Optimal Regularization Parameter Research Articles

Iterative reconstruction methods and the resolution principle for fast-ion loss detector measurements

Fast-ion loss detectors (FILDs) are crucial for analyzing fast-ion dynamics in magnetically confined fusion plasmas. A core challenge is to derive an accurate ion velocity distribution, requiring treatment of thousands of remapped camera frames for a full discharge. The ill-posed nature of this task necessitates regularization with a well-chosen regularization parameter and computationally efficient methods. In this work, we introduce the ‘resolution principle,’ a novel criterion for selecting the optimal regularization parameter, providing a distinction between genuine features and artefacts smaller than the diagnostic resolution in the reconstruction, thereby preventing misinterpretations. This principle, coupled with three iterative reconstruction techniques—Kaczmarz’s method, coordinate descent, and Cimmino’s method—demonstrates enhanced reconstruction capabilities compared to conventional methods like Tikhonov regularization. Utilizing these techniques allows rapid processing of measurements from full discharges, removing the computational bottleneck and facilitating between-discharge reconstructions. By reconstructing 6000 camera frames from an ELMy H-mode discharge at ASDEX Upgrade, we capture the temporal evolution of gyroradii and pitch angles, unveiling a direct correlation between pitch-angle behavior and changes in the toroidal magnetic field for a specific subset of lost ions accelerated by edge-localized modes (ELMs) to energies approximately twice that of the injection energy.

Testing the suitability of v-Support Vector Machine for hyperspectral image classification

ABSTRACT This research presents the novel application of v-Support Vector Machine (v-SVM) to hyperspectral image classification. The essence of this work is to test the suitability of v-SVM for hyperspectral image classification. The v-SVM provides an enhancement to the regularisation parameter in the classical Support Vector Machine (SVM). The regularisation parameter controls the trade-off between obtaining a high training error and a low training error which is the ability of the model to generalise the unseen data (or test data). The value of the regularisation parameter in the classical SVM ranges from 0 to + ∞ ; this makes it usually challenging to determine the most appropriate optimal regularisation parameter value. The invention of the v-SVM has made it easier to find an appropriate optimal regularisation parameter value since the regularisation parameter is narrowed down from a wide range of 0 to + ∞ to a narrow range of 0 to 1 . In this study, two hyperspectral images of Indian Pines region in Northwest Indiana, USA and University of Pavia, Italy are used as test beds for the experiment. The result of the experiment shows that the v-SVM performed fairly better than the classical SVM; however, it fell short of the notable conventional classifiers.

A regularization strategy for discontinuity when modelling coupled water and heat flow in freezing unsaturated soil

Freezing tightly couples the water and heat flow. In most porous media, the interface between liquid and frozen water is not sharp and a slushy zone is present. There are two distinct approaches for mathematical modelling of freezing. It is the equilibrium approach which allows an instant freezing under given conditions and non-equilibrium approach where a specific timing in the freezing process is considered. In this contribution, we specifically target the equilibrium approach.The key mathematical model for the equilibrium approach is the Clausius–Clapeyron equation, which allows the derivation of a soil freezing curve relating temperature to pressure head. Implementing freezing soil accurately is not a straight-forward. Using the Clausius–Clapeyron equation creates a discontinuity in the freezing rate and latent heat at the freezing point. Little attention has been paid to the adequate description of the numerical treatment of this phenomenon and to the computational challenges that it poses. Numerical approximation of this discontinuous system is prone to spurious oscillations. In this contribution, we show the application of regularization of the discontinuous term. This treatment successfully stabilizes the computation and can remove oscillations. To avoid over-regularization, we present here a minimax strategy to determine optimal regularization parameters. We further compare an over-regularized setup with the non-equilibrium approach, where we show that a successful regularization is equivalent to incorporating a minimal timing to the freezing process. Finally – for validating our implementation and computational approach – experimental laboratory data of the volumetric water content and temperature profiles from previously published soil freezing experiments were represented here with the optimally regulized equilibrium approach.

Analysis of Logistic Regression Regularization in Wild Elephant Classification with VGG-16 Feature Extraction

The research article explores the intersection of image-based wildlife classification and logistic regression regularization, focusing on the classification of wild elephant species. It begins by highlighting the significance of ecological research in biodiversity monitoring and conservation and introduces Convolutional Neural Networks (CNNs) as potent tools for feature extraction from images. The VGG-16 model is particularly emphasized for its ability to capture hierarchical representations of visual features crucial for classification tasks. The integration of VGG-16 feature extraction with logistic regression regularization is proposed as a compelling approach, offering a balance between sophisticated feature representation and efficient classification algorithms. The literature review delves into image-based wildlife classification, emphasizing the role of CNNs, especially VGG-16, in extracting discriminative features. It discusses the fusion of VGG-16 features with logistic regression and the challenges in this field, such as dataset annotation and environmental variability. The method section outlines the dataset acquisition, feature extraction using the VGG-16 architecture, and model configuration using logistic regression with lasso and ridge regularization. The process of finding the optimal regularization parameter (lambda) and model evaluation through cross-validation is detailed. Results showcase the optimal lambda values for lasso and ridge regularization and compare the performance of logistic lasso and logistic ridge models. Misclassification analysis reveals factors influencing classification accuracy, including feature variability and contextual complexity. The discussion reflects on the implications of the findings, emphasizing the importance of lambda selection and addressing challenges in wildlife classification. It suggests avenues for further research, such as advanced modeling techniques and feature engineering approaches. In conclusion, the study contributes to advancing wildlife classification efforts by leveraging state-of-the-art techniques and sheds light on opportunities to enhance classification accuracy in wildlife conservation.

Single shot interferenceless coded aperture correlation holography via a learnable Wiener deconvolution network

One of the challenges in interferenceless coded aperture correlation holography (I-COACH) is high-quality single-shot reconstruction, as conventional cross-correlation reconstruction algorithm requires recording multiple holograms and complex reconstruction operations, resulting in serious background noise. Here, we present a deep learning based single-shot reconstruction by introducing a learnable Wiener deconvolution network in I-COACH. By feeding the point spread hologram (PSH) of I-COACH system and object hologram (OH) into Wiener deconvolution, a mapping relationship between Wiener deconvolution result and ground truth is generated. A Res-UNet is trained to learn optimal filter and noise regularization parameters, thereby achieving high quality reconstruction. Moreover, the training dataset used in our network are simulated using PSH that is obtained through only one experiment acquisition in advance, greatly simplifying experimental OH dataset acquisition. Compared to the conventional correlation reconstruction methods, the proposed Wiener deconvolution network can conveniently realize high-quality single-shot reconstruction in I-COACH, and the axial sensitivity in 3D reconstruction can be demonstrated by varying scattering degree of coded phase mask. Importantly, this Wiener deconvolution solution will provide an enlightening reference for dynamic imaging in I-COACH.

Conjugate gradient method with regularization in estimating mold surface heat flux during continuous casting

The reconstruction of the boundary heat flux between solidifying steel and water-cooled mold wall using measured temperature data is recognized as an inverse heat conduction problem (IHCP). A Tikhonov spatial regularization approach to enhance the smoothness of the Conjugate Gradient Method (CGMr) was proposed which incorporates three different orders of spatial regularization: zeroth, first, and second order. The optimal regularization parameter was selected using a modified L-curve method. The accuracy of the CGMr is investigated with Case 1: a triangular time-spatial variation heat flux, and Case 2: a step change in the form of rectangular variation heat flux. The effects of measurement noise, grid points and time-step size are investigated. The results show that the minimum relative error (eRMS) of the predicted Case 1 heat flux is 1.98%, 7.64%, and 8.02% for zeroth-, first-, and second-order spatial regularization, respectively. The corresponding values for the predicted Case 2 heat flux are 3.82%, 13.42%, and 14.91%. Subsequently, CGMr algorithm is applied to calculate the heat flux in a mold simulator experiment. By comparing the relationship between heat fluxes reconstructed by CGMr after different iteration numbers, it is observed that the recovered heat flux of 2.14 MW/m2 with zeroth regularization remains highly stable.

Magnetics only real-time equilibrium reconstruction on ASDEX Upgrade

Real-time reconstruction of the magnetic equilibrium provides fundamental control of plasma shape and position in a tokamak. Details of the implementation of the equilibrium reconstruction code developed for the ASDEX Upgrade tokamak (JANET++) are summarized. Cubic Hermite splines are introduced as current density basis functions for solving the Grad–Shafranov equation. The choice of the optimal Tikhonov regularization parameter is discussed. The code is validated by comparing the results of the equilibrium reconstruction with those of further equilibrium reconstructions available on ASDEX Upgrade (CLISTE and IDE). In a high time resolution study of a discharge with edge localized modes (ELM), the poloidal asymmetry of the fits and magnetic probe measurements suggest that the real-time equilibrium reconstruction captures the essential features of the current density redistribution in an ELMing edge plasma. An efficient algorithm to locate multiple X-points and identify the active one in advanced X-divertor and snowflake divertor configurations is presented.

An improved composite ship magnetic field model with ellipsoid and magnetic dipole arrays.

In order to simultaneously maintain the ship magnetic field modeling accuracy, reduce the number of coefficient matrix conditions and the model computational complexity, an improved composite model is designed by introducing the magnetic dipole array model with a single-axis magnetic moment on the basis of the hybrid ellipsoid and magnetic dipole array model. First, the improved composite model of the ship's magnetic field is established based on the magnetic dipole array model with 3-axis magnetic moment, the magnetic dipole array model with only x-axis magnetic moment, and the ellipsoid model. Secondly, the set of equations for calculating the magnetic moments of the composite model is established, and for the problem of solving the pathological set of equations, the least-squares estimation, stepwise regression method, Tikhonov, and truncated singular value decomposition regularization methods are introduced in terms of the magnetic field, and generalized cross-validation is used to solve the optimal regularization parameters. Finally, a ship model test is designed to compare and analyze the effectiveness of the composite and hybrid models in four aspects: the number of coefficient matrix conditions of the model equation set, the relative error of magnetic field fitting, the relative error of magnetic field extrapolation, and the computational time complexity. The modeling results based on the ship model test data show that the composite model can be used for modeling the magnetic field of ships, and compared with the hybrid model, it reduces the number of coefficient matrix conditions and improves the computational efficiency on the basis of retaining a higher modeling accuracy, and it can be effectively applied in related scientific research and engineering.

Using learned priors to regularize the Helmholtz equation least-squares method

The Helmholtz equation least-squares (HELS) method is a valuable tool for estimating equivalent sound sources of a radiating object. It solves an inverse problem by mapping measured pressures to a set of basis functions satisfying the Helmholtz equation in spherical coordinates. However, this problem is often ill-posed, necessitating additional regularization methods, in which often variations of Ridge or Lasso are used. These conventional methods do not explicitly consider the distribution underlying the source radiations (besides sparsity) and are often used in the context of obtaining only a point estimate, even in the presence of ambiguity in the data. In this work, we propose the use of empirical priors through a normalizing flow model to enhance the inversion results obtained with the HELS method. We first validate our approach using numerical data and subsequently demonstrate its superior performance in interpolating a measured violin directivity compared to Lasso and Ridge methods, even when optimal regularization parameters are selected.

Learning-Assisted Fast Determination of Regularization Parameter in Constrained Image Reconstruction.

To leverage machine learning (ML) for fast selection of optimal regularization parameter in constrained image reconstruction. Constrained image reconstruction is often formulated as a regularization problem and selecting a good regularization parameter value is an essential step. We solved this problem using an ML-based approach by leveraging the finding that for a specific constrained reconstruction problem defined for a fixed class of image functions, the optimal regularization parameter value is weakly subject-dependent and the dependence can be captured using few experimental data. The proposed method has four key steps: a) solution of a given constrained reconstruction problem for a few (say, 3) pre-selected regularization parameter values, b) extraction of multiple approximated quality metrics from the initial reconstructions, c) predicting the true quality metrics values from the approximated values using pre-trained neural networks, and d) determination of the optimal regularization parameter by fusing the predicted quality metrics. The effectiveness of the proposed method was demonstrated in two constrained reconstruction problems. Compared with L-curve-based method, the proposed method determined the regularization parameters much faster and produced substantially improved reconstructions. Our method also outperformed state-of-the-art learning-based methods when trained with limited experimental data. This paper demonstrates the feasibility and improved reconstruction quality by using machine learning to determine the regularization parameter in constrained reconstruction. The proposed method substantially reduces the computational burden of the traditional methods (e.g., L-curve) or relaxes the requirement of large training data by modern learning-based methods, thus enhancing the practical utility of constrained reconstruction.

Efficient learning methods for large-scale optimal inversion design

In this work, we investigate various approaches that use learning from training data to solve inverse problems, following a bi-level learning approach. We consider a general framework for optimal inversion design, where training data can be used to learn optimal regularization parameters, data fidelity terms, and regularizers, thereby resulting in superior variational regularization methods. In particular, we describe methods to learn optimal $ p $ and $ q $ norms for $ {\rm L}^p-{\rm L}^q $ regularization and methods to learn optimal parameters for regularization matrices defined by covariance kernels. We exploit efficient algorithms based on Krylov projection methods for solving the regularized problems, both at training and validation stages, making these methods well-suited for large-scale problems. Our experiments show that the learned regularization methods perform well even when there is some inexactness in the forward operator, resulting in a mixture of model and measurement error.

Impedance analysis of alkaline water electrolysis based on distribution of relaxation time

Electrochemical Impedance Spectroscopy (EIS) is an important tool for identifying electrochemical processes and evaluating electrolyzer performance. Fitting EIS data with equivalent circuits often requires prior knowledge and involves inherent uncertainties. This work performed the experimental measurements of visualized zero-gap water electrolyzer equipped with four different flow channels, and then explored an efficient impedance analysis procedure for Alkaline Water Electrolysis (AWE) coupling with the Distribution Relaxation Time (DRT) method. By determining the optimal regularization parameter λ, typical characteristic peaks were identified corresponding to ion transfer, charge transfer, and mass transfer impedance, respectively. The flow channel structure significantly impacted two-phase flow distribution, with the pin-type channel showing a more uniform flow. Based on the optimal pin-type flow channel structure, the influences of operating parameters (current density, flow rate, and temperature) on the electrolysis performance were experimentally measured, and the impact mechanism was disclosed using the DRT method. The results illustrate that the charge transfer impedance Rt is greatly associated with current density and ohmic resistance RO is highly dependent on flow rate and temperature. At high current densities, the bubble coverage plays an indispensable role in the mass transfer impedance process. This work offers a quantitative method to characterize the AWE performance, which can be employed to optimize the structure and operating parameters of electrolyzers.

Classifying dynamic motor imagery with the locals-balanced extreme learning machine

The dynamic motor imagery (dMI) provides additional benefits as compared to the traditional motor imagery (MI) in training and neurorehabilitation field. The objective of this work is to develop a brain-computer interface (BCI) for dMI electroencephalograph (EEG). We propose a novel method by combining synchronization likelihood (SL) based functional brain network (FBN) and modified extreme learning machine (ELM) to interpret EEG. The proposed method 1) uses L1-norm and adaptive threshold instead of L2-norm and empirical threshold in SL method; 2) improves the procedure of FBN calculations (namely, SL matrix binarization) by combining threshold and MST methods; 3) detects two defects in standard ELM in fusion, and proposes the locals-balanced ELM (LBELM); 4) employs the special version of leave-one-out cross validation (LOO) approach improved the computational complexity of optimal threshold for binarization, the most effective fusion of two complementary features, and the optimal regularization parameters for regularized LBELM. As compared with the empirical threshold, the recognition rate of the optimal threshold increases by 1.39–11.11 %. Similarly, as compared with the regularized ELM, the recognition rate of LBELM increases by 2.78–9.73 %.

Adaptive Tikhonov regularization and dynamic control points for accurate shape parameter control of plasmas

Precise control of plasma shape parameters, such as elongation and triangularity is duly needed to achieve high-performance tokamak plasmas, for which we propose adaptive search schemes of (1) optimum regularization parameter for the Tikhonov regularization, and (2) control points to specify the key shape parameters such as elongation and triangularity. Many control points that exceed the number of actuator coils become an ill-conditioned problem, which is successfully resolved by Tikhonov regularization with adaptively optimized free parameters. Furthermore, we develop dynamically changed control points by using the Cauchy Condition Surface scheme, where elongation and triangularity become direct control values. By virtue of both the adaptive Tikhonov regularization scheme and the dynamic control point, we achieved accurate shape control with elongation up to 1.93 and triangularity up to 0.65 in JT-60SA, where the allowable speed for the change of the elongation is 0.1 s−1. We also verified the resilience of our developed our logics to the noises. The sequence of the result will contribute to enhance equilibrium controllability in upcoming JT-60SA experiments and provide the robust shape parameter control scheme for ITER and DEMO.

A self-attention driven retinex-based deep image prior model for satellite image restoration

A self attention driven Deep Image Prior (DIP) framework has been proposed in this work for restoring satellite images corrupted by speckled interference and contrast deficiency. The retinex-based framework incorporated here-in leverages the benefits of DIP approach for image restoration, thus requiring only a single input image, eliminating the need for ground truth or training data. An attention framework is incorporated into the architecture of DIP networks to effectively capture fine textures, enhancing the restoration capability of the model. Two generative networks are employed to obtain the luminance and reflectance maps, with the model's loss functions specifically designed to tackle speckle interference and contrast distortions present in the input. These generated maps eventually reconstruct the enhanced version of the image. Satellite images from different sensors are used to demonstrate and compare the performance of the model. Various state-of-the-art models are evaluated and compared with the proposed strategy using different image quality metrics and statistical tests. The experimental results, incorporating both visual and statistical inferences, demonstrate the superiority and efficiency of the model. Additionally, an ablation analysis is performed to determine optimal regularization parameters, and the significance of integrating attention modules at different architecture layers is also demonstrated.

The Tikhonov-L-curve regularization method for determining the best geoid gradients from SWOT altimetry

The Surface Water and Ocean Topography (SWOT) mission generates dense altimetry data that, when used in geoid gradient component estimations through least-squares collocation (LSC), lead to an ill-conditioned problem. Such problems also arise in geodetic network designs. This study introduces the Tikhonov-L-curve regularization to effectively address this challenge. By pinpointing the maximum curvatures of the L-curve, we discern optimal regularization parameters, countering issues stemming from the dense data of SWOT and the resulting ill-conditioned covariance matrices. Our approach not only stabilizes LSC solutions but also achieves gradient accuracies at 1-microrad levels compared to theoretical values. Additionally, we experimented with a strategic removal process that selectively eliminates adjacent geoid gradients. This technique considerably improves geoid gradient component determinations, especially evident at a threshold distance of 0.755 km within an 8′× 8′ data selection window. While our findings are rooted in simulated SWOT data, they are pivotal for future research intending to employ real SWOT data, anticipated by late 2023. This work serves as a precursor for marine gravity field determinations, emphasizing the importance of stabilized LSC solutions to avoid misleading seafloor signatures due to data compactness.

Implementation Aspects in Regularized Structural Equation Models

This article reviews several implementation aspects in estimating regularized single-group and multiple-group structural equation models (SEM). It is demonstrated that approximate estimation approaches that rely on a differentiable approximation of non-differentiable penalty functions perform similarly to the coordinate descent optimization approach of regularized SEMs. Furthermore, using a fixed regularization parameter can sometimes be superior to an optimal regularization parameter selected by the Bayesian information criterion when it comes to the estimation of structural parameters. Moreover, the widespread penalty functions of regularized SEM implemented in several R packages were compared with the estimation based on a recently proposed penalty function in the Mplus software. Finally, we also investigate the performance of a clever replacement of the optimization function in regularized SEM with a smoothed differentiable approximation of the Bayesian information criterion proposed by O’Neill and Burke in 2023. The findings were derived through two simulation studies and are intended to guide the practical implementation of regularized SEM in future software pieces.

Fast robust enhanced trend filter: A promising tool for automatically extracting high precision friction coefficient under unknown noise

Friction coefficient is the core parameter of material friction performance test. However, it often suffers from complex unknown noise, which frequently follows non-Gaussian distribution, such as outliers during the test phase. Moreover, the amount of test data is often very large that lead to the heavy computational burden. Thus, how to efficiently and accurately extract the friction coefficient is becoming a challenging task. To address this challenge, this paper proposes a fast trend filtering method based on Robust Enhanced Trend Filtering (RobustETF) which combines mix of Gaussian (MoG) and non-convex sparsity-inducing functions to extend l1 trend filtering, called Fast RobustETF. First, the sliding window strategy is used to segment the original data, and the wear stage is distinguished via judging the data margin factor inside the window. Then the window data with the largest and smallest margins is selected as the characteristic data segment of the stable and severe wear stage, and we consider the trend kurtosis and variance into the selection of optimal regularization parameters for different wear stages. Then, RobustETF is used in each window for extracting high precision friction coefficient under unknown noise. Finally, the trend signals in all windows are integrated and reconstructed to complete the precise extraction of the friction coefficient. Finally, simulation signals and real friction coefficient signals are used to verify the performance of Fast RobustETF by the comparison with other filtering methods.

Three-dimensional P-wave model of the shallow crustal structure, a complementary method for detecting a trapped hydrocarbon: a case study in the DehDasht region, SW Iran

Abstract Local P-wave tomography is an efficient method to study geologically complex areas where the seismic exploration methods are not ideal for unraveling the shallow crustal heterogeneity due to the great thickness of evaporitic deposits. Despite the complex geological features in the salt-rich DehDasht region, SW Iran, we used >11 000 micro-earthquake events, which have been recorded by a temporary seismic network (deployed between 18 October 2016 and 1 July 2017), to derive the three-dimensional velocity structure based on the first arrival time. We selected a subset of events (1571 micro-earthquakes) by various strict criteria for our processing, and then the 1D velocity model was calculated by the computer program VELEST. Afterward, the 3D initial model of the inversion procedure with 1.5-km horizontal and 1-km deep intervals was parametrized using the calculated 1D model. Finally, the observed data (first arrival P-wave traveltimes and events locations) was inverted with an optimum regularization parameter and iteration using the computer program SIMULPS14. Our tomographic results indicate the DehDasht Basin as a relatively low-velocity zone filled out dominantly by the Gachsaran Formation and surrounded by the high-velocity Asmari-Pabdeh-Sarvak Formations. The basin has a bowl shape that is elongated in the NW–SE direction or an oval on a horizontal view. The depth of the basin varies between 3 and 5 km and contains many folding-faulting systems, which lead to locally low-velocity patches. Moreover, some evaporate deposits, which are overlying the Gachsaran Formation, emerge as a thin low-velocity layer (e.g. Aghajari, etc.).

Numerical and experimental study on acoustic tomographic reconstruction of flow field

This paper reports the acoustic vector tomography (AVT) method to reconstruct the airflow as a vector field. In order to increase the efficiency of reconstruction process, proposed radial basis functions approximate the flow velocity components. Tikhonov-Gaussian regularization combined with Generalized Singular Value Decomposition method and modified L-curve are introduced to solve the ill-posed problem and select the optimal regularization parameters. The feasibility and validity of the method are verified by numerical simulation and experiment. The numerical results confirmed the effectiveness of the proposed method with higher accuracy, better anti-noise capability and shorter consuming time compared with other reconstruction methods. Besides, a physical experiment is performed for further testing. We measured the incident flow and vortex field using the proposed acoustic method. The results show that the tendency and data of the acoustical reconstructed flow field are consistent with the strip display and anemometer results. The relative errors of most measurement points are under 15% and our proposed acoustic method is effective in practical velocity field measurement.