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To rationally utilize the sample information and label information in multi-label data and improve the classification performance of the model, multi-label feature selection (DHSR) via dual Hilbert-Schmidt independence criterion (HSIC) and sparse regularization was proposed. This method introduces dual HSIC as a regular term on the basis of linear mapping to enhance the dependency between pseudo-label space and feature space, and enhance the dependency between pseudo-label space and real label space, respectively. Moreover, L2.1 norm was used as a sparse regularity term to improve the generalization ability of the model and reduce the computational complexity of the model. Finally, the results of comparison experiments on several classical multi-label datasets verify the effectiveness and superiority of DHSR. [ABSTRACT FROM AUTHOR]

In this paper, we propose an alternating block variant of the linearized Bregman iterations for a class of regularized nonnegative matrix factorization (NMF) problems. The proposed method exploits the block structure of NMF, utilizes the smooth adaptable property of the loss function based on the Bregman distance, and at the same time follows the iterative regularization idea of the linearized Bregman iterations method. Theoretically, we show that the proposed method is a descent method by adjusting the involved parameters. Finally, we end with several illustrative numerical experiments. [ABSTRACT FROM AUTHOR]

We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the ℓ 0 norm. Specifically, the ℓ 0 model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the ℓ 0 norm regularization term. Such an ℓ 0 model is non-convex. Existing exact algorithms for solving the problems require the availability of closed-form formulas for the proximity operator of convex functions involved in the objective function. When such formulas are not available, numerical computation of the proximity operator becomes inevitable. This leads to inexact iteration algorithms. We investigate in this paper how the numerical error for every step of the iteration should be controlled to ensure global convergence of the inexact algorithms. We establish a theoretical result that guarantees the sequence generated by the proposed inexact algorithm converges to a local minimizer of the optimization problem. We implement the proposed algorithms for three applications of practical importance in machine learning and image science, which include regression, classification, and image deblurring. The numerical results demonstrate the convergence of the proposed algorithm and confirm that local minimizers of the ℓ 0 models found by the proposed inexact algorithm outperform global minimizers of the corresponding ℓ 1 models, in terms of approximation accuracy and sparsity of the solutions. [ABSTRACT FROM AUTHOR]

Periodic transient shocks of vibration signals often reflect the failure of mechanical components. With the time-frequency (TF) distribution (TFD), Transient-extracting transform (TET) can descript and extract the fault-related transient component effectively. Nevertheless, vibrations collected from practical sources are always contaminated by strong background noise, thus the transient shocks are often submerged by noise components. Therefore, how to effectively extract the weak transient component from noise is an important task to achieve the bearing fault diagnosis. Considering the above issue, this paper developed a generalized mini-max concave (GMC) penalty based TET (GMCTET) for bearing fault feature enhancement. Specifically, the GMC penalty based-sparse regularization is firstly applied to the raw signal. Benefiting from the good ability of GMC penalty-based sparse regularization in both sparsity and signal fidelity. The transient shocks are initially presented, and the loss of energy amplitude of the raw signal during the processing is reduced simultaneously. Next, TET can well characterize these transient shocks via a highly readable TFD, and the transient component is extracted based on the TF coefficients. The shock structures in transient component are further highlighted after TET treatment. Finally, the bearing fault frequencies are identified through the spectrum of the extracted transient component. The effectiveness of GMCTET is verified from the comparative analysis results of the simulation and experimental studies. [ABSTRACT FROM AUTHOR]

The analysis of remote sensing data and the classification of images are complex problems because understanding spatial patterns and intricate geometric structures of the data from which meaningful interrelationship pixels are extracted is essential in the remote sensing community. CNN is one of the Machine Learning methods often used in Remote Sensing problems. However, high-resolution aerial view classification often leverages large-scale data with a huge number of parameters of the CNN model. A large number of parameters makes it hard to be applied to remote imaging peripherals because it requires high capacity of storage and memory. We propose a training framework to solve that problem that produces a model with minimum parameters without sacrificing accuracy. To this end, we train EfficientNet using Weighted Loss of INS to compensate imbalanced classes while keeping the upper layer frozen to preserve essential features deriving from transfer learning. Moreover, we utilize Sparse Regularization on the loss function to make the model focussing on the global object. Finally, as post-training, the trained model is pruned to reduce the number of parameters within the network. Using this method on the AID Dataset, the best results are achieved by EfficientNet-B0 with Freeze 2 Layer, INS Weighted Loss, Sparse regularization with λ = 0.001, and Global Unstructured Conv2D Pruning with an accuracy of 96.81% on test data with total parameters of 2,463,501. This study proves that Weighted Loss and Sparse Regularization can help the model to improve accuracy while Pruning enhances efficiency by reducing the number of parameters by half without significantly lowering performance. [ABSTRACT FROM AUTHOR]

Abstract Seismic prospecting has been widely used in the exploration and development of underground geological resources, such as mineral products (e.x., coal, uranium deposit), oil and gas, groundwater, and so forth. Seismic impedance is a physical characteristic parameter of underground formation, which can be used in lithologic classification, rock characterization, stratigraphic correlation, and further mineral reservoir prediction, reserve estimation, and so forth. To estimate impedance from seismic data, one must perform reflectivity series inversion first. Under a simple exponential integration transformation, the reflectivity series can give the final estimated impedance. Sparse-spike seismic inversion is the most common method to obtain reflectivity series with high resolution. It adopts a sparse regularization to impose sparsity on reflectivity series. From sparse reflectivity series, the final estimated impedance has blocky features to make formation interfaces and geological edges precise, which is very important to accurately delineate the distribution range of mineral resources. The development of sparse-spike seismic inversion is still facing major challenges of fast optimization algorithms in real-life application, especially for massive seismic data in 3D case. Semismooth Newton algorithm (SNA), which is a second order mehtod and has super-linear, even quadratic convergence rate, is used to solve sparse-spike seismic inversion. The proposed algorithm has been compared with common used algorithms through a synthetic seismic trace and a 3D real seismic data volume. The results show that the proposed algorithm has faster convergence rate and fewer computation time. It provides a new effective algorithm to solve sparse-spike seismic inversion.

Limited resources for edge computing platforms in airborne and spaceborne imaging payloads prevent using complex image processing models. Model pruning can eliminate redundant parameters and reduce the computational load, enhancing processing efficiency on edge computing platforms. Current challenges in model pruning for remote-sensing object detection include the risk of losing target features, particularly during sparse training and pruning, and difficulties in maintaining channel correspondence for residual structures, often resulting in retaining redundant features that compromise the balance between model size and accuracy. To address these challenges, we propose the L1 reweighted regularization (L1RR) pruning method. Leveraging dynamic and self-adaptive sparse modules, we optimize L1 sparsity regularization, preserving the model's target feature information using a feature attention loss mechanism to determine appropriate pruning ratios. Additionally, we propose a residual reconstruction procedure, which removes redundant feature channels from residual structures while maintaining the residual inference structure through output channel recombination and input channel recombination, achieving a balance between model size and accuracy. Validation on two remote-sensing datasets demonstrates significant reductions in parameters and floating point operations (FLOPs) of 77.54% and 65%, respectively, and a 48.5% increase in the inference speed on the Jetson TX2 platform. This framework optimally maintains target features and effectively distinguishes feature channel importance compared to other methods, significantly enhancing feature channel robustness for difficult targets and expanding pruning applicability to less difficult targets. [ABSTRACT FROM AUTHOR]

The gravity inversion methods play a fundamental role in subsurface exploration, facilitating the characterization of geological structures and economic deposits. In this study, we conduct a comparative analysis of two widely used regularization methods, Tikhonov (L2) and Sparse (L1) regularization, within the framework of the gravity inversion. To assess their performance, we constructed two distinct synthetic models by implementing tensor meshes, considering station spacing to discretize the subsurface environment precisely. Both methods have proven ability to recover density distributions, while minimizing the inherent non-uniqueness and ill-posed nature of the gravity inversion problems. The Tikhonov regularization yields stable results, presenting smooth model parameters even with limited prior information and noisy data. Conversely, the Sparse regularization, utilizing sparsity-promoting penalties, excels in capturing sharp geological features and identifying anomalous regions, such as mineralized zones. Applying these methodologies to real gravity data from the Safu manganese deposit in northwest Iran, we assess their efficacy in recovering the geometry of dense ore deposits. The Sparse regularization demonstrates superior performance, yielding lower misfit values and sharper boundaries during individual inversions. This underscores its capacity to provide a more accurate representation of the depth and edges of anomalous targets in this specific case. However, both methods represent the same top depth of the target in the real case study, but the lower depth and density distribution were not the same in the XZ cross-sections. The inversion results imply the presence of a near-surface deposit characterized by a high-density contrast and linear distribution, attributed to the high grade of manganese mineralization. [ABSTRACT FROM AUTHOR]

The l 2 regularization is usually used to deal with the problems of under-determinacy and measurement noise for the conventional sensitivity-based model updating damage detection methods. However, the l 2 regularization technique often provides overly smooth solutions and thus cannot exhibit the sparsity of the structural damage due to the promotion of the 2-norm term on smoothness. In the study, a structural damage detection method is proposed based on an improved modal flexibility sensitivity function and an iterative reweighted l p (IR l p) regularization. Specifically, the sensitivity function is established by introducing changes in the mode shapes into the derivative of eigenvalue and can be applied to identify the localized damage more accurately. Additionally, IR l p regularization is proposed to deal with the ill-posed problem of damage detection in a noisy environment. The proposed IR l p regularization is compared with the l 1 and l 2 regularizations through a numerical and an experimental examples. The numerical and experimental results indicate that the IR l p regularization can more accurately locate and quantify the single and multiple damages under the noise situation. The maximum identification errors are only 5.16% and 5.67%, respectively. Moreover, compared to the basic modal flexibility sensitivity function, the improved function is more sensitive to the damage. The maximum identification error of the improved function is less than 6%, while the relative errors are significantly larger in the basic function. [ABSTRACT FROM AUTHOR]

In a number of tomographic applications, data cannot be fully acquired, resulting in severely underdetermined image reconstruction. Conventional methods in such cases lead to reconstructions with significant artifacts. To overcome these artifacts, regularization methods are applied that incorporate additional information. An important example is TV reconstruction, which is known to be efficient in compensating for missing data and reducing reconstruction artifacts. On the other hand, tomographic data are also contaminated by noise, which poses an additional challenge. The use of a single regularizer must therefore account for both the missing data and the noise. A particular regularizer may not be ideal for both tasks. For example, the TV regularizer is a poor choice for noise reduction over multiple scales, in which case ℓ 1 curvelet regularization methods are well suited. To address this issue, in this paper, we present a novel variational regularization framework that combines the advantages of different regularizers. The basic idea of our framework is to perform reconstruction in two stages. The first stage is mainly aimed at accurate reconstruction in the presence of noise, and the second stage is aimed at artifact reduction. Both reconstruction stages are connected by a data proximity condition. The proposed method is implemented and tested for limited-view CT using a combined curvelet–TV approach. We define and implement a curvelet transform adapted to the limited-view problem and illustrate the advantages of our approach in numerical experiments. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU), an essential procedure for various environmental applications, has garnered significant attention within remote sensing communities. Among different groups of HU methods, nonnegative matrix factorization (NMF)-based ones have gained widespread popularity due to their high capability of simultaneously extracting endmembers and their corresponding abundances. However, converting a 3-D hyperspectral data cube into a 2-D matrix format leads to the loss of spatial and potential correlation information. Consequently, in recent years, nonnegative tensor factorization (NTF) methods, which preserve the 3-D nature of hyperspectral data cube, have been extensively embraced by numerous researchers. Nevertheless, incorporating prior information into NTF-based problems faces limitations owing to the inconsistency of such information, particularly concerning $\ell _{1}$ norm sparsity and the abundance sum-to-one constraint (ASC). To address this limitation, our study introduces a novel general regularization term. This term leverages sparsity and ASC simultaneously, integrating it into a matrix-tensor factorization framework. Our proposed method, named a matrix-tensor-based HU method with general $\ell _{q}$ norm regularization (MTUHL$_{q}$), is established on the block term decomposition (BTD) paradigm, which ensures physical interpretability and simple implementation. To investigate the performance of the proposed MTUHL$_{q}$, a series of experiments on both synthetic and real hyperspectral datasets were conducted. The results of the implemented experiments indicated that the proposed method outperformed other state-of-the-art HU methods.

Previous vibration-based damage detection studies mostly focus on developing a more sensitive optimization function to promote the effectiveness of damage identification. However, a few studies have conducted comparative analyses on the detection performance of different optimization functions. In the study, changes in the frequency and mode shape are applied as the inputs to different optimization functions for damage identification. Three optimization functions are established using the frequency residuals, the combinations of frequency and mode shape residuals, and the modal flexibility residuals, respectively. Considering the sparsity of damage element distribution, an iterative reweighted l1/2 (IRl1/2) regularization is added as a norm penalty to the optimization function. A numerical model and an experimental example are applied to assess the performance of distinct optimization functions. The results show that the increase in modal data number cannot significantly improve the detection accuracy when the number meets the basic requirements for identifying damage. The detection error of the optimization function established by combining the frequency and mode shape residuals is 6.65% and 5.18% using the first four and fourteen-order noisy modal data, respectively. Furthermore, the optimization function constructed using the modal flexibility residuals requires more less modal data to identify damage than the other two functions. [ABSTRACT FROM AUTHOR]

Strain measurement is considered inherently suitable for structural health monitoring due to the ease of extracting damage-sensitive features. However, the need for pre- and post-damage feature extraction, especially in the absence of baseline data for aging infrastructures in service, has engendered skepticism concerning the practical efficacy of strain-based damage diagnosis. To address this, this study incorporates limited prior information on structures and sparse regularization to ascertain the locations and severities of structural damages based on dynamic strain response data. A model-assisted approach is presented, including the typical three-step process of damage feature extraction, finite element modeling, and analytical sensitivity-based model updating. In particular, sparse regularization technique aids in robustly identifying structural damage by tackling the hindrance encountered during model updating, involving ill-posedness and the impact of measurement and modeling uncertainties. The approach's effectiveness is substantiated through a numerical investigation of a Bailey truss bridge model exposed to operating loads and an experiment with a steel beam equipped with an array of fiber Bragg grating sensors. The results demonstrate that using the proposed damage diagnosis approach enables accurately locating and quantifying element-level damages, even when significant modeling errors or a lack of baseline features exist. [ABSTRACT FROM AUTHOR]

Impact force identification has always been of significance for structure health monitoring especially on the applications involving composite materials. As a typical inverse problem, impact force reconstruction and localization is undoubtedly a challenging task. The well-known ℓ 1 sparse regularization has a tendency to underestimate the amplitude of impact forces. To alleviate this limitation, we propose an accelerated generalized minimax-concave (AGMC) for sparse regularization that employs a non-convex generalized minimax-concave (GMC) penalty as the regularizer and incorporates an acceleration technique to expedite the attainment of the global minimum. Compared with the classic ℓ 1-norm penalty, the GMC penalty can not only induce sparsity in the estimation, but also maintain the convexity of the cost function, so that the global optimal solution can be obtained through convex optimization algorithms. This method is applied to solve the impact force identification problem with unknown force locations to simultaneously reconstruct and localize impact forces in the under-determined case utilizing a limited number of sensors. Meanwhile, K-sparsity criterion is used to adaptively select regularization parameters by taking advantage of the sparse prior knowledge on impact forces. Simulations and experiments are conducted on a composite plate to verify the computational efficiency and robustness of the AGMC method in terms of impact force reconstruction and localization, particularly in the presence of noise. Results demonstrate that the proposed AGMC method achieves faster convergence and provides more accurate and sparse reconstruction and localization of impact forces compared to other state-of-the-art sparse regularization methods. [ABSTRACT FROM AUTHOR]

When the sparse regularizer is convex and its proximal operator has a closed‐form, first‐order iterative algorithms based on proximal operators can effectively solve the sparse optimization problems. Recently, plug‐and‐play (PnP) algorithms have achieved significant success by incorporating advanced denoisers to replace the proximal operators in iterative algorithms. However, convex sparse regularizers such as the ℓ1$$ {\ell}_1 $$‐norm tend to underestimate the large values within the sparse solutions. In contrast, the convex non‐convex (CNC) sparse regularization enables the non‐convex regularizer while preserving the convexity of the objective function. In this paper, we propose several PnP algorithms for solving the CNC sparse regularization model and discuss their convergence properties. Specifically, we first derive the proximal operator for CNC sparse regularization in iterative form and subsequently integrate it with several first‐order algorithms to yield different PnP algorithms. Then, based on the monotone operator theory, we prove that the proposed PnP algorithms are convergent under the condition that the data‐fidelity term is strongly convex and the residuals of the denoisers are contractive. We also emphasized the significance of strong convexity in the data‐fidelity term for the CNC sparse regularization model. Additionally, we demonstrate the superiority of the proposed PnP algorithms through extensive image restoration tasks. [ABSTRACT FROM AUTHOR]

As the feature dimension of data continues to expand, the task of selecting an optimal subset of features from a pool of limited labeled data and extensive unlabeled data becomes more and more challenging. In recent years, some semi-supervised feature selection methods (SSFS) have been proposed to select a subset of features, but they still have some drawbacks limiting their performance, for e.g., many SSFS methods underutilize the structural distribution information available within labeled and unlabeled data. To address this issue, we proposed a semi-supervised feature selection method based on an adaptive graph with global and local constraints (SFS-AGGL) in this paper. Specifically, we first designed an adaptive graph learning mechanism that can consider both the global and local information of samples to effectively learn and retain the geometric structural information of the original dataset. Secondly, we constructed a label propagation technique integrated with the adaptive graph learning in SFS-AGGL to fully utilize the structural distribution information of both labeled and unlabeled data. The proposed SFS-AGGL method is validated through classification and clustering tasks across various datasets. The experimental results demonstrate its superiority over existing benchmark methods, particularly in terms of clustering performance. [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]

Near-field acoustic holography (NAH) based on compressing sensing (CS) theory enables accurate reconstruction of sound fields using a limited number of sampling points. However, the successful implementation of this technique depends on two crucial factors: (1) the appropriate selection or construction of the spatial basis and (2) an effective sparse regularization process. To enhance reconstruction performance for elongated sound sources, this paper proposes a novel sound field reconstruction method that combines prolate spheroidal wave functions (PSWFs) with the orthogonal matching pursuit (OMP) algorithm. In this method, PSWFs serve as a sparse spatial basis for representing the radiated sound field. The sparse coefficients are determined by the OMP algorithm in a linear subspace composed of basic functions that best match the residual error. The OMP algorithm effectively identifies significant components before potentially selecting incorrect ones by setting an appropriate stopping rule. Numerical simulations are conducted using a line-array source model. The results show that the proposed method can accurately reconstruct the sound pressures of the elongated source model using a relatively small number of samplings. In addition, the proposed method exhibits robustness across a wide frequency range, diverse array configurations and various sampling numbers. The experimental results further validate the feasibility and reliability of the proposed method. [ABSTRACT FROM AUTHOR]

Spherical radial basis function (SRBF) is an effective method for calculating regional gravity field models. Calculating gravity field models with high accuracy and resolution requires dense basis functions, resulting in complex models. This study investigated the application of sparse regularization in SRBFs-based regional gravity field modeling. L1-norm regularization, also known as the least absolute shrinkage selection operator (LASSO), was employed in the parameter estimation procedure. LASSO differs from L2-norm regularization in that the solution obtained by LASSO is sparse, specifically with a portion of the parameters being zero. A sparse model would be advantageous for improving the numerical efficiency by reducing the number of SRBFs. The optimization problem of the LASSO was solved using the fast iterative shrinkage threshold algorithm, which is known for its high efficiency. The regularization parameter was selected using the Akaike information criterion. It was specifically tailored to the L1-norm regularization problem. An approximate covariance matrix of the estimated parameters in the sparse solution was analytically constructed from a Bayesian viewpoint. Based on the remove–compute–restore technique, a regional geoid model of Colorado (USA) was calculated. The numerical results suggest that the LASSO adopted in this study provided competitive results compared to Tikhonov regularization; however, the number of basis functions in the final model was less than 25% of the Tikhonov regularization. Without significantly reducing model accuracy, the LASSO solution provides a very simple model. This is the first study to apply the LASSO to SRBFs-based modeling of the regional gravity field in real gravity observation data. [ABSTRACT FROM AUTHOR]

Limited resources for edge computing platforms in airborne and spaceborne imaging payloads prevent using complex image processing models. Model pruning can eliminate redundant parameters and reduce the computational load, enhancing processing efficiency on edge computing platforms. Current challenges in model pruning for remote-sensing object detection include the risk of losing target features, particularly during sparse training and pruning, and difficulties in maintaining channel correspondence for residual structures, often resulting in retaining redundant features that compromise the balance between model size and accuracy. To address these challenges, we propose the L1 reweighted regularization (L1RR) pruning method. Leveraging dynamic and self-adaptive sparse modules, we optimize L1 sparsity regularization, preserving the model’s target feature information using a feature attention loss mechanism to determine appropriate pruning ratios. Additionally, we propose a residual reconstruction procedure, which removes redundant feature channels from residual structures while maintaining the residual inference structure through output channel recombination and input channel recombination, achieving a balance between model size and accuracy. Validation on two remote-sensing datasets demonstrates significant reductions in parameters and floating point operations (FLOPs) of 77.54% and 65%, respectively, and a 48.5% increase in the inference speed on the Jetson TX2 platform. This framework optimally maintains target features and effectively distinguishes feature channel importance compared to other methods, significantly enhancing feature channel robustness for difficult targets and expanding pruning applicability to less difficult targets.

In a number of tomographic applications, data cannot be fully acquired, resulting in severely underdetermined image reconstruction. Conventional methods in such cases lead to reconstructions with significant artifacts. To overcome these artifacts, regularization methods are applied that incorporate additional information. An important example is TV reconstruction, which is known to be efficient in compensating for missing data and reducing reconstruction artifacts. On the other hand, tomographic data are also contaminated by noise, which poses an additional challenge. The use of a single regularizer must therefore account for both the missing data and the noise. A particular regularizer may not be ideal for both tasks. For example, the TV regularizer is a poor choice for noise reduction over multiple scales, in which case ℓ1 curvelet regularization methods are well suited. To address this issue, in this paper, we present a novel variational regularization framework that combines the advantages of different regularizers. The basic idea of our framework is to perform reconstruction in two stages. The first stage is mainly aimed at accurate reconstruction in the presence of noise, and the second stage is aimed at artifact reduction. Both reconstruction stages are connected by a data proximity condition. The proposed method is implemented and tested for limited-view CT using a combined curvelet–TV approach. We define and implement a curvelet transform adapted to the limited-view problem and illustrate the advantages of our approach in numerical experiments.

Impact force identification is important for structure health monitoring especially in applications involving composite structures. Different from the traditional direct measurement method, the impact force identification technique is more cost effective and feasible because it only requires a few sensors to capture the system response and infer the information about the applied forces. This technique enables the acquisition of impact locations and time histories of forces, aiding in the rapid assessment of potentially damaged areas and the extent of the damage. As a typical inverse problem, impact force reconstruction and localization is a challenging task, which has led to the development of numerous methods aimed at obtaining stable solutions. The classical ℓ2 regularization method often struggles to generate sparse solutions. When solving the under-determined problem, ℓ2 regularization often identifies false forces in non-loaded regions, interfering with the accurate identification of the true impact locations. The popular ℓ1 sparse regularization, while promoting sparsity, underestimates the amplitude of impact forces, resulting in biased estimations. To alleviate such limitations, a novel non-convex sparse regularization method that uses the non-convex ℓ1–2 penalty, which is the difference of the ℓ1 and ℓ2 norms, as a regularizer, is proposed in this paper. The principle of alternating direction method of multipliers (ADMM) is introduced to tackle the non-convex model by facilitating the decomposition of the complex original problem into easily solvable subproblems. The proposed method named ℓ1–2-ADMM is applied to solve the impact force identification problem with unknown force locations, which can realize simultaneous impact localization and time history reconstruction with an under-determined, sparse sensor configuration. Simulations and experiments are performed on a composite plate to verify the identification accuracy and robustness with respect to the noise of the ℓ1−2-ADMM method. Results indicate that compared with other existing regularization methods, the ℓ1–2-ADMM method can simultaneously reconstruct and localize impact forces more accurately, facilitating sparser solutions, and yielding more accurate results. [ABSTRACT FROM AUTHOR]

Substructuring approaches possess many superiorities over traditional global approaches in damage identification because large-size global structures are replaced by small and manageable substructures. This paper proposes a substructural time series model for locating and quantifying the damage in complex systems. A substructural autoregressive moving average with exogenous inputs (ARMAX) model is established to extract the frequencies and mode shapes of substructures as indicators for damage detection. The detection of structural damage is essentially an inverse problem, and the damage in structure bears sparse properties. The inverse problem of substructural damage identification is efficiently solved via sparse regularization, and structural damage can be located and quantified through the nonzero terms in the solution vector. The accuracy of the proposed method is demonstrated by the numerical simulation of a frame structure and shaking table test of a shear building structure. As the substructural properties are more sensitive to local structural damage than the global properties, the substructural ARMAX model is quite accurate and efficient to be used in the damage identification of a complex system. [ABSTRACT FROM AUTHOR]

We consider a minimization problem whose objective function is the sum of a fidelity term, not necessarily convex, and a regularization term defined by a positive regularization parameter λ multiple of the ℓ 0 norm composed with a linear transform. This problem has wide applications in compressed sensing, sparse machine learning and image reconstruction. The goal of this paper is to understand what choices of the regularization parameter can dictate the level of sparsity under the transform for a global minimizer of the resulting regularized objective function. This is a critical issue but it has been left unaddressed. We address it from a geometric viewpoint with which the sparsity partition of the image space of the transform is introduced. Choices of the regularization parameter are specified to ensure that a global minimizer of the corresponding regularized objective function achieves a prescribed level of sparsity under the transform. Results are obtained for the spacial sparsity case in which the transform is the identity map, a case that covers several applications of practical importance, including machine learning, image/signal processing and medical image reconstruction. [ABSTRACT FROM AUTHOR]

Community detection is an important topic in network analysis, and recently many community detection methods have been developed on top of the Nonnegative Matrix Factorization (NMF) technique. Most NMFbased community detection methods only utilize the first-order proximity information in the adjacency matrix, which has some limitations. Besides, many NMF-based community detection methods involve sparse regularizations to promote clearer community memberships. However, in most of these regularizations, different nodes are treated equally, which seems unreasonable. To dismiss the above limitations, this article proposes a community detection method based on node centrality under the framework of NMF. Specifically, we design a new similarity measure which considers the proximity of higher-order neighbors to form a more informative graph regularization mechanism, so as to better refine the detected communities. Besides, we introduce the node centrality and Gini impurity to measure the importance of nodes and sparseness of the community memberships, respectively. Then, we propose a novel sparse regularization mechanism which forces nodes with higher node centrality to have smaller Gini impurity. Extensive experimental results on a variety of real-world networks show the superior performance of the proposed method over thirteen stateof-the-art methods. [ABSTRACT FROM AUTHOR]

In structural health monitoring (SHM), damage detection is a final target to know the real status of the objective structure. Vibration-based damage detection is a commonly used method, since it makes full use of the dynamic characteristics. Improving the efficiency of this kind of methods has attracted increasing attentions. The existing uncertainty of identified modal parameters using measured data may significantly affect the detection accuracy. Furthermore, an optimization algorithm with a better convergence speed can improve the detection accuracy and reduce the computational time. This article presents the work to develop a novel damage detection method based on fundamental Bayesian two-stage model and sparse regularization. In this method, the most probable value of modal parameters and the associated posterior uncertainty are combined to investigate the effect of uncertainty on damage detection. The usage of the sparse regularization in the objective function can decrease the complexity of modeling and avoid the overfitting problem. A machine learning method combining intelligent swarm optimization algorithm with K -means clustering was used to carry out the optimization. Finally, a method combining three existing theory, that is, fundamental Bayesian two-stage model, sparse regularization, and I-Jaya algorithm, was developed. To investigate the efficiency of the proposed method, the traditional objective functions with and without the sparse regularization were also used for the comparison. The proposed method was verified by an ASCE benchmark example, and then it is applied into an experimental structure. The results show that due to the consideration of uncertainty, the objective function based on the fundamental Bayesian model and sparse regularization has a better performance. [ABSTRACT FROM AUTHOR]

As the feature dimension of data continues to expand, the task of selecting an optimal subset of features from a pool of limited labeled data and extensive unlabeled data becomes more and more challenging. In recent years, some semi-supervised feature selection methods (SSFS) have been proposed to select a subset of features, but they still have some drawbacks limiting their performance, for e.g., many SSFS methods underutilize the structural distribution information available within labeled and unlabeled data. To address this issue, we proposed a semi-supervised feature selection method based on an adaptive graph with global and local constraints (SFS-AGGL) in this paper. Specifically, we first designed an adaptive graph learning mechanism that can consider both the global and local information of samples to effectively learn and retain the geometric structural information of the original dataset. Secondly, we constructed a label propagation technique integrated with the adaptive graph learning in SFS-AGGL to fully utilize the structural distribution information of both labeled and unlabeled data. The proposed SFS-AGGL method is validated through classification and clustering tasks across various datasets. The experimental results demonstrate its superiority over existing benchmark methods, particularly in terms of clustering performance.

Accurate engine gas path component fault diagnosis methods are key to ensuring the reliability and safety of engine operations. At present, the effectiveness of the data-driven gas path component fault diagnosis methods has been widely verified in engineering applications. The deep stack neural network (DSN), as a common deep learning neural network, has been gaining more attention in gas path fault diagnosis studies. However, various gas path component faults with strong coupling effects could occur simultaneously, resulting the DSN method less effective for engine gas path fault diagnosis. In order to improve the prediction performance of the DSN handling multiple gas path component fault diagnosis, a sparse regularization and representation method was proposed. The sparse regularization term is used to expand the traditional deep stacking neural network in the sparse representation, and the predicted output tag is close to the target output tag through this term. The diagnosis performance of six different neural network methods were compared by various engine gas path component fault diagnosis types. The results show that the proposed sparse regularization method significantly improves the prediction performance of the DSN, with an accuracy rate 99.9% under various gas path component fault conditions, which is higher than other methods. The proposed engine gas path component fault diagnosis method can handle multiple coupling gas path faults, and help engine operators to develop maintenance plans for the purpose of engine health management.

Moving force identification (MFI) is one of the challenging tasks in structural health monitoring (SHM) of bridges. As an inverse problem, continuous attention is needed to address the ill-posedness of MFI system matrix, computational efficiency and accuracy. Therefore, a novel regularized adaptive matching pursuit (NRAMP) framework is proposed for MFI using multiple criteria and prior knowledge in this study. Firstly, a relationship between moving forces and structural responses is established. With the utilization of redundant matrix, the MFI problem is converted into one of the sparse recoveries. A new adaptive criterion related to atoms both in the sparse regularization and LSQR factorization is introduced into the regularized orthogonal matching pursuit (ROMP) process. The ill-posedness of system matrix in sparse recovery can be reduced greatly, and the unknown sparsity problem can be skipped. Furthermore, the optimal atoms of redundant matrix will be selected repeatedly based on another criterion related to prior knowledge that the static axle-weight of a vehicle is the main component of moving vehicle force. The residual in each iteration will be saved and the atoms with the smallest residual are chosen at last. Finally, to assess the feasibility of the proposed method, numerical simulations on identification of single moving force with impulse components and two unequal moving forces, and experimental verifications on MFI of a model vehicle moving on a beam in laboratory are also carried out. The results show that the relative percentage errors between the identified and true gross vehicle weight keep under 3.6% in all measured cases, and the executive time of the proposed method is far less than that due to common OMP methods. [ABSTRACT FROM AUTHOR]

Semantic segmentation of remote-sensing (RS) images is one of the most fundamental tasks in the understanding of a remote-sensing scene. However, high-resolution RS images contain plentiful detailed information about ground objects, which scatter everywhere spatially and have variable sizes, styles, and visual appearances. Due to the high similarity between classes and diversity within classes, it is challenging to obtain satisfactory and accurate semantic segmentation results. This paper proposes a Dynamic High-Resolution Network (DyHRNet) to solve this problem. Our proposed network takes HRNet as a super-architecture, aiming to leverage the important connections and channels by further investigating the parallel streams at different resolution representations of the original HRNet. The learning task is conducted under the framework of a neural architecture search (NAS) and channel-wise attention module. Specifically, the Accelerated Proximal Gradient (APG) algorithm is introduced to iteratively solve the sparse regularization subproblem from the perspective of neural architecture search. In this way, valuable connections are selected for cross-resolution feature fusion. In addition, a channel-wise attention module is designed to weight the channel contributions for feature aggregation. Finally, DyHRNet fully realizes the dynamic advantages of data adaptability by combining the APG algorithm and channel-wise attention module simultaneously. Compared with nine classical or state-of-the-art models (FCN, UNet, PSPNet, DeepLabV3+, OCRNet, SETR, SegFormer, HRNet+FCN, and HRNet+OCR), DyHRNet has shown high performance on three public challenging RS image datasets (Vaihingen, Potsdam, and LoveDA). Furthermore, the visual segmentation results, the learned structures, the iteration process analysis, and the ablation study all demonstrate the effectiveness of our proposed model. [ABSTRACT FROM AUTHOR]

Feature selection, as an essential preprocessing tool, aims to identify a subset of crucial features by eliminating redundant and noisy features according to a predefined criterion. In recent years, sparse learning has received considerable attention. As an important component of sparse learning, sparse regularization has been widely used in feature selection to enforce irrelevant feature coefficients to be small or exactly zero, which is especially suitable for selecting the discriminative and relevant features. In this paper, we attempt to provide a survey on various sparse regularization based methods. We group the existing sparse regularization based methods into two categories, i.e., convex sparse regularization based feature selection and non-convex sparse regularization based feature selection. This survey not only compares the common and different characters of sparse regularizations based feature selection methods, but also offers useful guidance for practitioners of feature selection. [ABSTRACT FROM AUTHOR]

In this paper, elliptic optimal control problems with L 1 -control cost and box constraints on the control are considered. To numerically solve the optimal control problems, we use the First optimize, then discretize approach. We focus on the inexact alternating direction method of multipliers (iADMM) and employ the standard piecewise linear finite element approach to discretize the subproblems in each iteration. However, in general, solving the subproblems is expensive, especially when the discretization is at a fine level. Motivated by the efficiency of the multigrid method for solving large-scale problems, we combine the multigrid strategy with the iADMM algorithm. Instead of fixing the mesh size before the computation process, we propose the strategy of gradually refining the grid. Moreover, to overcome the difficulty whereby the L 1 -norm does not have a decoupled form, we apply nodal quadrature formulas to approximately discretize the L 1 -norm and L 2 -norm. Based on these strategies, an efficient multilevel heterogeneous ADMM (mhADMM) algorithm is proposed. The total error of the mhADMM consists of two parts: the discretization error resulting from the finite-element discretization and the iteration error resulting from solving the discretized subproblems. Both errors can be regarded as the error of inexactly solving infinite-dimensional subproblems. Thus, the mhADMM can be regarded as the iADMM in function space. Furthermore, theoretical results on the global convergence, as well as the iteration complexity results o (1 / k) for the mhADMM, are given. Numerical results show the efficiency of the mhADMM algorithm. [ABSTRACT FROM AUTHOR]

Feature selection for multilabel data is a challenging and meaningful work. The information contained in multilabel data is more abundant, which may help further mine knowledge and aid decision-making in various real-life applications. However, the difficulty also increases in dealing with multilabel data because the relations between labels and features need to be considered simultaneously. Missing labels and noises may exist in multilabel data, which may affect the feature selection process. Aiming at solving these problems, a robust feature selection approach is constructed under the sparse learning framework based on the least squares regression model in this study. First, a novel objective function is built by considering the robustness of the method and the manifold information. Nonnegative matrix factorization (NMF) is used to compress the label matrix to reduce false label information, which may mislead the feature selection process. The l2,1-norm is adopted to constrain the least squares regression term. Manifold regularizers are used to construct low-dimensional manifold embeddings of the original feature and label space, retaining the local manifold structure of the data. Furthermore, the correlations between features and labels are explored, and an improved weight matrix is designed. Then, an iteration algorithm is proposed to solve the objective function. Extensive experiments are performed to analyze the proposed approach, which is compared with state-of-the-art algorithms on public multilabel datasets. The experimental results verify the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

This paper proposes a sparse regularization technique for ratemaking under practical constraints. In tariff analysis of general insurance, rating factors with many categories are often grouped into a smaller number of classes to obtain reliable estimate of expected claim cost and make the tariff simple to reference. However, the number of rating-class segmentation combinations is often very large, making it computationally impossible to compare all the possible segmentations. In such cases, an L1 regularization method called the fused lasso is useful for integrating adjacent classes with similar risk levels in its inference process. Particularly, an extension of the fused lasso, known as the group fused lasso, enables consistent segmentation in estimating expected claim frequency and expected claim severity using generalized linear models. In this study, we enhance the group fused lasso by imposing ordinal constraints between the adjacent classes. Such constraints are often required in practice based on bonus–malus systems and actuarial insight on risk factors. We also propose an inference algorithm that uses the alternating direction method of multipliers. We apply the proposed method to motorcycle insurance claim data, and demonstrate how some adjacent categories are grouped into clusters with approximately homogeneous levels of expected claim frequency and severity. [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.

Spherical radial basis function (SRBF) is an effective method for calculating regional gravity field models. Calculating gravity field models with high accuracy and resolution requires dense basis functions, resulting in complex models. This study investigated the application of sparse regularization in SRBFs-based regional gravity field modeling. L1-norm regularization, also known as the least absolute shrinkage selection operator (LASSO), was employed in the parameter estimation procedure. LASSO differs from L2-norm regularization in that the solution obtained by LASSO is sparse, specifically with a portion of the parameters being zero. A sparse model would be advantageous for improving the numerical efficiency by reducing the number of SRBFs. The optimization problem of the LASSO was solved using the fast iterative shrinkage threshold algorithm, which is known for its high efficiency. The regularization parameter was selected using the Akaike information criterion. It was specifically tailored to the L1-norm regularization problem. An approximate covariance matrix of the estimated parameters in the sparse solution was analytically constructed from a Bayesian viewpoint. Based on the remove–compute–restore technique, a regional geoid model of Colorado (USA) was calculated. The numerical results suggest that the LASSO adopted in this study provided competitive results compared to Tikhonov regularization; however, the number of basis functions in the final model was less than 25% of the Tikhonov regularization. Without significantly reducing model accuracy, the LASSO solution provides a very simple model. This is the first study to apply the LASSO to SRBFs-based modeling of the regional gravity field in real gravity observation data.

Near-field acoustic holography (NAH) based on compressing sensing (CS) theory enables accurate reconstruction of sound fields using a limited number of sampling points. However, the successful implementation of this technique depends on two crucial factors: (1) the appropriate selection or construction of the spatial basis and (2) an effective sparse regularization process. To enhance reconstruction performance for elongated sound sources, this paper proposes a novel sound field reconstruction method that combines prolate spheroidal wave functions (PSWFs) with the orthogonal matching pursuit (OMP) algorithm. In this method, PSWFs serve as a sparse spatial basis for representing the radiated sound field. The sparse coefficients are determined by the OMP algorithm in a linear subspace composed of basic functions that best match the residual error. The OMP algorithm effectively identifies significant components before potentially selecting incorrect ones by setting an appropriate stopping rule. Numerical simulations are conducted using a line-array source model. The results show that the proposed method can accurately reconstruct the sound pressures of the elongated source model using a relatively small number of samplings. In addition, the proposed method exhibits robustness across a wide frequency range, diverse array configurations and various sampling numbers. The experimental results further validate the feasibility and reliability of the proposed method.

A trained-based Born iterative method (TBIM) is developed for electromagnetic imaging (EMI) applications. The proposed TBIM consists of a nested loop; the outer loop executes TBIM iteration steps, while the inner loop executes a trained iterative shrinkage thresholding algorithm (TISTA). The applied TISTA runs linear Landweber iterations implemented with a trained regularization network designed based on U-net architecture. A normalization process was imposed on the linear operator to make the linear inverse problem in TBIM consistent with TISTA assumptions. The iterative utilization of the regularization network in TISTA is a bottleneck that demands high memory allocation through the training process. Therefore, TISTA within each TBIM step was trained separately. The TISTA regularization network in each TBIM step was initialized using the weights from the previous TBIM step. The abovementioned approach achieved high-quality image restoration after running a few TBIM steps while maintaining low memory allocation through the training process. The numerical results illustrated show the superiority of the proposed TBIM compared with another three inverse scattering schemes. In addition, verification of experimental results based on the Fresnel institute database is demonstrated. [ABSTRACT FROM AUTHOR]

An electromagnetic imaging (EMI) framework is proposed based on contrast-source (CS) formulation. The CS data and state misfits are cast to form a multi-cost problem. The framework implements a nonlinear Landweber–Kaczmarz (LWKZ) algorithm that conveys the multi-cost minimization. The iteration step lengths associated with the cost terms are updated based on the maximum eigenvalues of the cost terms’ Jacobian matrices. Unlike in other CS schemes, preconditioning is not required in the proposed CS-based LWKZ (CSLWKZ), as the eigenvalues balance the cost terms through each iteration step. Furthermore, an efficient approach to calculate the eigenvalues is outlined, which significantly reduces the CSLWKZ computations. At the end of the CSLWKZ scheme, a first-norm projection operator is enforced on the contrast vector to achieve sparseness. Numerical results of a range of validity tests and a comparison with three other CS frameworks demonstrate the efficiency of the proposed approach. In addition, experimental results based on the Fresnel Institute database are illustrated. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of robust angle of arrival (AOA) target localization in the presence of uniformly distributed noise which is modeled as the mixture of Laplacian distribution and uniform distribution. Motivated by the distribution of noise, we develop a localization model by using the ℓ p -norm with 0 ≤ p < 2 as the measurement error and the ℓ 1 -norm as the regularization term. Then, an estimator for introducing the proximal operator into the framework of the alternating direction method of multipliers (POADMM) is derived to solve the convex optimization problem when 1 ≤ p < 2 . However, when 0 ≤ p < 1 , the corresponding optimization problem is nonconvex and nonsmoothed. To derive a convergent method for this nonconvex and nonsmooth target localization problem, we propose a smoothed POADMM estimator (SPOADMM) by introducing the smoothing strategy into the optimization model. Eventually, the proposed algorithms are compared with some state-of-the-art robust algorithms via numerical simulations, and their effectiveness in uniformly distributed noise is discussed from the perspective of root-mean-squared error (RMSE). The experimental results verify that the proposed method has more robustness against outliers and is less sensitive to the selected parameters, especially the variance of the measurement noise. [ABSTRACT FROM AUTHOR]

In many real-world applications, collecting and labeling the data is expensive and time-consuming. Thus, there is a need to obtain a high-performance learner by leveraging the data or knowledge from other domains. Transfer learning is a promising method to solve the above problems. In this paper, we propose a multitask transfer learning method, which aims to improve the performance of the target learner by transferring knowledge from the related source tasks. First, we formulate the target learner as a nonlinear function, which is approximated by the linear combination of the eigenfunctions. Further, to transfer knowledge from the source tasks, we constrain the target model to be the linear combination of the source models according to the previous work. However, knowledge from some source tasks may not be useful for adaptation, so we add a sparse constraint to the objective function to select the related source tasks. Different from previous transfer learning methods, our method transfers knowledge by jointly learning the source tasks and the target task. Besides, it can select the source tasks associated with the target task by the sparse constraint. Empirically, the method exhibits protection against negative transfer. Finally, we compare our proposed method with three single-task learning methods and six state-of-the-art multitask learning methods on two data sets. When compared with the second best results, the nMSE of our method achieves a relative improvement of 10.85 % with a training size of 100 on the SARCOS data set and a relative improvement of 4.26 % with a training ratio of 20 % on the Isolet data set. Experimental results show that our proposed method can effectively improve the performance of the target task by transferring knowledge from the related source tasks. [ABSTRACT FROM AUTHOR]

Many models assumed to be able to predict the response of structural systems fail to efficiently accomplish that purpose because of two main reasons. First, some structures in operation undergo localized damage that degrades their mechanical performances. To reflect this local loss of performance, the stiffness matrix associated with the structure should be locally corrected. Second, the nominal model is sometimes too coarse grained for reflecting all structural details, and consequently, the predictions are expected to deviate from the measurements. In that case, there is no small region of the model that needs to be repaired, but the entire domain needs to be repaired; therefore, the entire structure-stiffness matrix should be corrected. In the present work, we propose a methodology for locally correcting or globally enriching the models from collected data, which is, upon its turn, completed beyond the sensor's location. The proposed techniques consist in the first case of an L1-minimization procedure that, with the support of data, aims at the same time period to detect the damaged zone in the structure and to predict the correct solution. For the global enrichment, instead, the methodology consists of an L2-minimization procedure with the support of measurements. The results obtained showed, for the local problem, a correction up to 90% with respect to the initially incorrectly predicted displacement of the structure, and for the global one, a correction up to 60% was observed (this results concern the problems considered in the present study, but they depend on different factors, such as the number of data used, the geometry or the intensity of the damage). The benefits and potential of such techniques are illustrated on four different problems, showing the large generality and adaptability of the methodology. [ABSTRACT FROM AUTHOR]