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We enhanced the performance of linear prediction (LP) for bone-conducted (BC) speech signals by deriving a regularized version of the modified covariance (MC) method. The spectral estimation accuracy is discussed for the purpose of assessing the performance of LP. Inherently, BC speech has an expanded spectral dynamic range that causes ill-condition in conventional spectral estimation methods. To overcome this problem, we focus on the covariance method and its modified version, the MC method. In the field of numerical analysis, we often face the situation where an ill-conditioned case occurs in finding the solution. To deal with this situation, the regularized least squares method is utilized. Motivated by this idea, we derive the regularized MC (RMC) method in this study for BC speech analysis. The RMC method has the effect of compressing the spectral dynamic range of the input speech signal, and this effect mitigates the ill-conditioned problem of LP. Through experiments, we show that the RMC method provides a more accurate spectral estimation than conventional spectral estimation methods for BC speech where synthetic and real BC speeches are considered. The performance of the RMC method is affected by the setting of the regularization parameter. A way to determine the regularization parameter in practice is experimentally derived. The RMC method with such a setting provides the best performance of spectral estimation for BC speech. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parameterized three-operator splitting algorithm to solve nonconvex minimization problems with the sum of three non-convex functions, where two of them have Lipschitz continuous gradients. We establish the convergence of the proposed algorithm under the KurdykaŁojasiewicz assumption by constructing a suitable energy function with a non-increasing property. As applications, we employ the proposed algorithm to solve low-rank matrix recovery and image inpainting problems. Numerical results demonstrate the efficiency and effectiveness of the proposed algorithm compared to other algorithms. [ABSTRACT FROM AUTHOR]

Elastic net model is widely used in high-dimensional statistics for parameter regression and variable selection, which has been proved that the performance is often better than the lasso. However, it can only deals with data containing Gaussian noise, so it is not suitable for modern complex highdimensional data. Fortunately, an adaptive and robust minimization model, which combines the lp-norm data fidelity and elastic net regularization, has been proposed to deal with different types of noises and inherit the advantages of the elastic net in prediction accuracy. The double non-smoothness in objective function makes it challenging to minimize the model. After investigation, we find that the optimization algorithm is currently limited to the first-order alternating direction method of multipliers (ADMM), which is relatively lower in the recovered solutions' accuracy and relatively slower in the calculation speed. Therefore, we are committed to developing a fast and effective algorithm based on second-order information. Specifically, we propose a preconditioned proximal point algorithm (abbreviated as P-PPA) to solve the considered model by adding a proximal term. In theory, we analyze the consistency between the solution of the surrogate model and the original model. In addition, a key subproblem in P-PPA is solved by superlinear or even quadratically convergent semismooth Newton methods from the dual perspective. Finally, a large number of numerical experiments on high-dimensional simulated and real examples fully verify that our proposed algorithm is superior to ADMM in terms of calculation accuracy and speed. [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]

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 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]

This paper is first study for considering the elliptic equation with Caputo derivative and nonlocal integral condition. We obtain the upper bound of some information of the mild solution. The second contribution is to provide the lower bound of the solution and its derivative at terminal time. Moreover, we prove the non-correction of the problem in the sense of Hadamard. We continue to provide the regularized solution. We also establish the convergence rate between the regularized solution and the sought solution. The main tool is the use of upper and lower bounds of the Mittag-Leffler function, combined with analysis in Hilbert scale space. [ABSTRACT FROM AUTHOR]

The inverse single-frequency problem of scalar acoustics in three-dimensional space is considered. It consists in determining the characteristics of acoustic inhomogeneities lying in a flat layer from the distribution of the complex amplitude of the acoustic field in a flat recording layer. To effectively solve it, a special numerical algorithm is used, previously proposed and justified by the authors. As its component part, the algorithm uses solutions to special one-dimensional Fredholm equations of the 1st kind, and in the case of ambiguity in the solution of the latter, their normal solutions (solutions with a minimum norm) are sought. To regularize this ill-posed inverse problem, Tikhonov regularization and the TSVD method are used. A systematic numerical study is carried out of the influence of various parameters in the data recording scheme on the accuracy of the approximate solutions obtained using the algorithm. In particular, we study the dependence of this accuracy on the position of point sources and composite sources that cause sound vibrations, its dependence on the position of the data recording layer, and on the number of planes in which the recording sensors lie. It is shown that acceptable accuracy of approximate solutions can be obtained even with two such layers. In addition, an approach to the numerical study of the ambiguity of the solution to the inverse problem under consideration is proposed. It is based on special theoretical statements given in the article, and on the same numerical algorithm for solving the inverse problem. The approach is focused on comparing several normal solutions of one-dimensional integral equations from the problem under consideration. These normal solutions are calculated with respect to various elements. An example of using this theory to numerically estimate the non-uniqueness of a solution is given. [ABSTRACT FROM AUTHOR]

Iterative regularization exploits the implicit bias of optimization algorithms to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in modern machine learning, where it provides both a new perspective on algorithms analysis, and significant speed-ups compared to explicit regularization. In this work, we propose and study the first iterative regularization procedure with explicit computational steps able to handle biases described by non smooth and non strongly convex functionals, prominent in low-complexity regularization. Our approach is based on a primal-dual algorithm of which we analyze convergence and stability properties, even in the case where the original problem is unfeasible. The general results are illustrated considering the special case of sparse recovery with the ℓ 1 penalty. Our theoretical results are complemented by experiments showing the computational benefits of our approach. [ABSTRACT FROM AUTHOR]

The Pauli–Villars regularization is appropriate to discuss the UV sensitivity of low-energy observables because it mimics how the contributions of new particles at high energies cancel large quantum corrections from the light particles in the effective field theory. We discuss the UV sensitivity of the Casimir energy density and pressure in an extra-dimensional model in this regularization scheme, and clarify the condition on the regulator fields to preserve the Lorentz symmetry of the vacuum state. Some of the conditions are automatically satisfied in spontaneously broken supersymmetric models, but supersymmetry is not enough to ensure the Lorentz symmetry. We show that the necessary regulators can be introduced as bulk fields. We also evaluate the Casimir energy density with such regulators, and its deviation from the result obtained in the analytic regularization. [ABSTRACT FROM AUTHOR]

Compressive sensing (CS), a breakthrough technology in image processing, provides a privacy-preserving layer and image reconstruction while performing sensing and recovery processes, respectively. Unfortunately, it still faces high-complexity, low-security, and low-quality reconstruction challenges during image processing. Therefore, this article presents a secure low-complexity CS scheme with preconditioning prior regularization reconstruction. More specifically, the original image is compressed by a low-complexity LFSR-based sparse circulant matrix to obtain measurements. It is worth noting that measurements achieve preliminary distribution equalization through the Tanh sequence to acquire processed measurements. Furthermore, the privacy-preserving edge processing for processed measurements can achieve high security. Finally, preconditioning prior regularization CS reconstruction is designed to improve reconstruction performance. Simulation results and analyses demonstrate that the proposed scheme can achieve low-complexity sampling, high security, and superior reconstruction performance. [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]

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]

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 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]

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]

River bathymetry is critical for many aspects of water resources management. We propose and demonstrate a bathymetry inversion method using a deep‐learning‐based surrogate for shallow water equations solvers. The surrogate uses the convolutional autoencoder with a shared‐encoder, separate‐decoder architecture. It encodes the input bathymetry and decodes to separate outputs for flow field variables. Utilizing the differentiability of the surrogate, a gradient‐based optimizer is used to perform bathymetry inversion. Two physically based constraints on the ranges of both bed elevation and slope have to be added as inversion loss regularizations to contract the solution space. Using the "L‐curve" criterion, a heuristic approach is proposed to determine the regularization parameters. Both the surrogate model and the inversion algorithm show good performance. The bathymetry inversion progresses in two distinctive stages, which resembles the sculptural process of initial broad‐brush calving and final fine detailing. The inversion loss due to flow prediction error and the two regularizations play dominant roles in the initial and final stages, respectively. The surrogate architecture (whether with both velocity and water surface elevation or velocity only as outputs) does not have significant impact on inversion result. The methodology proposed in this work, an example of differentiable parameter learning, can be similarly used in the inversion of other important distributed parameters such as roughness coefficient. Key Points: Gradient‐based optimization is used to perform inversion with automatic differentiation enabled by the surrogate based on CNN autoencoderPhysically based regularizations on the ranges of bed elevation and slope are crucial for useable inversion resultsThe methodology works for both simple cases and complex real‐world cases [ABSTRACT FROM AUTHOR]

Reference prior algorithms are primarily available for models that have asymptotic posterior normality (i.e., regular case), barring for a specific class of models whose posteriors are not asymptotically normal (i.e., non-regular case). In particular, the current reference prior methodology is contingent on models belonging to regular or non-regular cases. This highlights that the existing reference prior theory lacks a unified approach. A partial breakthrough in unifying the reference prior theory came with Berger et al. (2009) deriving an explicit form of reference prior for single group models (i.e., models with a scalar parameter or models that have all the parameters on equal footing or importance). Unfortunately, their approach does not generalize to multi-group models (i.e., models that have parameters' subsets ordered according to their importance). In this paper, we show that their main result can be extended with modifications to multi-group models. As a consequence, we obtain a general scheme for deriving conditional reference priors. We also prove that the invariance property of reference priors under particular transformations hold for both regular and non-regular cases. We show the usefulness of our approach by computing reference priors for models that have no known reference priors. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Hamiltonian regularization of scalar conservation laws, which is parametrized by $ \ell>0 $ and conserves an $ H^1 $ energy. We prove the existence of global weak solutions for this regularization. Furthermore, we demonstrate that as $ \ell $ approaches zero, the unique entropy solution of the original scalar conservation law is recovered, providing justification for the regularization.This regularization belongs to a family of non-diffusive, non-dispersive regularizations that were initially developed for the shallow-water system and extended later to the Euler system. This paper represents a validation of this family of regularizations in the scalar case. [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]

The initial inversion model is typically established in a transient electromagnetic nonlinear inversion, assuming the accurate capture of the number of layers in the geoelectric model; however, this assumption leads to significantly poorer inversion results for complex models when obtaining the exact number of layers from available a priori information, which is challenging. This study proposes a segmented regularized inversion method to enhance inversion accuracy and stability under varying conditions. The process involves two key steps: Firstly, a segmented initial model is established based on preliminary information. The layering criteria and layer thickness threshold for each segment are set during inversion to reduce dependence on the accuracy of the preliminary information. Secondly, a segmented regularization constraint is added to the objective function to improve the efficiency and stability of the inversion, as numerous parameters can exacerbate the problem of inversion ambiguity. Subsequently, an improved sparrow search algorithm (ISSA) is utilized to optimize the inversion objective function. This enhances the efficiency of searching for the objective function and the algorithm's ability to escape local optimal solutions. The proposed method is evaluated using one-dimensional and two-dimensional models with different initial models and inversion algorithms and applied to the inversion of on-site exploration data in a coal mining area in Chongqing. Comparative results demonstrate that the proposed segmented regularization method, based on the improved sparrow search algorithm, exhibits superior practicality and a higher fitting accuracy. [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]

Non-negative Tucker decomposition (NTD) is a powerful tool for data representation to capture rich internal structure information from non-negative high-dimensional tensor data. Arguing that NTD methods often give global-like information, graph constraint has been introduced to capture the important local nonlinear structure of data. However, existing methods generally use fixed graphs and lack the ability to adaptively learn the optimal graph that best benefits the learning task at hand. In this paper, we propose an Adaptive Graph Regularized Non-negative Tucker Decomposition (AGRNTD) model. Not only is the new model able to capture the global multilinear structure of tensor data, but also it adaptively learns the optimal graph to capture local manifold information. An updating rule is designed to optimize the new model with the guarantee of local convergence. By mapping and visualizing the features, our method exhibits better feature extraction compared with other algorithms. The clustering results on five real-world datasets demonstrate the effectiveness and robustness of our method. [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]

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]

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]

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]

We investigate the problem of learning a water quality model (BOD-DO model) from given data. Assuming that all parameters in the model are constants, we reformulate the problem as a system of linear equations for the unknown terms. Since in practice the system is often under-determined or over-determined and the observed data are noisy, we use an |$l^{1}$| -weighted regularization method to find a stable approximate solution. Then, Nesterov's algorithm is used to solve the regularized problem. Learning models with variable coefficients are also discussed. Numerical examples show that our approach works well with noisy data and has the ability to learn the BOD-DO model. [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]

In this paper, combining the inertial technique and the projection strategy, we propose an improved inertial projection method for solving convex constrained monotone nonlinear equations. The direction obtained by embedding the inertial extrapolation step into the design of the search direction satisfies the independent sufficient descent property under any line search. The global convergence of the proposed method is theoretically investigated. Numerical comparisons with the other four methods show that the proposed algorithm has superior numerical performance. In addition, as a practical application, applying it to solve the sparse signal problems in compressed sensing and the regularized decentralized logistic regression and the results are promising. [ABSTRACT FROM AUTHOR]

Impact force identification is of great importance for composite structural health monitoring due to the poor impact resistance of composite materials. Convex sparse regularization method based on L 1-norm tends to underestimate the amplitude of the impact force. This paper proposes a novel method using fully overlapping group sparsity based on Lp -norm regularization (FOGS L p) for impact force identification, which can localize the impact force and reconstruct its time history simultaneously with limited measurements in under-determined cases. The FOGS L p method takes more sparse prior information into account by combining the non-convex Lp -norm (0 < p < 1) and fully overlapping group sparsity to promote sparse solutions, thus improving the accuracy of the reconstructed impact force. An accelerated grouped shrinkage-thresholding algorithm is employed to solve the non-convex optimization problem under the majorization-minimization framework. The Nesterov's acceleration strategy is modified to accommodate the requirements of non-convex optimization. Simulations and experiments are conducted on composite panels to validate the effectiveness of the FOGS L p method. Results demonstrate the efficiency and robustness of the FOGS L p method to localize the impact force and reconstruct its time history simultaneously while 25 potential impact points are monitored using two sensors. Compared with L 1-norm, Lp -norm, and L 2,1-norm regularization methods, the proposed method performs best in both simulations and experiments. [ABSTRACT FROM AUTHOR]

Local minimizers of nonhomogeneous quasiconvex variational integrals with standard pgrowth of the type ... feature almost everywhere BMO-regular gradient provided that f belongs to the borderline Marcinkiewicz space L(n, ∞). [ABSTRACT FROM AUTHOR]

The multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach can suffer from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of regularization of the EOMs. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here, we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to 106 bath modes and find that for these problems, the PSI requires roughly 3–4 orders of magnitude fewer Hamiltonian evaluations and 2–3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH and 2–3/1–2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to ∼ 1.3 × 1 0 9 parameters to obtain accurate dynamics. [ABSTRACT FROM AUTHOR]

Series arc fault is the main cause of electrical fire in low-voltage distribution system. A fast and accurate detection system can reduce the risk of fire effectively. In this paper, series arc experiment is carried out for different kinds of electrical load. The time-domain current is analyzed by Morlet wavelet. Then, the multiscale wavelet coefficients are expressed as the coefficient matrix. In order to meet the data dimension requirements of neural networks, a color domain transformation method is used to transform the feature matrix into an image. A regularization method based on gamma transform is proposed for small sample data sets. The results showed that the proposed regularization method improved the validation set accuracy of ResNet50 from 66.67% to 96.53%. The overfitting problem of neural network was solved. In addition, this method fused fault features of 64 different scales, and provided a valuable manually labeled arc fault dataset. Compared with the threshold detection method, this method was more objective. The use of image features increased intuitiveness and generality. Compared with other typical lightweight networks, this method had the best detection performance. [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]

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]

Over the past 3 decades, inversions for ice sheet basal drag have become commonplace in glaciological modeling. Such inversions require regularization to prevent over-fitting and ensure that the structure they recover is a robust inference from the observations, confidence which is required if they are to be used to draw conclusions about processes and properties of the ice base. While L-curve analysis can be used to select the optimal regularization level, the treatment of L-curve analysis in glaciological inverse modeling has been highly variable. Building on the history of glaciological inverse modeling, we demonstrate general best practices for regularizing glaciological inverse problems, using a domain in the Filchner–Ronne catchment of Antarctica as our test bed. We show a step-by-step approach to cost function normalization and L-curve analysis. We explore the spatial and spectral characteristics of the solution as a function of regularization, and we test the sensitivity of L-curve analysis and regularization to model resolution, effective pressure, sliding nonlinearity, and the flow equation. We find that the optimal regularization level converges towards a finite non-zero limit in the continuous problem, associated with a best knowable basal drag field. Nonlinear sliding laws outperform linear sliding in our analysis, with both a lower total variance and a more sharply cornered L-curve. By contrast, geometry-based approximations for effective pressure degrade inversion performance when added to a sliding law, but an actual hydrology model may marginally improve performance in some cases. Our results with 3D inversions suggest that the additional model complexity may not be justified by the 2D nature of the surface velocity data. We conclude with recommendations for best practices in future glaciological inversions. [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]

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]

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]

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]

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]

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]