Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice,simultaneous impact localization and time history reconstruction can hardly be achieved,due to the illposed and under-determined problems induced by the constrained and harsh measuring conditions.Although l_(1) regularization can be used to obtain sparse solutions,it tends to underestimate solution amplitudes as a biased estimator.To address this issue,a novel impact force identification method with l_(p) regularization is proposed in this paper,using the alternating direction method of multipliers(ADMM).By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators,ADMM can address the challenge effectively.To mitigate the sensitivity to regularization parameters,an adaptive regularization parameter is derived based on the K-sparsity strategy.Then,an ADMM-based sparse regularization method is developed,which is capable of handlingl_(p) regularization with arbitrary p values using adaptively-updated parameters.The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure.Additionally,an investigation into the optimal p value for achieving high-accuracy solutions vial_(p) regularization is conducted.It turns out that?_(0.6)regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classicl_(1) regularization method.The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.

Low-Rank Multi-View Subspace Clustering Based on Sparse Regularization

Multi-view Subspace Clustering (MVSC) emerges as an advanced clustering method, designed to integrate diverse views to uncover a common subspace, enhancing the accuracy and robustness of clustering results. The significance of low-rank prior in MVSC is emphasized, highlighting its role in capturing the global data structure across views for improved performance. However, it faces challenges with outlier sensitivity due to its reliance on the Frobenius norm for error measurement. Addressing this, our paper proposes a Low-Rank Multi-view Subspace Clustering Based on Sparse Regularization (LMVSC- Sparse) approach. Sparse regularization helps in selecting the most relevant features or views for clustering while ignoring irrelevant or noisy ones. This leads to a more efficient and effective representation of the data, improving the clustering accuracy and robustness, especially in the presence of outliers or noisy data. By incorporating sparse regularization, LMVSC-Sparse can effectively handle outlier sensitivity, which is a common challenge in traditional MVSC methods relying solely on low-rank priors. Then Alternating Direction Method of Multipliers (ADMM) algorithm is employed to solve the proposed optimization problems. Our comprehensive experiments demonstrate the efficiency and effectiveness of LMVSC-Sparse, offering a robust alternative to traditional MVSC methods.

Sparse reconstruction for fluorescence molecular tomography via a fast iterative algorithm

Fluorescence molecular tomography(FMT)is a fast-developing optical imaging modalitythat has great potential in early diagnosis of disease and drugs development.However,recon-struction algorithms have to address a highly ill-posed problem to fulfll 3D reconstruction inFMT.In this contribution,we propose an efficient iterative algorithm to solve the large-scalereconstruction problem,in which the sparsity of fluorescent targets is taken as useful a prioriinformation in designing the reconstruction algorithm.In the implementation,a fast sparseapproximation scheme combined with a stage-wise learning strategy enable the algorithm to dealwith the ill-posed inverse problem at reduced computational costs.We validate the proposed fastiterative method with numerical simulation on a digital mouse model.Experimental results demonstrate that our method is robust for different finite element meshes and different Poissonnoise levels.

Graph Regularized Sparse Coding Method for Highly Undersampled MRI Reconstruction

The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) was proposed. The graph regularized sparse coding showed the potential in maintaining the geometrical information of the data. In this study, it was incorporated with two-level Bregman iterative procedure that updated the data term in outer-level and learned dictionary in innerlevel. Moreover,the graph regularized sparse coding and simple dictionary updating stages derived by the inner minimization made the proposed algorithm converge in few iterations, meanwhile achieving superior reconstruction performance. Extensive experimental results have demonstrated GSCMRI can consistently recover both real-valued MR images and complex-valued MR data efficiently,and outperform the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.

Text Detection in Natural Scene Images Using Morphological Component Analysis and Laplacian Dictionary

Text in natural scene images usually carries abundant semantic information. However, due to variations of text and complexity of background, detecting text in scene images becomes a critical and challenging task. In this paper, we present a novel method to detect text from scene images. Firstly, we decompose scene images into background and text components using morphological component analysis(MCA), which will reduce the adverse effects of complex backgrounds on the detection results.In order to improve the performance of image decomposition,two discriminative dictionaries of background and text are learned from the training samples. Moreover, Laplacian sparse regularization is introduced into our proposed dictionary learning method which improves discrimination of dictionary. Based on the text dictionary and the sparse-representation coefficients of text, we can construct the text component. After that, the text in the query image can be detected by applying certain heuristic rules. The results of experiments show the effectiveness of the proposed method.

Magnetic susceptibility inversion method with full tensor gradient data using low-temperature SQUIDs

Full tensor magnetic gradient measurements are available nowadays. These are essential for determining magnetization parameters in deep layers. Using full or partial tensor magnetic gradient measurements to determine the subsurface properties, e.g., magnetic susceptibility, is an inverse problem. Inversion using total magnetic intensity data is a traditional way.Because of di culty in obtaining the practical full tensor magnetic gradient data, the corresponding inversion results are not so widely reported. With the development of superconducting quantum interference devices(SQUIDs), we can acquire the full tensor magnetic gradient data through field measurements. In this paper, we study the inverse problem of retrieving magnetic susceptibility with the field data using our designed low-temperature SQUIDs. The solving methodology based on sparse regularization and an alternating directions method of multipliers is established. Numerical and field data experiments are performed to show the feasibility of our algorithm.

Sparse Deep Neural Network for Nonlinear Partial Differential Equations

More competent learning models are demanded for data processing due to increasingly greater amounts of data available in applications.Data that we encounter often have certain embedded sparsity structures.That is,if they are represented in an appropriate basis,their energies can concentrate on a small number of basis functions.This paper is devoted to a numerical study of adaptive approximation of solutions of nonlinear partial differential equations whose solutions may have singularities,by deep neural networks(DNNs)with a sparse regularization with multiple parameters.Noting that DNNs have an intrinsic multi-scale structure which is favorable for adaptive representation of functions,by employing a penalty with multiple parameters,we develop DNNs with a multi-scale sparse regularization(SDNN)for effectively representing functions having certain singularities.We then apply the proposed SDNN to numerical solutions of the Burgers equation and the Schrödinger equation.Numerical examples confirm that solutions generated by the proposed SDNN are sparse and accurate.

Non-convex sparse optimization-based impact force identification with limited vibration measurements

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 classicalℓ2 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 popularℓ1 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-convexℓ1-2 penalty,which is the difference of theℓ1 andℓ2 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 namedℓ1-2-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 theℓ1-2-ADMM method.Results indicate that compared with other existing regularization methods,theℓ1-2-ADMM method can simultaneously reconstruct and localize impact forces more accurately,facilitating sparser solutions,and yielding more accurate results.