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The epigenetic clock evaluates human biological age based on DNA methylation patterns. It takes the form of a regression model where the methylation ratio at CpG sites serves as the predictor and age as the response variable. Due to the large number of CpG sites and their correlation, Elastic Net is commonly used to train the models. However, existing standard epigenetic clocks, trained on multiracial data, may exhibit biases due to genetic and environmental differences among specific racial groups. Developing epigenetic clocks suitable for a specific single-race population requires collecting and analyzing hundreds or thousands of samples, which costs a lot of time and money. Therefore, an efficient method to construct accurate epigenetic clocks with smaller sample sizes is needed. We propose Transfer Elastic Net, a transfer learning approach that trains a model in the target population using the information of parameters estimated by the Elastic Net in a source population. Using this method, we constructed Horvath's, Hannum's, and Levine's types of epigenetic clocks from blood samples of 143 Japanese subjects. The DNA methylation data were transformed through principal component analysis to obtain more reliable clocks. The developed clocks demonstrated the smallest prediction errors compared to both the original clocks and those trained with the Elastic Net on the same Japanese data. Transfer Elastic Net can also be applied to develop epigenetic clocks for other specific populations, and is expected to be applied in various fields. [ABSTRACT FROM AUTHOR]

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]

The epigenetic clock evaluates human biological age based on DNA methylation patterns. It takes the form of a regression model where the methylation ratio at CpG sites serves as the predictor and age as the response variable. Due to the large number of CpG sites and their correlation, Elastic Net is commonly used to train the models. However, existing standard epigenetic clocks, trained on multiracial data, may exhibit biases due to genetic and environmental differences among specific racial groups. Developing epigenetic clocks suitable for a specific single-race population requires collecting and analyzing hundreds or thousands of samples, which costs a lot of time and money. Therefore, an efficient method to construct accurate epigenetic clocks with smaller sample sizes is needed. We propose Transfer Elastic Net, a transfer learning approach that trains a model in the target population using the information of parameters estimated by the Elastic Net in a source population. Using this method, we constructed Horvath’s, Hannum’s, and Levine’s types of epigenetic clocks from blood samples of 143 Japanese subjects. The DNA methylation data were transformed through principal component analysis to obtain more reliable clocks. The developed clocks demonstrated the smallest prediction errors compared to both the original clocks and those trained with the Elastic Net on the same Japanese data. Transfer Elastic Net can also be applied to develop epigenetic clocks for other specific populations, and is expected to be applied in various fields.

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.

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.

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., (© 2024. The Author(s).)

Feature selection can alleviate the problem of the curse of dimensionality by selecting more discriminative features, which plays an important role in multi-label learning. Recently, embedded feature selection methods have received increasing attentions. However, most existing methods learn the low-dimensional embeddings under the guidance of the local structure between the original instance pairs, thereby ignoring the high-order structure between instances and being sensitive to noise in the original features. To address these issues, we propose a feature selection method named discriminative multi-label feature selection with adaptive graph diffusion (MFS-AGD). Specifically, we first construct a graph embedding learning framework equipped with adaptive graph diffusion to uncover a latent subspace that preserves the higher-order structure information between four tuples. Then, the Hilbert–Schmidt independence criterion (HSIC) is incorporated into the embedding learning framework to ensure the maximum dependency between the latent representation and labels. Benefiting from the interactive optimization of the feature selection matrix, latent representation and similarity graph, the selected features can accurately explore the higher-order structural and supervised information of data. By further considering the correlation between labels, MFS-AG is extended to a more discriminative version,i.e., LMFS-AG. Extensive experimental results on various benchmark data sets validate the advantages of the proposed MFS-AGD and LMFS-AGD methods. • Presenting a new multi-label feature selection method that cleverly combines the feature selection, latent representation learning and manifold embedding. • Integrating a graph diffusion constraint into feature selection to explore the high-order manifold structure of instances. • Maximizing the HSIC measurement between the embedding space and the label space improves the discriminability of selected features. • Designing an efficient optimization algorithm to solve the objective problem with good convergence. [ABSTRACT FROM AUTHOR]

Physics-driven and data-driven methods are commonly used for impact force identification. Due to system identification errors, physics-driven methods often suffer from force oscillations and peak underestimations, leading to poor accuracy. Data-driven methods generally require massive experimental data, incurring expensive costs. Hence, achieving accurate and low-cost impact force identification in the presence of system identification errors remains a significant challenge. In this paper, we proposed a data-physics hybrid-driven deep learning method for impact force identification, named DPH-TrLSTM. The method utilizes the time-reversed long short-term memory (TrLSTM) network to establish the causal relationship from response to force. The data-physics hybrid (DPH) loss function is employed to mitigate the adverse effect of system identification errors. The DPH-TrLSTM method only requires the transfer matrix and a small amount of experimental data obtained from the system identification step, eliminating the need for additional experiments. Experimental results from 40 impact forces at eight locations on a composite plate demonstrated that the DPH-TrLSTM method could achieve mean peak and relative errors below 1.0% and 2.5%, respectively, significantly outperforming the three regularization methods. This result suggests that the proposed method can perform high-accuracy impact force identification even when system identification errors exist. Moreover, the effect of system identification errors on the method's performance can be evaluated using the min–max curve, thereby determining its applicable scope. The study further reveals that system identification errors are the key reason for the poor performance of the three regularization methods. The choice of measurement points may affect the performance of DPH-TrLSTM, primarily due to system identification errors rather than the condition number of the transfer matrix. [ABSTRACT FROM AUTHOR]

• A novel moving force identification method is proposed by integrating L1 and weighted L2 regularization. • A weighted L2 regularization strategy is presented to enhance identification accuracy of constant forces. • Constant and time-varying components of moving forces are identified from separated responses with higher accuracy. • The effectiveness of the proposed method is verified by numerical simulations and experimental verifications. • The proposed method outperforms the existing L1 and L2 regularization methods in accuracy and robustness. Existing regularization methods have been proven effective in the ill-posed problem of moving force identification (MFI). However, both the constant and time-varying components of moving forces cannot be accurately identified at the same time, especially under higher measurement noises. To address this issue, a new MFI method is proposed by integrating the L1 and weighted L2 regularization methods in this study, where the presented weighted L2 regularization strategy achieves a more nuanced balance of moving force components through the incorporation of weight coefficients. Furthermore, the inherent solving characteristics of L1 and weighted L2 regularization methods are fully utilized to solve different components in moving forces separately. Numerical simulations and experimental verifications are carried out to assess the effectiveness of the proposed method. The results show that the proposed method can accurately identify moving forces even under 25% higher noise levels and it can effectively evaluate the axle loads and gross vehicle weight of the experimental vehicle. Besides, comparative studies further show that the proposed method outperforms the existing L1 and L2 regularization methods in the identification of both constant and time-varying forces, which provides a potential MFI tool for a higher accuracy and noise robustness to fix the MFI problem in practice. [ABSTRACT FROM AUTHOR]

The present work proposes a seismic response estimation framework for post-earthquake structural condition assessment via acceleration measurements. An augmented sparse state space model is first derived to represent the underlying governing equations of the system of interest with hysteresis nonlinearity. A Bayesian filter is then utilized to provide the displacement estimate under an earthquake excitation by fusing the identified sparse state space model with the measured system acceleration. To avoid subjective assumptions on the process and observation noises in the Bayesian filter, a double-loop process is proposed, where the inner loop is an online Bayesian filtering by the unscented Kalman filter with Robbins-Monro algorithm, while the outer loop is an offline Bayesian updating by the transitional Markov chain Monte Carlo method. The feasibility of the framework is demonstrated on a simple illustrative example and a followed engineering application to the state estimation of a bridge pier finite element model. The results indicate the capability of the framework to properly infer the system displacement, including its residual components. [ABSTRACT FROM AUTHOR]

The tensor train rank (TT-rank) has achieved promising results in tensor completion due to its ability to capture the global low-rankness of higher-order (> 3) tensors. On the other hand, in recent times, quaternions have demonstrated their remarkable suitability as a framework for encoding color pixels, leading to exceptional performance across a range of color image processing tasks. In this paper, we encode the three channels of color pixels using the three imaginary parts of quaternions, leveraging the structural advantages of quaternions to fully preserve the potential relationships between color pixel channels. Subsequently, we extend the TT-rank to higher-order quaternion tensors to capture the global low-rank structure of higher-dimensional data. Specifically, the quaternion tensor train (QTT) decomposition is presented, and based on that the quaternion TT-rank (QTT-rank) is naturally defined. In addition, to utilize the local sparse prior of the quaternion tensor, a general and flexible transform framework is defined. Combining both the global low-rank and local sparse priors of the quaternion tensor, we propose a novel quaternion tensor completion model, i.e. , QTT-rank minimization with sparse regularization in a transformed domain. Furthermore, to facilitate QTT-rank minimization for processing color images and enhancing its performance with color videos, we extend KA, a tensor augmentation method, to quaternion tensors, introducing quaternion KA (QKA). Numerical experiments conducted on color image and color video inpainting tasks showcase the superiority of the proposed method over state-of-the-art alternatives. [ABSTRACT FROM AUTHOR]

The total focusing method (TFM) is considered as the standard in ultrasonic phased array imaging and plays a vital role in industrial non-destructive testing (NDT). By utilizing the full matrix capture (FMC) dataset, the TFM can focus on every point within the specified imaging region, and is more accurate than the traditional ultrasonic phased array imaging methods. However, the TFM is essentially a delay and sum technique that often operates linearly on the time-domain signals and takes no prior information into account, so its image quality remains inadequate when dealing with defects in close proximity or scattering materials. To address this problem, this paper formulates the imaging principle of the TFM as a Boolean matrix and establishes the discretized tensor-based model. Subsequently, the model is addressed by employing the sparse regularization strategy, taking into some characteristics of industrial NDT. Regarding the solution algorithm, due to the generation of negative values by the fast iterative shrinkage threshold algorithm (FISTA), this paper introduces the rectified linear unit (ReLU) function as a non-negative constraint and presents a dedicated solution algorithm (ReLU-FISTA) for acquiring detection results. Through verification of simulation and experiment, the proposed approach exhibits superior capabilities of defect characterization and noise suppression when compared to the TFM, leading to substantial enhancements in image quality. [ABSTRACT FROM AUTHOR]