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Summary A method for identifying the distribution of moving heavy vehicle loads is proposed for cable‐stayed bridges based on a sparse l1 optimization technique. This method is inspired by the recently developed compressive sensing (CS) theory, which is a technique for obtaining sparse signal representations for underdetermined linear measurement equations. In this study, sparse l1 optimization is employed to localize the moving heavy vehicle loads of cable‐stayed bridges through cable force measurements. First, a simplified equivalent load of vehicles on cable‐stayed bridges is presented. Then, the relationship between the cable forces and the moving heavy vehicle loads is established based on the influence lines. With the hypothesis of a sparse distribution of vehicle loads on the bridge deck (which is practical for long‐span bridges), moving heavy vehicle loads are identified by minimizing the ‘l2‐norm'of the difference between the observed and simulated cable forces caused by the moving vehicles penalized by the ‘l1‐norm’ of the moving heavy vehicle load vector. A numerical example of an actual cable‐stayed bridge is employed to verify the proposed method. The robustness and accuracy of this identification approach (with measurement noise for multi‐vehicle spatial localization) are validated. Copyright © 2015 John Wiley & Sons, Ltd.

This paper focuses on the compressed sensing ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization model and develops new bounds on cumulative coherence μ1(s) $\\mu _1(s)$ . It is pointed out that if cumulative coherence μ1(s) $\\mu _1(s)$satisfies Equation (2) or (11), then the sparse signal can stably recover in noise model and exactly recover in free noise by ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization model. From this paper, it is found that based on some condition of cumulative coherence, the ℓ1−ℓ2 $\\ell _1-\\ell _2$ ‐minimization model can exactly recover s‐sparse signals in noiseless cases and stably recover s‐sparse signals in the noise cases.

Based on the Support Vector Machine (SVM) and Twin Parametric Margin SVM (TPMSVM), this paper proposes two sparse models, named Sparse SVM (SSVM) and Sparse TPMSVM (STPMSVM). The study aims to achieve high sparsity, rapid prediction, and strong generalization capability by transforming the classical quadratic programming problems (QPPs) into linear programming problems (LPPs). The core idea stems from a clear geometric motivation: introducing an ℓ1-norm penalty on the dual variables to break the inherent rotational symmetry of the traditional ℓ2-norm on the normal vector. Through a theoretical reformulation using the Karush–Kuhn–Tucker (KKT) conditions, we achieve a transformation from explicit symmetry-breaking to implicit structural constraints—the ℓ1 penalty term does not appear explicitly in the final objective function, while the sparsity-inducing effect is fundamentally encoded within the objective functions and their constraints. Ultimately, the derived linear programming models naturally yield highly sparse solutions. Extensive experiments are conducted on multiple synthetic datasets under various noise conditions, as well as on 20 publicly available benchmark datasets. Results demonstrate that the two sparse models achieve significant sparsity at the support vectors level—on the benchmark datasets, SSVM, and STPMSVM reduce the number of support vectors by an average of 56.21% compared with conventional SVM, while STPMSVM achieves an average reduction of 39.11% compared with TPMSVM—thereby greatly improving prediction efficiency. Notably, SSVM maintains accuracy comparable to conventional SVM under low-noise conditions while attaining extreme sparsity and prediction efficiency. In contrast, STPMSVM offers enhanced robustness to noise and maintains a better balance between sparsity and accuracy, preserving the desirable properties of TPMSVM while improving prediction efficiency and robustness.

Data acquisition and high-dimensional signal processing often require the recovery of sparse representations of signals to minimize the resources needed for data collection. ℓp quasi-norm minimization excels in exactly reconstructing sparse signals from fewer measurements, but it is NP-hard and challenging to solve. In this paper, we propose two distinct Iteratively Re-weighted ℓ1 Minimization (IRℓ1) formulations for solving this non-convex sparse recovery problem by introducing two novel reweighting strategies. These strategies ensure that the ϵ-regularizations adjust dynamically based on the magnitudes of the solution components, leading to more effective approximations of the non-convex sparsity penalty. The resulting IRℓ1 formulations provide first-order approximations of tighter surrogates for the original ℓp quasi-norm objective. We prove that both algorithms converge to the true sparse solution under appropriate conditions on the sensing matrix. Our numerical experiments demonstrate that the proposed IRℓ1 algorithms outperform the conventional approach in enhancing recovery success rate and computational efficiency, especially in cases with small values of p.

Sparse signal processing theory has been applied to synthetic aperture radar (SAR) imaging. In compressive sensing (CS), the sparsity is usually considered as a known parameter. However, it is unknown practically. For many functions of CS, we need to know this parameter. Therefore, the estimation of sparsity is crucial for sparse SAR imaging. The sparsity is determined by the size of regularization parameter. Several methods have been presented for automatically estimating the regularization parameter, and have been applied to sparse SAR imaging. However, these methods are deduced based on an observation matrix, which will entail huge computational and memory costs. In this paper, to enhance the computational efficiency, an efficient adaptive parameter estimation method for sparse SAR imaging is proposed. The complex image-based sparse SAR imaging method only considers the threshold operation of the complex image, which can reduce the computational costs significantly. By utilizing this feature, the parameter is pre-estimated based on a complex image. In order to estimate the sparsity accurately, adaptive parameter estimation is then processed in the raw data domain, combining with the pre-estimated parameter and azimuth-range decouple operators. The proposed method can reduce the computational complexity from a quadratic square order to a linear logarithm order, which can be used in the large-scale scene. Simulated and Gaofen-3 SAR data processing results demonstrate the validity of the proposed method.

This paper investigates the sparse β model with 1 penalty in the field of network data models, which is a hot topic in both statistical and social network research. We present a refined algorithm designed for parameter estimation in the proposed model. Its effectiveness is highlighted through its alignment with the proximal gradient descent method, stemming from the convexity of the loss function. We study the estimation consistency and establish an optimal bound for the proposed estimator. Empirical validations facilitated through meticulously designed simulation studies corroborate the efficacy of our methodology. These assessments highlight the prospective contributions of our methodology to the advanced field of network data analysis.

This paper focuses on the sufficient condition of block sparse recovery with the l 2 / l 1 -minimization. We show that if the measurement matrix satisfies the block restricted isometry property with δ 2 s | I < 0.6246 , then every block s -sparse signal can be exactly recovered via the l 2 / l 1 -minimization approach in the noiseless case and is stably recovered in the noisy measurement case. The result improves the bound on the block restricted isometry constant δ 2 s | I of Lin and Li (Acta Math. Sin. Engl. Ser. 29(7):1401-1412, 2013 ).

Due to the rapid rise of energy consumption and limited battery power of wireless user equipment (UE), low power communication becomes very important. Heterogeneous network deployment can significantly reduce regional power consumption. For heterogeneous network scenarios, this paper proposes an uplink low-power resource allocation scheme considering battery power limitation and user QoS requirements. Based on the assumption that each user has access to at most one base station (BS), the scheme is modeled as a mixed integer nonlinear programming (MINLP) problem. Since each user has access to one BS at most, the transmitting power matrix from the UE to the BSs (UE-to-BS matrix) is a sparse matrix. The MINLP problem can be transformed into an optimization problem searching sparse solution. In this paper, the reweighted L1 norm is introduced as a penalty function to remove the integer constraint and to regulate the sparsity of the UE-to-BS transmitting power matrix. In order to obtain the optimal resource allocation scheme, a reweighted L1 norm penalty based radio resource management (RRM) algorithm is proposed. Simulation results show that the reweighted L1 norm penalty based RRM algorithm has good convergence performance and the results are very close to optimal solutions. The proposed resource management scheme can prolong the working time of low-energy users and guarantee the QoS requirements of UE in the system.

Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides (optimally) sparse approximations of the original image. Due to the common assumption that images are typically governed by anisotropic features, directional representation systems have often been utilized. One prominent example of this class are shearlets , which have the additional benefit of allowing faithful implementations. Numerical results show that shearlets significantly outperform wavelets in inpainting tasks. One of those software packages, ShearLab, even offers the flexibility of using a different parameter for each scale, which is not yet covered by shearlet theory. In this paper, we first introduce universal shearlet systems which are associated with an arbitrary scaling sequence, thereby modeling the previously mentioned flexibility. In addition, this novel construction allows for a smooth transition between wavelets and shearlets and therefore enables us to analyze them in a uniform fashion. For a large class of such scaling sequences, we first prove that the associated universal shearlet systems form band-limited Parseval frames for $L arrow up (\\mathbb{R} arrow up )$ consisting of Schwartz functions. Second, we analyze the inpainting performance of this class of universal shearlet systems within a distributional model situation using an $\\ell1}$-analysis minimization algorithm for reconstruction. Our main result states that, provided that the scaling sequence is comparable to the size of the (scale-dependent) gap, asymptotically perfect inpainting is achieved.

Seismic data restoration is a major strategy to provide reliable wavefield when field data dissatisfy the Shannon sampling theorem. Recovery by sparsity-promoting inversion often get sparse solutions of seismic data in a transformed domains, however, most methods for sparsity-promoting inversion are line-searching methods which are efficient but are inclined to obtain local solutions. Using trust region method which can provide globally convergent solutions is a good choice to overcome this shortcoming. A trust region method for sparse inversion has been proposed, however, the efficiency should be improved to suitable for large-scale computation. In this paper, a new L1 norm trust region model is proposed for seismic data restoration and a robust gradient projection method for solving the sub-problem is utilized. Numerical results of synthetic and field data demonstrate that the proposed trust region method can get excellent computation speed and is a viable alternative for large-scale computation.