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We consider the regularized Landau-Pekar equations with positive speed of sound and prove the existence of subsonic traveling waves. We provide a definition of the effective mass for the regularized Landau-Pekar equations based on the energy-velocity expansion of subsonic traveling waves. Moreover we show that this definition of the effective mass agrees with the definition based on an energy-momentum expansion of low energy states. [ABSTRACT FROM AUTHOR]

This paper proposes a fractional structure and texture aware Retinex (FSTAR) model for image decomposition with application to low-light enhancement. First, a novel structure aware measure called Maximum Fractional Difference (MFD) is introduced, which is the maximum of fractional differences of the input image in eight symmetric directions. Then fractional structure and texture aware maps are built based on MFD and Huber function from robust statistics, which are used as weighted matrices in the regularization terms of reflectance and illumination components. To ensure the intrinsic physical constraints of Retinex on two components, two extra penalty terms are incorporated into the objective function of FSTAR to penalize deviations of the estimated components from the corresponding constraints. The FSTAR is solved via an alternating iterative algorithm; i.e., the objective function is minimized with respect to one variable with another variable fixed, and this process is done alternately until termination condition is met. Qualitative and quantitative evaluations of FSTAR on three low-light image datasets, compared to ten state-of-the-art methods, show its superior performance in Retinex decomposition and low-light image enhancement. • Present texture aware measure based on fractional directional difference for texture extraction. • Propose fractional structure-texture aware Retinex model with constraints on two components. • Model is faithful to intrinsic physical meaning of Retinex in theory and easy to solve numerically. • Model has outstanding performance in terms of image decomposition and low-light enhancement. [ABSTRACT FROM AUTHOR]

Video stabilization plays a pivotal role in enhancing video quality by eliminating unwanted jitter in shaky videos. This paper introduces a novel video stabilization algorithm that leverages low‐rank constraint and trajectory optimization to effectively eliminate undesirable motion and generate stabilized videos. In the proposed algorithm, a low‐rank constraint regularization term is incorporated to enhance the smoothness of motion trajectories. Additionally, a predictive path smoothness term is integrated to ensure the consistency of motion across neighbouring frames. To address the problem of excessive cropping resulting from aggressive smoothing, a flexible local window strategy that emphasizes local motion relationships within the trajectories is introduced. The experimental results show that, compared to other excellent video stabilization algorithms, the proposed algorithm improves the stability metric by approximately 2.3%. Furthermore, in the stabilized videos generated by the algorithm, an approximate improvement of 2.18 dB in average image temporal fidelity and a 5.7% increase in average structural similarity between adjacent frames are achieved. The code that implements the proposed method is publicly accessible at https://github.com/CZS0319/VS_Low‐Rank_Constraint_Trajectory_Optimization. [ABSTRACT FROM AUTHOR]

The randomized sparse Kaczmarz (RSK) method is an algorithm used to calculate sparse solutions for the basis pursuit problem. In this paper, we propose an algorithm framework for computing sparse solutions of linear systems, which includes the sparse Kaczmarz and sparse block Kaczmarz algorithms. In order to overcome the limitations of the l1 penalty, we design an effective and new randomized sparse Kaczmarz algorithm (RSK-MCP) based on the non-convex minimax-concave penalty (MCP) in sparse signal reconstruction. Additionally, we prove that the RSK-MCP algorithm is equivalent to the randomized coordinate descent method for the corresponding dual problem. Based on this result, we demonstrate that the RSK-MCP algorithm exhibits linear convergence, meaning it converges to a sparse solution of the MCP model when the regularization of MCP is a strongly convex function. Numerical experiments indicate that the RSK-MCP algorithm outperforms RSK-L1 in terms of both efficiency and accuracy [ABSTRACT FROM AUTHOR]

This paper presents novel way to achieve fast and accurate Artificial Neural Network (ANN) modeling of Radio Frequency (RF) front end Low Noise Amplifier (LNA). Multilayer perceptron neural network is implemented to model high gain, ultra-low noise pseudomorhic High Electron Mobility Transistor (pHEMT) based LNA. Datasets are developed for input and output that is obtained from the Electro-Magnetic simulator. Different neural networks such as PatternNet, FitNet, and CascadeForwardNet with different algorithms are trained, tested, and compared to learn the behavior of the amplifier, and the best model is analyzed. Neural networks are modeled for LNA S-parameters and NF. It is observed that greater than 99% accuracy is achieved for PatternNet Bayesian regularization algorithm with less number of hidden layers and also it is found that the simulation results are almost similar to the developed ANN. [ABSTRACT FROM AUTHOR]

The problem of signal desynchronization in passive imaging based on noise correlation for defect detection in elastic plates is investigated. Although a post-processing resynchronization process relying on the symmetry of noise correlation functions can be applied prior to the imaging algorithm, perfect synchronization might not be achieved experimentally. Effect of such residual synchronization errors on the defect detection performance is quantified as a function of their probability density function. A mathematical regularization process is then proposed to reduce the standard deviation of the resynchronization errors by a factor of N − 1 / N (N is the number of sensors), which results in a significant improvement in the detection performance. Finally, these theoretical results are validated through a simple flexural-wave propagation simulation. [ABSTRACT FROM AUTHOR]

Cold forming of polycarbonate films results in the formation of shear bands in the necking zone. The numerical results obtained from standard viscoplastic material models exhibit mesh size dependency, requiring mathematical regularization. For this purpose, we present in this work a large deformation gradient theory for a viscoplastic isotropic material model published before. We extend our model to a micromorphic model by introducing a new micromorphic variable as an additional degree of freedom along with its first gradient. This variable represents a microequivalent plastic strain. The relation between the macroequivalent plastic strain and the micromorphic variable is accomplished by a micromorphic coupling modulus. This coupling forces proximity between the macro- and microvariables, leading to the targeted regularization effect. The micromorphic model is implemented as a three-dimensional initial boundary value problem in an in-house finite element tool. The analysis is performed for both uniaxial and biaxial specimens. The provided numerical examples show the ability of our model to regularize shear bands within the specimens and address the issue of localization. [ABSTRACT FROM AUTHOR]

Standard beams are mainly used for the calibration of strain sensors using their load reconstruction models. However, as an ill-posed inverse problem, the solution to these models often fails to converge, especially when dealing with dynamic loads of different frequencies. To overcome this problem, a piecewise Tikhonov regularization method (PTR) is proposed to reconstruct dynamic loads. The transfer function matrix is built both using the denoised excitations and the corresponding responses. After singular value decomposition (SVD), the singular values are divided into submatrices of different sizes by utilizing a piecewise function. The regularization parameters are solved by optimizing the piecewise submatrices. The experimental result shows that the MREs of the PTR method are 6.20% at 70 Hz and 5.86% at 80 Hz. The traditional Tikhonov regularization method based on GCV exhibits MREs of 28.44% and 29.61% at frequencies of 70 Hz and 80 Hz, respectively, whereas the L-curve-based approach demonstrates MREs of 29.98% and 18.42% at the same frequencies. Furthermore, the PREs of the PTR method are 3.54% at 70 Hz and 3.73% at 80 Hz. The traditional Tikhonov regularization method based on GCV exhibits PREs of 27.01% and 26.88% at frequencies of 70 Hz and 80 Hz, respectively, whereas the L-curve-based approach demonstrates PREs of 29.50% and 15.56% at the same frequencies. All in all, the method proposed in this paper can be extensively applied to load reconstruction across different frequencies. [ABSTRACT FROM AUTHOR]

This study explores the effects of using space-fractional derivatives and adding multiplicative noise, modeled by a Wiener process, on the solutions of the space-fractional stochastic regularized long wave equation. New fractional stochastic solutions are constructed, and the consistency of the obtained solutions is examined using the transition between phase plane orbits. Their bifurcation and dependence on initial conditions are investigated. Some of these solutions are shown graphically, illustrating both the individual and combined influences of fractional order and noise on selected solutions. These effects appear as alterations in the amplitude and width of the solutions, and as variations in their smoothness. [ABSTRACT FROM AUTHOR]

Contrastive learning has actively been used for unsupervised graph representation learning owing to its success in computer vision. Most graph contrastive learning methods use instance discrimination. It treats each instance as a distinct class against a query instance as the pretext task. However, such methods inevitably cause a class collision problem because some instances may belong to the same class as the query. Thus, the similarity shared through instances from the same class cannot be reflected in the pre-training stage. To address this problem, we propose graph contrastive learning with consistency regularization (GCCR), which introduces a consistency regularization term to graph contrastive learning. Unlike existing methods, GCCR can obtain a graph representation that reflects intra-class similarity by introducing a consistency regularization term. To verify the effectiveness of the proposed method, we performed extensive experiments and demonstrated that GCCR improved the quality of graph representations for most datasets. Notably, experimental results in various settings show that the proposed method can learn effective graph representations with better robustness against transformations than other state-of-the-art methods. • We propose a graph contrastive learning method to address the class collision problem. • We suggest a novel loss function that adds a consistency regularization term. • Our method obtains effective graph representation reflecting intra-class similarity. • Experimental results show that our method outperforms previous state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Distributed learning has attracted considerable attention in recent years due to its power to deal with big data in various science and engineering problems. Based on a divide-and-conquer strategy, this paper studies the distributed robust regression algorithm associated with correntropy losses and coefficient regularization in the scheme of kernel networks, where the kernel functions are not required to be symmetric or positive semi-definite. We establish explicit convergence results of such distributed algorithm depending on the number of data partitions, robustness and regularization parameters. We show that with suitable parameter choices the distributed robust algorithm can obtain the optimal convergence rate in the minimax sense, and simultaneously reduce the computational complexity and memory requirement in the standard (non-distributed) algorithms. [ABSTRACT FROM AUTHOR]

Distributed algorithms are receiving renewed attention across multiple disciplines due to the dramatically increasing demand of big data processing. We consider a class of consensus optimization problems over a static network system of multiple agents, where each of local cost functions is a sum of a smooth function and a non-Lipschitz regularization term. This kind of problems is widely found in scientific and engineering areas such as machine learning and data analysis. Inspired by Bian and Chen (SIAM J. Opt. 23(3), 1718–1741 2017), we propose a decentralized smoothing quadratic regularization algorithm (abbreviated as D-SQRA) for solving the composite consensus problem with non-Lipschitz singularities. To some extent, D-SQRA can be seen as an extension in the decentralized setup of the smoothing quadratic regularization algorithm (SQRA) proposed in (SIAM J. Opt. 23(3), 1718–1741 2017). Our main contribution is to show that D-SQRA can inherit the theoretical properties of its centralized counterpart, i.e., SQRA, in both sides of convergence and worst-case iteration complexity to achieve an ϵ scaled stationary point. We also present some numerical examples on sparse sensing problems based on synthetic and real datasets to corroborate the effectiveness of the proposed decentralized algorithm. [ABSTRACT FROM AUTHOR]

Tucker decomposition is widely used for image representation, data reconstruction, and machine learning tasks, but the calculation cost for updating the Tucker core is high. Bilevel form of triple decomposition (TriD) overcomes this issue by decomposing the Tucker core into three low-dimensional third-order factor tensors and plays an important role in the dimension reduction of data representation. TriD, on the other hand, is incapable of precisely encoding similarity relationships for tensor data with a complex manifold structure. To address this shortcoming, we take advantage of hypergraph learning and propose a novel hypergraph regularized nonnegative triple decomposition for multiway data analysis that employs the hypergraph to model the complex relationships among the raw data. Furthermore, we develop a multiplicative update algorithm to solve our optimization problem and theoretically prove its convergence. Finally, we perform extensive numerical tests on six real-world datasets, and the results show that our proposed algorithm outperforms some state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The era of Industry 4.0 is gradually transforming our society into a data-driven one, which can help us uncover valuable information from accumulated data, thereby improving the level of social governance. The detection of anomalies, is crucial for maintaining societal trust and fairness, yet it poses significant challenges due to the ubiquity of anomalies and the difficulty in identifying them accurately. This paper aims to enhance the performance of the current Graph Convolutional Network (GCN)-based Graph Anomaly Detection (GAD) algorithm on datasets with extremely low proportions of anomalous labels. This goal is achieved through modifying the GCN network structure and conducting feature extraction, thus fully utilizing three types of information in the graph: node label information, node feature information, and edge information. Firstly, we theoretically demonstrate the relationship between label propagation and feature convolution, indicating that the Label Propagation Algorithm (LPA) can serve as a regularization penalty term for GCN, aiding in training and enabling learnable edge weights, providing a basis for incorporating node label information into GCN networks. Secondly, we introduce a method to aggregate node and edge features, thereby incorporating edge information into GCN networks. Finally, we design different GCN trainable weights for node features and co-embedding features. This design allows different features to be projected into different spaces, greatly enhancing model expressiveness. Experimental results on the DGraph dataset demonstrate superior AUC performance compared to baseline models, highlighting the feasibility and efficacy of the proposed approach in addressing GAD tasks in the scene with extremely low proportions of anomalous data. [ABSTRACT FROM AUTHOR]

Vibration monitoring is one of the most effective approaches for bearing fault diagnosis. Within this category of techniques, sparsity constraint-based regularization has received considerable attention for its capability to accurately extract repetitive transients from noisy vibration signals. The optimal solution of a sparse regularization problem is determined by the regularization term and the data fitting term in the cost function according to their weights, so a tradeoff between sparsity and data fidelity has to be made inevitably, which restricts conventional regularization methods from maintaining strong sparsity-promoting capability and high fitting accuracy at the same time. To address the limitation, a stepwise sparse regularization (SSR) method with an adaptive sparse dictionary is proposed. In this method, the bearing fault diagnosis is modeled as a multi-parameter optimization problem, including time indexes of the sparse dictionary and sparse coefficients. Firstly, sparsity-enhanced optimization is conducted by amplifying the regularization parameter, making the time indexes and the number of atoms adaptively converge to the moments when impulses occur and the number of impulses, respectively. Then, fidelity-enhanced optimization is carried out by removing the regularization term, thereby obtaining the high-precision reconstruction amplitudes. Simulations and experiments verify that the reconstruction accuracy of the SSR method outperforms other sparse regularization methods under most noise conditions, and thus the proposed method can provide more accurate results for bearing fault diagnosis. [ABSTRACT FROM AUTHOR]

High-resolution wide-swath (HRWS) imaging is the research focus of the modern spaceborne synthetic-aperture radar (SAR) imaging field, with significant relevance and vast application potential. Staggered SAR, as an innovative imaging system, mitigates blind areas across the entire swath by periodically altering the radar pulse repetition interval (PRI), thereby extending the swath width to multiples of that achievable by conventional systems. However, the staggered mode introduces inherent challenges, such as nonuniform azimuth sampling and echo data loss, leading to azimuth ambiguities and substantially impacting image quality. This paper proposes a sparse SAR imaging method for the low-oversampled staggered mode via compound regularization. The proposed method not only effectively suppresses azimuth ambiguities arising from nonuniform sampling without necessitating the restoration of missing echo data, but also incorporates total variation (TV) regularization into the sparse reconstruction model. This enhances the accurate reconstruction of distributed targets within the scene. The efficacy of the proposed method is substantiated through simulations and real data experiments from spaceborne missions. [ABSTRACT FROM AUTHOR]

This article explores the solution of the regularized long-wave equation (RLWE) and modified RLWE (MRLWE) using a semi-analytical approach known as the homotopy perturbation transform method (HPTM), revealing the characteristics of shallow water waves and ion-acoustic plasma waves. The effectiveness and accuracy of the technique are demonstrated by solving scenarios involving a single solitary wave (SSW) and two solitary waves (TSW) presented and compared with the exact solution of the RLWE. Furthermore, we introduced a fuzzy model for both RLWE and MRLWE, considering uncertainties in the coefficients related to the wave amplitude, and to understand the behavior of both fuzzy RLWE (FRLWE) and fuzzy MRLWE (FMRLWE) in the SSW by examining various numerical results using MATLAB. [ABSTRACT FROM AUTHOR]

We propose a coderivative-based generalized regularized Newton method with positive definite regularization term (GRNM-PD) to solve C 1 , 1 optimization problems. In GRNM-PD, a general positive definite symmetric matrix is used to regularize the generalized Hessian, in contrast to the recently proposed GRNM, which uses the identity matrix. Our approach features global convergence and fast local convergence rate even for problems with nonisolated solutions. To this end, we introduce the p-order semismooth ∗ property which plays the same role in our analysis as Lipschitz continuity of the Hessian does in the C 2 case. Imposing only the metric q-subregularity of the gradient at a solution, we establish global convergence of the proposed algorithm as well as its local convergence rate, which can be superlinear, quadratic, or even higher than quadratic, depending on an algorithmic parameter ρ and the regularity parameters p and q. Specifically, choosing ρ to be one, we achieve quadratic local convergence rate under metric subregularity and the strong semismooth ∗ property. The algorithm is applied to a class of nonsmooth convex composite minimization problems through the machinery of forward–backward envelope. The greater flexibility in the choice of regularization matrices leads to notable improvement in practical performance. Numerical experiments on box-constrained quadratic programming problems demonstrate the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

This article presents a novel approach to image restoration utilizing a unique non-convex l 1 / 2 -TV regularization model. This model integrates the l 1 / 2 -quasi norm as a regularization function, introducing non-convexity to promote sparsity and unevenly penalize elements, thereby enhancing restoration outcomes. To tackle this model, an efficient algorithm named the Alternating Direction Method of Multipliers, based on the Lagrangian multiplier, is introduced. This effectively prevents the penalty parameter from reaching infinity and ensures excellent convergence behavior. The proposed algorithm decomposes the optimization problem into subproblems, for which closed-form solutions are derived, particularly addressing the challenging l 1 / 2 regularization problem. To validate its effectiveness, a comprehensive set of experiments are conducted to compare its performance with existing methods. The experimental results demonstrate that the proposed model performs well in both qualitative and quantitative evaluations. Consequently, the proposed model is not only efficient and stable but also exhibits excellent convergence behavior. • A novel regularization model for image restoration, based on non-convex total variation is proposed in this work. • We propose an effective solution approach to solve the model using the Alternating Direction Method of Multipliers (ADMM). • The proposed solution provides the closed-form thresholding formula for regularization model. • Extensive numerical experiments demonstrate the superiority of the proposed method over compared methods. [ABSTRACT FROM AUTHOR]

The task of link prediction has become a fundamental research problem in the analysis of complex networks. However, most existing non-negative matrix factorization (NMF) methods are decoding models and solely consider a single type of structural information around node pairs in networks, resulting in sub-optimal prediction accuracy. To solve these limitations, we propose a novel model, namely Graph Regularized Autoencoder-inspired Non-negative Matrix Factorization via jointly Clustering information and Biased random walk (GRANMFCB for short), for link prediction. Specifically, GRANMFCB comprises both encoder and decoder components, fully leveraging the advantages of autoencoders. In addition, clustering information and high-order structures are utilized to preserve abundant structural information around node pairs and against sparsity of networks. Finally, effective iterative multi-multiplication updating rules are proposed to optimize the objective function and the convergence is strictly proved. Extensive experimental results on twelve real-world networks show that our proposed model outperforms the state-of-the-art approaches. Codes are available at https://github.com/litongf/GRANMFCB. [ABSTRACT FROM AUTHOR]

In this paper, a novel non-convex fractional-order image denoising model is proposed to suppress the staircase effect produced by the TV model while maintaining a neat contour. The model combines ℓ q (0 < q < 1) quasi-norm and fractional-order regularization, and employs a diffusion coefficient with a faster convergence rate to preserve more image edges and details. Additionally, an adaptive regularization parameter is designed to adjust the denoising performance of the algorithm. To obtain the optimal approximate solution of the model, an enhanced primal-dual algorithm is adopted and the complexity and convergence of the algorithm are theoretically analyzed. Finally, the effectiveness of the proposed method is demonstrated through numerical experiments. • A new non-convex FOTV model is proposed. • A new diffusion coefficient is introduced to retain more edge details of the image. • The existing primal-dual algorithm is improved, and the convergence of this algorithm is analyzed. • An adaptive regularization parameter is designed. [ABSTRACT FROM AUTHOR]

Nonlocal regularization is frequently used to resolve the mesh dependency issue that is caused by strain softening in finite-element (FE) simulations. Some or all variables that affect strain softening are assumed to depend on the local, neighboring, or both in this method. The weight function is the main component of a regularization method. There are three widely used weight functions, which include the Gaussian distribution (GD), Galavi and Schweiger (GS), and over-nonlocal (ON) functions. All of them could alleviate or eliminate the mesh dependency in simple boundary value problems (BVPs), such as plane strain compression; the evaluation of their performance in real-world BVPs is rare. A detailed comparison of these functions has been carried out based on an anisotropic sand model that accounts for the evolution of anisotropy. The increment of void ratio is assumed nonlocal. All functions give mesh-independent force–displacement relationships in drained and undrained plane strain compression tests. The shear band thickness shows a small variation when the mesh size is smaller than the internal length. None could eliminate the mesh dependency of shear band orientation. The GS method is the most efficient in eliminating the mesh dependency in the strip footing problem. The ON method could give excessive overpredictions of the volume expansion around strip footings, which leads to unrealistic low reaction forces on strip footings at large deformations. All three weight functions give mesh-independent results for the earth pressure that acts on a retaining wall. [ABSTRACT FROM AUTHOR]

We introduce a regularization method with two differential operators for solving a linear ill-posed operator equation system. The existence and uniqueness of regularized solutions to the problem are derived. With an a priori as well as an a posteriori parameter choice strategy, convergence and convergence rates of the regularized solution are also obtained. As an application, we apply the regularization to a simultaneous inversion of the source term and the initial value problem for a heat conduction equation, numerical experiments are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse problem for the time‐fractional two‐dimensional Cahn–Hilliard equation. The ill‐posedness and a conditional stability of the inverse problem are proved. We present a new iterative variational regularization method to solve it. The convergence rates of the regularized solutions under the a priori regularization parameter choice rule and a posteriori regularization parameter choice rule are obtained. Numerical examples illustrate the effectiveness and stability of our proposed method. [ABSTRACT FROM AUTHOR]

In this note we construct self-dual cosmic strings from an Abelian Higgs model in two-dimension with a polynomial formation of the potential energy density. By integrating the Einstein equations, we obtain an equivalent form to the sources, which is a nonlinear elliptic equation with singularities and complicated exponential terms. We prove the existence of a solution governing strings in the broken symmetry category on the whole plane, and the multiple string solutions are valid under a sufficient condition imposed only on the total number of strings. The technique of upper–lower solutions and the method of regularization are employed to show the existence of a solution when there are at least two distant string centers. When all the string centers are identical, a fixed-point theorem is used to study the properties of the nonlinear elliptic equation. Finally, we establish the sharp asymptotic estimate for the solutions at infinity and derive the dependence of the total gravitational curvature on the string number. [ABSTRACT FROM AUTHOR]

We introduce a lifted |$\ell _1$| (LL1) regularization framework for the recovery of sparse signals. The proposed LL1 regularization is a generalization of several popular regularization methods in the field and is motivated by recent advancements in re-weighted |$\ell _1$| approaches for sparse recovery. Through a comprehensive analysis of the relationships between existing methods, we identify two distinct types of lifting functions that guarantee equivalence to the |$\ell _0$| minimization problem, which is a key objective in sparse signal recovery. To solve the LL1 regularization problem, we propose an algorithm based on the alternating direction method of multipliers and provide proof of convergence for the unconstrained formulation. Our experiments demonstrate the improved performance of the LL1 regularization compared with state-of-the-art methods, confirming the effectiveness of our proposed framework. In conclusion, the LL1 regularization presents a promising and flexible approach to sparse signal recovery and invites further research in this area. [ABSTRACT FROM AUTHOR]

Anomaly detection methods are introduced to remove abnormalities from specific datasets. In the paper, mean shifted contrastive loss for anomaly detection, a new objective function named mean shifted contrastive loss (MSCL), was created to retain the pre-trained features over transfer learning which were lost in previous anomaly detection methods. MSCL stops learning after a certain epoch as the points get closer to the normalized center. The proposed work investigated that due to some noise in the extracted features from images, the points revolve around the normalized center, and the accuracy freezes after some epochs. To resolve this issue, a new loss function is proposed which has better performance. The proposed methodology obtains a highly effective AUROC score of 98.6% and 97.6% on the CIFAR-100 and CIFAR-10 datasets. [ABSTRACT FROM AUTHOR]

Brain functional network (BFN) has emerged as a practical path to explore biomarkers for early mild cognitive impairment (eMCI). Currently, most of BFNs only considered the topology structure between two brain regions and ignored the high‐order information among multiple brain regions. We proposed an adaptive manifold regularization method to construct a new BFN. Firstly, a traditional hypergraph was constructed through a low‐order BFN. Then, an adaptive hypergraph was obtained by updating the traditional hypergraph weight and structure through adaptive hypergraph learning. An adaptive hypergraph manifold regularization term was constructed by the Laplacian matrix of the adaptive hypergraph. Finally, the low‐order BFN was optimized through the adaptive hypergraph manifold regularization and L1$$ {L}_1 $$ sparse regularization. The experimental results confirmed that the proposed method outperformed other state‐of‐the‐art methods in classification performance and stability. This study revealed the causes of changes in topological properties and provided a reference for the clinical diagnosis of eMCI. [ABSTRACT FROM AUTHOR]

In seismic data processing, data recovery including reconstruction of the missing trace and removal of noise from the recorded data are the key steps in improving the signal-to-noise ratio (SNR). The reconstruction of seismic data and removal of noise becomes a sparse optimization problem that can be solved by using sparse regularization. Sparse regularization is a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed inverses feasible. It deals with ill-posedness by replacing an ill-posed inverse problem with a well-posed problem that has a solution close to the true solution. In the last 2 decades, interest has shifted from linear toward nonlinear regularization methods even for linear inverse problems. In inverse problems, regularizations serve as stabilizing the solution of ill-posed inverse problems and give a solution that adequately fits measurements without producing unjustifiably complex artifacts. In this paper, we present a novel sparse regularization based on a tensor-based dictionary method for inverse problems (seismic data interpolation and denoising). This regularization avoids the vectorization step for sparse representation of seismic data during the reconstruction process. The key step in sparsifying signals is the choice of sparsity-promoting dictionary learning. The learning-based approach can adaptively sparsify datasets but has high computational complexity and involves no prior-constraint pattern information for the dataset. Many existing dictionary learning methods would be computationally infeasible for the high dimensional seismic data processing. These methods also destroy the essential information as well as it reduces the discriminability and expressibility of the signal, since they deal with vectorization. In this paper, the orthogonal tensor dictionary learning that learns a dictionary from the input data by employing orthogonality and separability is proposed as sparse regularization for the inverse problems. The performance of the proposed method was validated in seismic data interpolation and denoising individually as well as simultaneously. Numerical examples of synthetic and real seismic datasets demonstrate the validity of the proposed method. The SNR of the recovered data confirms that the proposed method is the most effective method than K-singular value decomposition and orthogonal dictionary learning methods. [ABSTRACT FROM AUTHOR]

With the presence of a large number of inversion algorithms for inverse heat transfer problems (IHTPs) and non-IHTPs, a need for review to have a holistic view is seen. An exhaustive literature review, with the motivation of selecting the inversion technique best fit for a given problem, was made for a general inverse problem. For ill-posedness, a classification of available regularization algorithms namely Tikhonov's regularization, Bayesian regularization, mollification method, Beck's sequential approach and Alifanov's iterative approach, has been provided. Inversion methods like singular value decomposition, truncated singular value decomposition, Tikhonov regularization and total variation regularization are explained. Optimization methods namely steepest descent method, conjugate gradient method, Newton method, Levenberg–Marquardt method, Lagrange method, adjoint method, function specification method, genetic algorithm, differential evolution and particle swarm optimization (PSO) are reviewed. Further, a technique based on neural networks is studied, and wavelet methods like shrinking and wavelet vaguelette decomposition are reviewed. Associated literature has also been listed, highlighting the gaps. The usability of various algorithms in IHTP, starting from the golden section search method, for retrieval of a single parameter, to the regularized versions of the inversion technique, for retrieval of multiple parameters with uncertainty, demonstrates real-life applications to fins in IHTP. An inversion algorithm capable to handle every kind of nonlinearity is sought in literature, whose absence raises the research question, "Is there a technique that works globally for every inverse problem?", is asked prior to, "What if the available techniques were not utilized to an extent that they should?" is posed. In lieu of this gap, a general comparative framework is developed, such that an efficient technique is selected, based on the total minimum error, which can be used in any field of interest. [ABSTRACT FROM AUTHOR]

The Helmholtz equation least-squares (HELS) method is a valuable tool for estimating equivalent sound sources of a radiating object. It solves an inverse problem by mapping measured pressures to a set of basis functions satisfying the Helmholtz equation in spherical coordinates. However, this problem is often ill-posed, necessitating additional regularization methods, in which often variations of Ridge or Lasso are used. These conventional methods do not explicitly consider the distribution underlying the source radiations (besides sparsity) and are often used in the context of obtaining only a point estimate, even in the presence of ambiguity in the data. In this work, we propose the use of empirical priors through a normalizing flow model to enhance the inversion results obtained with the HELS method. We first validate our approach using numerical data and subsequently demonstrate its superior performance in interpolating a measured violin directivity compared to Lasso and Ridge methods, even when optimal regularization parameters are selected. [ABSTRACT FROM AUTHOR]

The sparse regularization (SReg) model has been prove to be an effective tool for the structural damage identification. However, the SReg model overly penalizes the larger components in the damage parameter leading to extra estimation bias, and it ignores the similarity information among different measurements that is useful for improving the performance of damage identification. To further improve the accuracy of damage identification, this study proposes a joint fraction function regularization model by jointing multiple fraction function regularization models, where fraction function regularizers are utilized to overcome the excessive penalty drawback, and the similarity of different measurements is employed through a data fusion technique. The numerical and experimental study show that, compared with the previous SReg models, the damage identification errors of the proposed model are reduced by 4.15% and 2.12% on average, respectively. [ABSTRACT FROM AUTHOR]

Domain adaptation solves the challenge of inadequate labeled samples in the target domain by leveraging the knowledge learned from the labeled source domain. Most existing approaches aim to reduce the domain shift by performing some coarse alignments such as domain-wise alignment and class-wise alignment. To circumvent the limitation, we propose a coarse-to-fine unsupervised domain adaptation method based on metric learning, which can fully utilize more geometric structure and sample-wise information to obtain a finer alignment. The main advantages of our approach lie in four aspects: (1) it employs a structure-preserving algorithm to automatically select the optimal subspace dimension on the Grassmannian manifold; (2) based on coarse distribution alignment using maximum mean discrepancy, it utilizes the smooth triplet loss to leverage the supervision information of samples to improve the discrimination of data; (3) it introduces structure regularization to preserve the geometry of samples; (4) it designs a graph-based sample reweighting method to adjust the weight of each source domain sample in the cross-domain task. Extensive experiments on several public datasets demonstrate that our method achieves remarkable superiority over several competitive methods (more than 1.5% improvement of the average classification accuracy over the best baseline). [ABSTRACT FROM AUTHOR]

This work elaborated an improved method to multiframe super-resolution (SR), which involves a nonlocal first-order regularization combined with a nonlocal p-Laplacian term. The nonlocal TV term excels at edge preserving, whilst the nonlocal p-Laplacian is commonly used to perfectly reconstruct image textures. Firstly, we discuss the existence and uniqueness of a solution to our new model in a well posed framework. Then, we derive a modified Primal-dual iteration to compute the super-resolved solution. Furthermore, we introduce a new bilevel optimization approach to learn two regularization parameters. The included tests validate that the introduced optimization procedure performs favorably compared to numerous SR approaches in terms of efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Corrupted data appears widely in many contemporary applications including voting behavior, high-throughput sequencing and sensor networks. In this article, we consider the sparse modeling via L0-regularization under the framework of high-dimensional measurement error models. By utilizing the techniques of the nearest positive semi-definite matrix projection, the resulting regularization problem can be efficiently solved through a polynomial algorithm. Under some interpretable conditions, we prove that the proposed estimator can enjoy comprehensive statistical properties including the model selection consistency and the oracle inequalities. In particular, the nonoptimality of the logarithmic factor of dimensionality will be showed in the oracle inequalities. We demonstrate the effectiveness of the proposed method by simulation studies. [ABSTRACT FROM AUTHOR]

Hyperspectral anomaly detection is an important unsupervised binary classification problem that aims to effectively distinguish between background and anomalies in hyperspectral images (HSIs). In recent years, methods based on low-rank tensor representations have been proposed to decompose HSIs into low-rank background and sparse anomaly tensors. However, current methods neglect the low-rank information in the spatial dimension and rely heavily on the background information contained in the dictionary. Furthermore, these algorithms show limited robustness when the dictionary information is missing or corrupted by high level noise. To address these problems, we propose a novel method called multi-dimensional low-rank (MDLR) for HSI anomaly detection. It first reconstructs three background tensors separately from three directional slices of the background tensor. Then, weighted schatten p-norm minimization is employed to enforce the low-rank constraint on the background tensor, and L F , 1 -norm regularization is used to describe the sparsity in the anomaly tensor. Finally, a well-designed alternating direction method of multipliers (ADMM) is employed to effectively solve the optimization problem. Extensive experiments on four real-world datasets show that our approach outperforms existing anomaly detection methods in terms of accuracy. [ABSTRACT FROM AUTHOR]

We develop a method for estimating a simple matrix for a multidimensional item response theory model. Our proposed method allows each test item to correspond to a single latent trait, making the results easier to interpret. It also enables clustering of test items based on their corresponding latent traits. The basic idea of our approach is to use the prenet (product-based elastic net) penalty, as proposed in factor analysis. For optimization, we show that combining stochastic EM algorithms, proximal gradient methods, and coordinate descent methods efficiently yields solutions. Furthermore, our numerical experiments demonstrate its effectiveness, especially in cases where the number of test subjects is small, compared to methods using the existing L 1 penalty. [ABSTRACT FROM AUTHOR]

The modeling of damage as an anisotropic phenomenon enables the consideration of arbitrarily oriented microcracks at the material point level. Yet, the incorporation of material softening into structural simulations still requires a regularization of for example, the degrading variable. There exist different possibilities for a regularization in case of anisotropic damage with varying numbers of nonlocal degrees of freedom corresponding to for example, the symmetric integrity tensor , the principal traces of the damage tensor or a scalar damage hardening variable. Here, we propose a finite strain formulation with a symmetric second order damage tensor of which all six independent components are regularized with a corresponding nonlocal degree of freedom. Due to the significant increase in computational cost caused by the full regularization of the damage tensor, alternative approaches for a reduced regularization with fewer nonlocal degrees of freedom are discussed. Thereafter, the results of a numerical example using the model with full regularization are presented. [ABSTRACT FROM AUTHOR]

Image deblurring based on sparse regularization has garnered significant attention, but there are still certain limitations that need to be addressed. For instance, convex sparse regularization tends to exhibit biased estimation, which can adversely impact the deblurring performance, while non-convex sparse regularization poses challenges in terms of solving techniques. Furthermore, the performance of the traditional iterative algorithm also needs to be improved. In this paper, we propose an image deblurring method based on convex non-convex (CNC) sparse regularization and a plug-and-play (PnP) algorithm. The utilization of CNC sparse regularization not only mitigates estimation bias but also guarantees the overall convexity of the image deblurring model. The PnP algorithm is an advanced learning-based optimization algorithm that surpasses traditional optimization algorithms in terms of efficiency and performance by utilizing the state-of-the-art denoiser to replace the proximal operator. Numerical experiments verify the performance of our proposed algorithm in image deblurring. [ABSTRACT FROM AUTHOR]

Trace regression has received a lot of attention due to its ability to account for matrix-type covariates, including panel data, images, and genomic microarrays as special cases. However, most of its existing research focuses on the case of mean regression. In this paper, we consider the expectile trace regression, which can provide a more diversified picture of the regression relationship at different expectiles, via the low-rank and group sparsity regularization. The upper bound for the statistical rate of convergence of the regularized estimator is established under some mild conditions. Some simulations, as well as a real data example, are also provided to illustrate the finite sample performance of the developed expectile trace regression. [ABSTRACT FROM AUTHOR]

In this article, we leverage over-parameterization to design regularization-free algorithms for the high-dimensional single index model and provide theoretical guarantees for the induced implicit regularization phenomenon. Specifically, we study both vector and matrix single index models where the link function is nonlinear and unknown, the signal parameter is either a sparse vector or a low-rank symmetric matrix, and the response variable can be heavy-tailed. To gain a better understanding of the role played by implicit regularization without excess technicality, we assume that the distribution of the covariates is known a priori. For both the vector and matrix settings, we construct an over-parameterized least-squares loss function by employing the score function transform and a robust truncation step designed specifically for heavy-tailed data. We propose to estimate the true parameter by applying regularization-free gradient descent to the loss function. When the initialization is close to the origin and the stepsize is sufficiently small, we prove that the obtained solution achieves minimax optimal statistical rates of convergence in both the vector and matrix cases. In addition, our experimental results support our theoretical findings and also demonstrate that our methods empirically outperform classical methods with explicit regularization in terms of both l 2 -statistical rate and variable selection consistency. for this article are available online. [ABSTRACT FROM AUTHOR]

The least absolute shrinkage and selection operator (LASSO) and its variants are widely used for sparse signal recovery. However, the determination of the regularization factor requires cross-validation strategy, which may obtain a sub-optimal solution. Motivated by the self-regularization nature of sparse Bayesian learning (SBL) approach and the framework of generalized LASSO, we propose a new hierarchical Bayesian model using automatic-weighting Laplace priors in this paper. In the proposed hierarchical Bayesian model, the posterior distributions of all the parameters can be approximated using variational Bayesian inference, resulting in closed-form solutions for all parameters updating. Moreover, the space alternating variational estimation strategy is used to avoid matrix inversion, and a fast algorithm (SAVE-WLap-SBL) is proposed. Comparing to existed SBL methods, the proposed method encourages the sparsity of signals more efficiently. Numerical experiments on synthetic and real data illustrate the benefit of these advances. [ABSTRACT FROM AUTHOR]

We propose a new method for principal component analysis (PCA) called feature grouping and sparse principal component analysis (FGSPCA). This method is designed to capture both grouping and sparsity structures in factor loadings simultaneously. To achieve this, we use a non‐convex truncated regularization that can adjust for sparsity and grouping effects automatically. This regularization encourages factor loadings with similar values to be either grouped together for feature grouping or be zero for feature selection, helping to reduce model complexity and improve interpretation. While other structured PCA methods often require prior knowledge to construct the regularization term, FGSPCA can capture grouping and sparsity structures without any prior information. We solve the resulting non‐convex optimization problem using an alternating algorithm that combines difference‐of‐convex programming, the augmented Lagrange method, and coordinate descent method. Our experiments show that FGSPCA performs well and efficiently on both synthetic and real‐world datasets. An implementation of FGSPCA is available on GitHub https://github.com/HaiyanJiang/FGSPCA. [ABSTRACT FROM AUTHOR]

Fuzzy K-Means (FKM) based on fuzzy theory is a classic method to effectively handle overlapping regions between clusters. However, redundant features and noises brought by increasing data dimensions affect the effectiveness of FKM. To cope with this issue, we propose a Discriminative Projection Fuzzy K-Means with adaptive neighbors (DPFKM) model, which embeds a discriminative subspace into FKM to facilitate learning of global structure and the most discriminative information. Firstly, a novel projection space with uncorrelated constraints are adopted to promote statistical independence among the data in the subspace as well as to enhance the ability of FKM to discern and utilize discriminative information. Secondly, the Frobenius norm is introduced as the regularization term to eliminate discrete solutions, while preserving the fuzziness and enhancing the sparsity of FKM. Finally, we propose a novel optimization method to finetune the model, with a particular focus on adaptive adjustment of the regularization parameter based on the proximity relationship between the samples and clusters. Comprehensive experiments are conducted on multiple data sets, and the results can prove the superiority of the proposed model. • The discriminative projection fuzzy K-means (DPFKM) is proposed to handle subspace data clustering. • DPFKM utilizes uncorrelated constraints to maintain discriminative information and global structure in subspace. • DPFKM adaptively determines the regularization parameter using neighbor relationship of samples and clusters. • Experiments on nine data sets show that our method realize a competitive performance in clustering results. [ABSTRACT FROM AUTHOR]

The 2019 new coronavirus illness (COVID-19) is an international public health emergency. Our social and healthcare systems are under a great deal of strain as a result of the daily increase in infection rates and fatalities. Doctors typically perform a chest Xray to identify the diseased areas of the lungs since pneumonia is a common type of infection that spreads in the lungs. In this paper, we propose a Convolution Neural Network via the li regularization model to detect COVID-19 patients using chest X-Ray images. Due to the lack of the COVID-19 benchmark dataset, we use deep learning techniques to identify the best pre-trained CNN model for this job by comparing 15 models. The suggested algorithm was tested on 1316 photos (116 COVID-19 cases, 328 healthy controls, and 872 pneumonia cases), with 66% for training, 17% for validation, and 17% for testing. The classification accuracy, loss, valueaccuracy, and value-loss values obtained by the suggested technique are 0.9912, 0.0187, 0.1119, and 0.9506 respectively. Additionally, the model effectively decreases training loss while boosting accuracy. The results show that proposed procedures are more effective than existing ones at identifying COVID-19 cases from chest X-ray pictures. [ABSTRACT FROM AUTHOR]

Image reconstruction of EIT mathematically is a seriously ill-posed inverse problem, which is easily affected by measurement noise. This fact leads to a relatively low spatial resolution, particularly in the accuracy of identifying object boundaries. This paper concerns with reconstructing a finite number of simple and small inclusions equipped with the homogeneous background conductivity. The sparsity with respect to the inclusions in the spacial representation domain is apriori assumed. We try to reexamine the multi-parameter constraints on mixing between ℓ1-norm and ℓ2-norm for attaining the sparse reconstruction as well as simultaneously enhancing the stability. On the basis of the reference approximation reconstructed by nonstationary iterated Tikhonov regularization (NITR) method, we propose a novel one-step proximal sparsity-promoting approach by one induced proximal shrink operator, abbreviated as one-step PNITR method. The proposed one-step PNITR method consists of twofold: one first performs NITR with mth iteration to generate the reference approximation, and then performs one-step proximal shrinkage processing and one forcing constraint function on it to obtain the final sparsity-promoting reconstruction. For the latter, the former aims to not only enhance higher reliability but also guarantee the sparsity. The proposed method can benefit from the double regularization effect. It is supposed to further improve the imaging quality in terms of sharpening the edges and reducing the artefacts. To validate the advantage of the proposed method, numerical simulations with synthetic data have been carried out. Also, qualitative and quantitative comparisons are conducted. Results indicate that the proposed approach can lead to substantial improvements in EIT image resolution. The performed numerical simulations show that our method is promising. [ABSTRACT FROM AUTHOR]

Full waveform inversion (FWI) can provide an accurate velocity model by matching observed and simulated seismograms. Mathematically, FWI is a highly ill-posed inverse problem that the observed data are independent of the model and cannot be inverted accurately. For a stable and reasonable inversion, proper regularization methods have to be taken into account. We propose a novel composite regularization for frequency-domain FWI problem, which uses a non-convex second-order total variation (TV) term and an overlapping group sparse TV (OGS-TV) regularization term. Compared with the conventional TV regularization, our method has better accuracy and robustness, and could effectively make use of the sparsity in the velocity model. Furthermore, the alternating direction multiplier algorithm with the adaptive selection of the penalty parameters is developed to solve this composite constraint problem, which can improve the stability of the FWI process. To illustrate the superior method both visually and quantitatively, we experimentally compare the proposed method with the conventional TV regularized FWI and the second-order total generalized variation regularized FWI and overlapping group sparsity regularized FWI on the well-known geological models. [ABSTRACT FROM AUTHOR]