saddlepoint Approximation

In uncertainty analysis and reliability-based multidisciplinary design and optimization(RBMDO)of engineering structures,the saddlepoint approximation(SA)method can be utilized to enhance the accuracy and efficiency of reliability evaluation.However,the random variables involved in SA should be easy to handle.Additionally,the corresponding saddlepoint equation should not be complicated.Both of them limit the application of SA for engineering problems.The moment method can construct an approximate cumulative distribution function of the performance function based on the first few statistical moments.However,the traditional moment matching method is not very accurate generally.In order to take advantage of the SA method and the moment matching method to enhance the efficiency of design and optimization,a fourth-moment saddlepoint approximation(FMSA)method is introduced into RBMDO.In FMSA,the approximate cumulative generating functions are constructed based on the first four moments of the limit state function.The probability density function and cumulative distribution function are estimated based on this approximate cumulative generating function.Furthermore,the FMSA method is introduced and combined into RBMDO within the framework of sequence optimization and reliability assessment,which is based on the performance measure approach strategy.Two engineering examples are introduced to verify the effectiveness of proposed method.