Minimization-based Method Research Articles

3D modeling and measurement of HTS tape stacks in linear superconducting magnetic bearings

Superconducting magnetic bearings (SMBs) are among the possible new technologies to be incorporated in maglev vehicles. Stacks of high-temperature superconductor (HTS) tapes can be used as an alternative to bulks, because stacks offer better mechanical properties, a better thermal conductivity and a simpler production process. Numerical modeling has been employed as a cost-effective, fast and reliable tool for improving the performance of SMBs. Several scenarios can be simulated with fast and relatively simple 2D models; however, in some cases using 3D models is inevitable. In this study, we use a full 3D model to solve the problem of magnetization of the tape stacks and obtaining the hysteresis force loop between a permanent magnet and the tape stacks. For this purpose, we employ an energy minimization-based method called minimum electromagnetic entropy production in 3D, combined with a homogenization technique and the Jc(B,θ) dependence of the HTS tape as input. The modeling results agree very well with the experiment both in the zero-field cooled and field-cooled conditions. The presented approach offers significant computational advantages, delivering faster and more efficient results compared to previously proposed 3D methods.

A bottom-up method for roof plane extraction from airborne LiDAR point clouds

Accurate roof plane extraction is a crucial step in constructing a three-dimensional model for buildings. Due to the significant differences in size and shape of building roofs in airborne light detection and ranging point clouds, many existing plane extraction methods are struggling to achieve good performance. To solve the above problem, a bottom–up method for roof plane extraction is proposed in this paper. Starting with the division of the roof point cloud into voxels, the initial planes are obtained in the voxels. The initial planes are then expanded by a parameter-adaptive region growing algorithm. Then, the grown planes are merged according to predefined constraints. Finally, an energy minimization-based method is applied to optimize the results of roof plane extraction. The performance of our proposed method is evaluated on the Vaihingen dataset and the DALES dataset. Experiments demonstrate that our proposed method achieves a superior roof plane extraction result.

A majorization–minimization-based method for nonconvex inverse rig problems in facial animation: algorithm derivation

Automated methods for facial animation are a necessary tool in the modern industry since the standard blendshape head models consist of hundreds of controllers, and a manual approach is painfully slow. Different solutions have been proposed that produce output in real-time or generalize well for different face topologies. However, all these prior works consider a linear approximation of the blendshape function and hence do not provide a high-enough level of detail for modern realistic human face reconstruction. A second-order blendshape approximation leads to higher fidelity facial animation but generates a non-linear least squares optimization problem with high dimensionality. We derive a method for solving the inverse rig in blendshape animation using quadratic corrective terms, which increases accuracy. At the same time, due to the proposed construction of the objective function, it yields a sparser estimated weight vector compared to the state-of-the-art methods. The former feature means lower demand for subsequent manual corrections of the solution, while the latter indicates that the manual modifications are also easier to include. Our algorithm is iterative and employs a Majorization–Minimization paradigm to cope with the increased complexity produced by adding corrective terms. The surrogate function is easy to solve and allows for further parallelization on the component level within each iteration. This paper is complementary to an accompanying paper (Racković et al. arxiv preprint. https://arxiv.org/abs/2302.04843, 2023) where we provide detailed experimental results and discussion, including highly-realistic animation data, and show a clear superiority of the results compared to the state-of-the-art methods.

Battling Gibbs phenomenon: On finite element approximations of discontinuous solutions of PDEs

In this paper, we want to clarify the Gibbs phenomenon when continuous and discontinuous finite elements are used to approximate discontinuous or nearly discontinuous PDE solutions from the approximation point of view. For a simple step function, we explicitly compute its continuous and discontinuous piecewise constant or linear projections on discontinuity matched or non-matched meshes. For the simple discontinuity-aligned mesh case, piecewise discontinuous approximations are always good. For the general non-matched case, we explain that the piecewise discontinuous constant approximation combined with adaptive mesh refinements is a good choice to achieve accuracy without overshoots. For discontinuous piecewise linear approximations, non-trivial overshoots will be observed unless the mesh is matched with discontinuity. For continuous piecewise linear approximations, the computation is based on a “far-away assumption”, and non-trivial overshoots will always be observed under regular meshes. We calculate the explicit overshoot values for several typical cases. Numerical tests are conducted for a singularly-perturbed reaction-diffusion equation and linear hyperbolic equations to verify our findings in the paper. Also, we discuss the L 1 -minimization-based methods and do not recommend such methods due to their similar behavior to L 2 -based methods and more complicated implementations.

Performance Evaluation of Group Sparse Reconstruction and Total Variation Minimization for Target Imaging in Stratified Subsurface Media

Sparse reconstruction methods have been successfully applied for efficient radar imaging of targets embedded in stratified dielectric subsurface media. Recently, a total variation minimization (TVM) based approach was shown to provide superior image reconstruction performance over standard L1-norm minimization-based method, especially in case of non-point-like targets. Alternatively, group sparse reconstruction (GSR) schemes can also be employed to account for embedded target extent. In this paper, we provide qualitative and quantitative performance evaluations of TVM and GSR schemes for efficient and reliable target imaging in stratified subsurface media. Using numerical electromagnetic data of targets buried in the ground, we demonstrate that GSR and TVM provide comparable reconstruction performance qualitatively, with GSR exhibiting a slight superiority over TVM quantitatively, albeit at the expense of less flexibility in regularization parameters.

Dynamical regularized echo state network for time series prediction

Echo state networks (ESNs) have been widely used in the field of time series prediction. However, it is difficult to automatically determine the structure of ESN for a given task. To solve this problem, the dynamical regularized ESN (DRESN) is proposed. Different from other growing ESNs whose existing architectures are fixed when new reservoir nodes are added, the current component of DRESN may be replaced by the newly generated network with more compact structure and better prediction performance. Moreover, the values of output weights in DRESN are updated by the error minimization-based method, and the norms of output weights are controlled by the regularization technique to prevent the ill-posed problem. Furthermore, the convergence analysis of the DRESN is given theoretically and experimentally. Simulation results demonstrate that the proposed approach can have few reservoir nodes and better prediction accuracy than other existing ESN models.

Characterization of Electrical Conductivity of Anisotropic CFRP Materials by Means of Induction Thermography Technique

Numerical simulations by means of finite elements are used to investigate the capacities of the induction thermography technique for the characterization of electrical conductivities of unidirectional carbon fiber reinforced polymer (CFRP) materials. A coupled electromagnetic-thermal model is presented using hexahedral elements to deal with the thin region of fully anisotropic physical properties. Eddy-current problem is solved using the $ {{T}}$ - $\Omega $ formulation to deduce heat source density power. Transient thermal problem is solved with a fixed time step. An error minimization-based method is presented to identify the electrical resistivity of unidirectional CFRP from the induction thermography measurement.

Fast Weighted Total Variation Regularization Algorithm for Blur Identification and Image Restoration

Images obtained from unconstrained environments may be blurred by unknown kernels and affected due to noise. This paper presents a new total variation minimization-based method for blindly deblurring such images. Unlike the alternating optimization-based algorithms, the proposed algorithm adopts a joint estimation strategy to estimate the unknown blurring kernel and the unknown image in an iterative manner, where each iteration performs two separate image denoising subproblems that admit fast implementation. Experiments are performed on multiple synthetic, grayscale, and color images, and the results demonstrate that the proposed method is effective in blind deblurring.

A Truncated Nuclear Norm Regularization Method Based on Weighted Residual Error for Matrix Completion.

Low-rank matrix completion aims to recover a matrix from a small subset of its entries and has received much attention in the field of computer vision. Most existing methods formulate the task as a low-rank matrix approximation problem. A truncated nuclear norm has recently been proposed as a better approximation to the rank of matrix than a nuclear norm. The corresponding optimization method, truncated nuclear norm regularization (TNNR), converges better than the nuclear norm minimization-based methods. However, it is not robust to the number of subtracted singular values and requires a large number of iterations to converge. In this paper, a TNNR method based on weighted residual error (TNNR-WRE) for matrix completion and its extension model (ETNNR-WRE) are proposed. TNNR-WRE assigns different weights to the rows of the residual error matrix in an augmented Lagrange function to accelerate the convergence of the TNNR method. The ETNNR-WRE is much more robust to the number of subtracted singular values than the TNNR-WRE, TNNR alternating direction method of multipliers, and TNNR accelerated proximal gradient with Line search methods. Experimental results using both synthetic and real visual data sets show that the proposed TNNR-WRE and ETNNR-WRE methods perform better than TNNR and Iteratively Reweighted Nuclear Norm (IRNN) methods.

Propagating sparse labels through edge-aware filters

In this paper, we show how linear, but not necessarily shift-invariant, filters can be used to propagate sparse labels throughout an image. We propose a new propagation method based on the domain transform filter, a linear, shift-varying filter whose kernel width varies based on local edge information. We contrast this against the more well-known energy minimization approach and show that it can produce significantly better results when the input labels contain errors. Finally, we show how minimization-based methods are better suited for purely user-guided applications.

Inversion Problems for Determining Physical Parameters of Porous Materials: Overview and Comparison Between Different Methods

Summary In modeling the acoustical behavior of porous materials, the determination of the physical parameters (that are airflow resistivity, open porosity, tortuosity and viscous and thermal characteristic lengths) is a fundamental issue. As an alternative to measuring some of these quantities directly, it is possible to use inverse strategies to calculate them once some of the acoustical parameters are experimentally known. In this work both analytical and minimization-based methods will be investigated to determine the physical parameters of porous materials. Among the analytical approaches (that are derived from dynamic density and bulk modulus expressions governing viscous and thermal dissipation of sound waves in rigid-framed porous media), several formulae have been proposed in literature and some will also be considered in the proposed analysis. In this paper only the procedures that are able to provide a complete set of physical data from acoustical tests will be investigated. The results will be compared with theoretical and experimental data and details related to the accuracy and reliability of the inversely determined parameters will also be reported and discussed.

Robust imaging of localized scatterers using the singular value decomposition and ℓ1 minimization

We consider narrow band, active array imaging of localized scatterers in a homogeneous medium with and without additive noise. We consider both single and multiple illuminations and study ℓ1 minimization-based imaging methods. We show that for large arrays, with array diameter comparable to range, and when scatterers are sparse and well separated, ℓ1 minimization using a single illumination and without additive noise can recover the location and reflectivity of the scatterers exactly. For multiple illuminations, we introduce a hybrid method which combines the singular value decomposition and ℓ1 minimization. This method can be used when the essential singular vectors of the array response matrix are available. We show that with this hybrid method we can recover the location and reflectivity of the scatterers exactly when there is no noise in the data. Numerical simulations indicate that the hybrid method is, in addition, robust to noise in the data. We also compare the ℓ1 minimization-based methods with others including Kirchhoff migration, ℓ2 minimization and multiple signal classification.