Sparse Regularization Model Research Articles

Efficient structural damage detection via the lω regularization and randomized extended Kaczmarz algorithm

Structural damage detection (SDD) is an important aspect of structural health monitoring. This study aimed to explore a new method IT ω -REK θ (ω = 1, 1/2; θ = 1,2,3) for SDD based on the lω sparse regularization model and the randomized extended Kaczmarz (REK) type algorithms. When ω = 1/2, the l1/2 sparse regularization model was applied to enhance the ill-posedness of the damage identification problem and ensure the sparsity of the solution. The REK, θ = 1, partially randomized extended Kaczmarz (θ = 2), and fast maximum-distance extended Kaczmarz (θ = 3) algorithms with different threshold operators were used to solve the lω regularization model. These algorithms could obtain optimal identification results and significantly improve computational efficiency by randomly and partially selecting the data of the sensitivity equations. Numerical and experimental studies on different structures showed that the proposed method could fast locate structural damage and accurately identify the damage extents, which was robust to the SDD problem with noise.

Learning a Non-Locally Regularized Convolutional Sparse Representation for Joint Chromatic and Polarimetric Demosaicking.

Division of focal plane color polarization camera becomes the mainstream in polarimetric imaging for it directly captures color polarization mosaic image by one snapshot, so image demosaicking is an essential task. Current color polarization demosaicking (CPDM) methods are prone to unsatisfied results since it's difficult to recover missed 15 or 14 pixels out of 16 pixels in color polarization mosaic images. To address this problem, a non-locally regularized convolutional sparse regularization model, which is advantaged in denoising and edge maintaining, is proposed to recall more information for CPDM task, and the CPDM task is transformed into an energy function to be solved by ADMM optimization. Finally, the optimal model generates informative and clear results. The experimental results, including reconstructed synthetic and real-world scenes, demonstrate that our proposed method outperforms the current state-of-the-art methods in terms of quantitative measurements and visual quality. The source code is available at https://github.com/roydon-luo/NLCSR-CPDM.

A joint fraction function regularization model for the structural damage identification

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

Cauchy non-convex sparse feature selection method for the high-dimensional small-sample problem in motor imagery EEG decoding.

The time, frequency, and space information of electroencephalogram (EEG) signals is crucial for motor imagery decoding. However, these temporal-frequency-spatial features are high-dimensional small-sample data, which poses significant challenges for motor imagery decoding. Sparse regularization is an effective method for addressing this issue. However, the most commonly employed sparse regularization models in motor imagery decoding, such as the least absolute shrinkage and selection operator (LASSO), is a biased estimation method and leads to the loss of target feature information. In this paper, we propose a non-convex sparse regularization model that employs the Cauchy function. By designing a proximal gradient algorithm, our proposed model achieves closer-to-unbiased estimation than existing sparse models. Therefore, it can learn more accurate, discriminative, and effective feature information. Additionally, the proposed method can perform feature selection and classification simultaneously, without requiring additional classifiers. We conducted experiments on two publicly available motor imagery EEG datasets. The proposed method achieved an average classification accuracy of 82.98% and 64.45% in subject-dependent and subject-independent decoding assessment methods, respectively. The experimental results show that the proposed method can significantly improve the performance of motor imagery decoding, with better classification performance than existing feature selection and deep learning methods. Furthermore, the proposed model shows better generalization capability, with parameter consistency over different datasets and robust classification across different training sample sizes. Compared with existing sparse regularization methods, the proposed method converges faster, and with shorter model training time.

On an Extension of a Spare Regularization Model

In this paper, we would first like to promote an interesting idea for identifying the local minimizer of a non-convex optimization problem with the global minimizer of a convex optimization one. Secondly, to give an extension of their sparse regularization model for inverting incomplete Fourier transforms introduced. Thirdly, following the same lines, to develop convergence guaranteed efficient iteration algorithm for solving the resulting nonsmooth and nonconvex optimization problem but here using applied nonlinear analysis tools. These both lead to a simplification of the proofs and to make a connection with classical works in this filed through a startling comment.

Plug‐and‐play algorithms for convex non‐convex regularization: Convergence analysis and applications

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 ‐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.

Lidar Reflective Tomography of the Target Under Incomplete View State

The lidar reflective tomography (LRT) system transmits a laser signal and obtains laser reflection projections of the target, which shows great potential for further long-distance noncooperative target detection. However, the received projections are normally in an incomplete view state. Hence, in this article, an improved algebraic reconstruction technique (ART) utilizing the sparse regularization model and nonlocal means (NLMs) algorithm is introduced and proposed for LRT reconstruction to restore incomplete signals or projections. By using the designed LRT outfield system, the comparative experiments are carried out to validate the effectiveness of the proposed method. By considering different investigation states, the improved NLM-ART sparse method shows great capability for LRT of noncooperative targets in long distance.

SRI3D: Two‐stream inflated 3D ConvNet based on sparse regularization for action recognition

AbstractAlthough most state‐of‐the‐art action recognition models have adopted a two‐stream 3D convolutional structure as a backbone network, few works have studied the impact of loss functions on action recognition models. In addition, sparsity is used as a key prior knowledge in many fields. However, as far as is known, no one has studied the influence of the sparsity of network output on the output of deep learning‐based action recognition models. Therefore, this paper proposes a novel two‐stream inflated 3D ConvNet based on the sparse regularization (SRI3D) model for action recognition. In order to allow the network to learn the sparsity of output, the ℓ1 norm is embedded in the loss function in regularization form in a plug‐and‐play manner. It can make the classification result after the fusion of the two‐stream network only be the category with the highest confidence in one of the streams and not the other cases. The proposed loss function based on sparse regularization makes the output vector of the neural network as sparse as possible so that the classification results will not be ambiguous. Experimental results show that compared with other state‐of‐the‐art models, this SRI3D has a competitive advantage on Kinetics‐400, Something‐Something V2, UCF‐101 and HMDB‐51.

Phase coherent noise reduction in digital holographic microscopy based on adaptive non-convex sparse regularization

Digital holographic microscopy is a new type of quantitative phase measurement tool. When a coherent light source is used for illumination, the phase coherent noise seriously affects the imaging quality and measurement accuracy. A method of phase coherent noise reduction based on adaptive non-convex sparse regularization is proposed in this paper. This denoising problem is considered as a sparse regularization model, which uses a non-convex penalty called the generalized minimax-concave; the penalty can lead to a more accurate estimation of the phase image amplitude and reduce most of the noise. Meanwhile, the threshold of the algorithm to solve this problem is guided by the edge credibility map adaptively. In edge regions, the threshold value is small so that edge details are preserved; however, in other regions, the threshold value is big so that the phase coherent noise is removed. The experimental results confirmed the validity of the proposed method.

Inverting Incomplete Fourier Transforms by a Sparse Regularization Model and Applications in Seismic Wavefield Modeling

We propose a sparse regularization model for inversion of incomplete Fourier transforms and apply it to seismic wavefield modeling. The objective function of the proposed model employs the Moreau envelope of the \(\ell _0\) norm under a tight framelet system as a regularization to promote sparsity. This model leads to a non-smooth, non-convex optimization problem for which traditional iteration schemes are inefficient or even divergent. By exploiting special structures of the \(\ell _0\) norm, we identify a local minimizer of the proposed non-convex optimization problem with a global minimizer of a convex optimization problem, which provides us insights for the development of efficient and convergence guaranteed algorithms to solve it. We characterize the solution of the regularization model in terms of a fixed-point of a map defined by the proximity operator of the \(\ell _0\) norm and develop a fixed-point iteration algorithm to solve it. By connecting the map with an \(\alpha \)-averaged nonexpansive operator, we prove that the sequence generated by the proposed fixed-point proximity algorithm converges to a local minimizer of the proposed model. Our numerical examples confirm that the proposed model outperforms significantly the existing model based on the \(\ell _1\)-norm. The seismic wavefield modeling in the frequency domain requires solving a series of the Helmholtz equation with large wave numbers, which is a computationally intensive task. Applying the proposed sparse regularization model to the seismic wavefield modeling requires data of only a few low frequencies, avoiding solving the Helmholtz equation with large wave numbers. This makes the proposed model particularly suitable for the seismic wavefield (SW) modeling. Numerical results show that the proposed method performs better than the existing method based on the \(\ell _1\) norm in terms of the SNR values and visual quality of the restored synthetic seismograms.

A novel joint sparse regularization model to structural damage identification by the generalized fused lasso penalty

The sparse regularization (SReg) model is widely used for structural damage identification by employing the sparsity peculiarity of the structural damage. The conventional SReg model often separately conducts damage identification on each measurement, while ignores the utilization of the similarity information among different measurements. In this paper, we propose a novel joint sparse regularization model for structural damage identification. In detail, combined with the sparsity of the structural damage by the conventional SReg model, our model employs the similarity of different measurements to further improve the damage identification performance, which is realized by the generalized fused lasso penalty. Numerical simulations on the six-bay planar truss structure and experimental studies on the cantilever beam structure illustrate that the damage identification accuracy of our model is promoted 3.59% and 20.75% than the conventional SReg one, respectively.

A Novel Downward‐Looking Linear Array SAR Imaging Method Based on Multiple Measurement Vector Model with L2,1‐Norm

Downward‐looking linear array synthetic aperture radar (DLLA SAR) is a kind of three‐dimensional (3‐D) radar imaging system. To obtain the superresolution along the crosstrack direction of DLLA SAR, the sparse regularization models with single measurement vector (SMV) have been widely applied. However, the robustness of the sparse regularization models with SMV is unsatisfactory, especially in the low signal‐to‐noise rate (SNR) environment. To solve this problem, we proposed a novel imaging method for DLLA SAR based on the multiple measurement vector (MMV) model with L2,1‐norm. At first, we exchange the processing order between the along‐track (AT) domain and the crosstrack (CT) domain to keep the same sparse structure of the signal in the crosstrack domain so that we can establish the imaging problem as a sparse regularization model based on the MMV model. Moreover, the mixed L2,1‐norm is introduced into the regularization term of the MMV model. Finally, the modified orthogonal matching pursuit (OMP) algorithm is designed for the MMV model with the L2,1‐norm. The simulations verify that the proposed method has better performance in the lower SNR environment and requires lower computation compared with the conventional methods.

Velocity modeling based on Rayleigh wave dispersion curve and sparse optimization inversion

<p style='text-indent:20px;'>This paper studies the S wave velocity modeling based on the Rayleigh wave dispersion curve inversion. We first discuss the forward simulation, and present a fast root-finding method with cubic-order of convergence speed to obtain the Rayleigh wave dispersion curve. With the Rayleigh wave dispersion curve as the observation data, and considering the prior geological anomalies structural information, we establish a sparse constraint regularization model, and propose an iterative solution method to solve for the S wave velocity. Experimental tests are performed both on the theoretical models and on the field data. It indicates from the experimental results that our new inversion scheme possesses the characteristics of easy calculation, high computational efficiency and high precision for model characterization.</p>

A Sparsity-Assisted Fault Diagnosis Method Based on Nonconvex Sparse Regularization

Sparse representation theory can be adopted for fault feature extraction and classification. Inspired by these two capabilities of sparse representation theory, this paper proposes a novel collaborative sparsity-assisted fault diagnosis (CSFD) method. Specifically, due to the repeatability and sparsity of fault feature signal in the whole signal, the feature extraction capability of sparse representation is utilized to extract fault features and construct a feature matrix. Subsequently, owing to the sparsity of fault classification problem itself, the classification capability of sparse representation is employed to achieve fault classification. Moreover, fault feature extraction is a key issue for fault diagnosis. Therefore, in order to improve the effectiveness of fault feature extraction, a RC-adjustment strategy with the ability to adaptively adjust regularization parameter is designed to assist the generalized minimax-concave (GMC) penalty for feature extraction. The advantage of the GMC penalty is that it can establish a nonconvex sparse regularization model with convex optimization solution. Finally, the proposed CSFD method is tested and verified by Case Western Reserve University (CWRU) bearing dataset and actual engineering dataset. Especially, the diagnostic accuracy of this method can reach 99.92%, which is nearly 7.68% higher than the traditional method based on L1 norm penalty. Enormous experiment results have thoroughly demonstrated the effectiveness of the proposed CSFD method for fault diagnosis.

Obtaining TFR From Incomplete and Phase-Corrupted m-D Signal in Real Time

In micromotion feature extraction, the incomplete and phase-corrupted radar echo may cause bad time–frequency representation (TFR) and prevent micromotion feature extraction. To solve the problem, we establish a sparse regularization model to reconstruct well-focused TF distributions. The regularization model is solved by the iterative soft-thresholding algorithm (ISTA). In each iteration, the hard thresholding function and least-square-error criterion are developed to estimate the phase errors. For micro-Doppler signal real-time processing to save radar time resources, the received signal can be directly sparse recovered in real time rather than waiting for the complete signal. Finally, the effectiveness of the proposed method is validated by the simulation results.

$L_p$ -Norm-Based Sparse Regularization Model for License Plate Deblurring

We propose an $L_{p}$ -norm-based sparse regularization model for license plate deblurring, which is motivated by distinctive properties of license plate images. For the blurred images, general deblurring methods may restore a good overall visual effect. However, in real-life traffic surveillance system, the deblurring results may be not good for license plates. The main reason lies in that general deblurring methods do not give sufficient thought to the features of license plate, which could be important priors for deblurring. Focusing on this issue, analysis on the statistical distribution characteristics of the license plates are launched, based on which an $L_{p}$ -norm-based regularization model is proposed. Furthermore, alternating direction method of multipliers are introduced to solve the model. Experimental results demonstrate that the proposed model performs favorably against the state-of-the-art license plate image deblurring methods.

Outer-Points shaver: Robust graph-based clustering via node cutting

Graph-based clustering is an efficient method for identifying clusters in local and nonlinear data patterns. Among the existing methods, spectral clustering is one of the most prominent algorithms. However, this method is vulnerable to noise and outliers. This study proposes a robust graph-based clustering method that removes the data nodes of relatively low density. The proposed method calculates the pseudo-density from a similarity matrix, and reconstructs it using a sparse regularization model. In this process, noise and the outer points are determined and removed. Unlike previous edge cutting-based methods, the proposed method is robust to noise while detecting clusters because it cuts out irrelevant nodes. We use a simulation and real-world data to demonstrate the usefulness of the proposed method by comparing it to existing methods in terms of clustering accuracy and robustness to noisy data. The comparison results confirm that the proposed method outperforms the alternatives.

An enhanced sparse regularization method for impact force identification

• An enhanced sparse regularization method is developed for improving impact force identification. • A weighted l 1 -norm convex optimization model for impact force identification is developed. • Iteratively reweighted l 1 -norm minimization algorithm is proposed for solving impact force identification. • Compared with existing regularizations, the enhanced sparse regularization has much sparser and more accurate result. The standard sparse regularization method based on l 1 -norm minimization for impact force identification has already proved to be an interesting alternative to the classical regularization method based on l 2 -norm minimization. However, choosing the l 1 -norm as a convex relaxation of the l 0 -norm, the corresponding sparse regularization model generally offers a sparse but underestimated solution. In this paper, considering the sparsity of impact force, an enhanced sparse regularization method based on reweighted l 1 -norm minimization is developed for reducing the peak force error and improving the identification accuracy of impact force. First, a weighted l 1 -norm convex optimization model is presented to overcome the ill-posed nature of the inverse problem of impact force identification. Second, to solve such a regularized model efficiently, an iteratively reweighted l 1 -norm minimization algorithm is introduced, where the weights are adaptively updated from the previous solution. The application of the iteratively reweighted scheme is to overcome the mismatch between l 1 -norm minimization and l 0 -norm minimization, while keeping the enhanced sparse regularization problem solvable and convex. Finally, numerical simulation and experimental verification including the single and double impact force identification on a plate structure are presented to illustrate the superior performance of the enhanced sparse regularization method compared to classical regularization approaches. Effects of reweighting iteration number, tuning parameters, initial conditions and response locations are successfully investigated in detail. Results demonstrate that compared with the standard l 1 -norm regularization method and the classical l 2 -norm regularization method, the enhanced sparse regularization method based on reweighted l 1 -norm minimization whose solution is much sparser, can greatly improve the identification accuracy of impact force. Moreover, the proposed method is much more robust to the choice of tuning parameters and noisy measurements.

Group sparse regularization for impact force identification in time domain

Impact force identification remains a challenging inverse problem, where a small error in structural responses may lead to a large deviation in the actual solution. Recently, sparse regularization has attracted a lot of interest in the field of force identification. However, the standard sparse regularization method for force identification does not consider the intrinsic structure of impact force, i.e., the nonzero elements occur in groups, called group sparsity. In this paper, by exploiting the group sparse structure of impact force time history, we develop a general group sparse regularization method based on minimizing mixed l2,1-norm for the inverse problem of impact force identification. First, the number and size of groups including a complete profile of impact force are determined for penalizing the sum of the l2-norm of groups associated with the pulse profile of impact force. Second, a general group sparse optimization model based on the mixed l2,1-norm penalty for impact force identification is constructed in time domain, leading to a non-smooth convex optimization problem. Third, given the transfer function and the impact response, an accelerated gradient descent method is developed to solve such a group sparse regularization model. Finally, experiments including identification of single and consecutive impact forces are conducted on a clamped-free thin plate to illustrate the effectiveness and applicability of the proposed approach. Experimental results demonstrate that the classical Tikhonov regularization methods can only identify the single impact force from weakly noisy responses; the group sparse regularization method can efficiently identify both single and consecutive impact forces from heavily noisy responses, and has a slightly better improvement of the peak force amplitude than the standard sparse regularization method.

Magnetic parameters inversion method with full tensor gradient data

Retrieval of magnetization parameters using magnetic tensor gradient measurements receives attention in recent years. Determination of subsurface properties from the observed potential field measurements is referred to as inversion. Little regularizing inversion results using full tensor magnetic gradient modeling so far has been reported in the literature. Traditional magnetic inversion is based on the total magnetic intensity (TMI) data and solving the corresponding mathematical physical model. In recent years, with the development of the advanced technology, acquisition of the full tensor gradient magnetic data becomes available. In this paper, we study invert the magnetic parameters using the full tensor magnetic gradient data. A sparse Tikhonov regularization model is established. In solving the minimization model, the conjugate gradient method is addressed. Numerical and field data experiments are performed to show feasibility of our algorithm.