Regularization Parameter Research Articles

Nanoscale morphology imaging for arbitrary surfaces by optical coherence tomography

The imaging of nanoscale morphology using optical methods on arbitrary surfaces poses challenges, particularly in the presence of large axial distances and irregular shapes. In this work, we introduce a novel nano-resolution imaging method along the longitudinal direction, utilizing optical coherence tomography (OCT) to measure arbitrary surface morphology comprehensively. Based on the sparsity of the primary profile, our approach allows the adjustment of parameters such as the asymmetric penalty function ϕ, the regularization parameters αi and a high-pass filter to accommodate the micro-structure of any arbitrary surface. Remarkably, our method achieves an exceptional spatial resolution of 3.04 nm. The technique has been validated by observing the surface morphology of spherical and aspherical lenses with nanometer resolution in the longitudinal direction. With the ability to detect impurities and scratches with a height of tens of nanometers, this method can be used to study the fine structure of complex surfaces. This makes it an ideal choice for experimental requirements demanding high-resolution imaging and a broad en-face perspective.

Short-Term Prediction of Rural Photovoltaic Power Generation Based on Improved Dung Beetle Optimization Algorithm

Addressing the challenges of randomness, volatility, and low prediction accuracy in rural low-carbon photovoltaic (PV) power generation, along with its unique characteristics, is crucial for the sustainable development of rural energy. This paper presents a forecasting model that combines variational mode decomposition (VMD) and an improved dung beetle optimization algorithm (IDBO) with the kernel extreme learning machine (KELM). Initially, a Gaussian mixture model (GMM) is used to categorize PV power data, separating analogous samples during different weather conditions. Afterwards, VMD is applied to stabilize the initial power sequence and extract numerous consistent subsequences. These subsequences are then employed to develop individual KELM prediction models, with their nuclear and regularization parameters optimized by IDBO. Finally, the predictions from the various subsequences are aggregated to produce the overall forecast. Empirical evidence via a case study indicates that the proposed VMD-IDBO-KELM model achieves commendable prediction accuracy across diverse weather conditions, surpassing existing models and affirming its efficacy and superiority. Compared with traditional VMD-DBO-KELM algorithms, the mean absolute percentage error of the VMD-IDBO-KELM model forecasting on sunny days, cloudy days and rainy days is reduced by 2.66%, 1.98% and 6.46%, respectively.

Mass‐lumping discretization and solvers for distributed elliptic optimal control problems

AbstractThe purpose of this article is to investigate the effects of the use of mass‐lumping in the finite element discretization with mesh size of the reduced first‐order optimality system arising from a standard tracking‐type, distributed elliptic optimal control problem with regularization, involving a regularization (cost) parameter on which the solution depends. We show that mass‐lumping will not affect the error between the desired state and the computed finite element state , but will lead to a Schur‐complement system that allows for a fast matrix‐by‐vector multiplication. We show that the use of the Schur‐complement preconditioned conjugate gradient method in a nested iteration setting leads to an asymptotically optimal solver with respect to the complexity. While the proposed approach is applicable independently of the regularity of the given target, our particular interest is in discontinuous desired states that do not belong to the state space. However, the corresponding control belongs to whereas the cost as . This motivates to use in order to balance the error and the maximal costs we are willing to accept. This can be embedded into a nested iteration process on a sequence of refined finite element meshes in order to control the error and the cost simultaneously.

Development and validation of colorimetric-assisted chemometrics methods based on the localized gold nanoparticles surface plasmon resonance for fast simultaneous estimation of anti-hepatitis C virus drugs in their combined dosage form: A comparative study with HPLC method

The present work describes a developed analytical method based on a colorimetric assay using gold nanoparticles (AuNPs) along with chemometric techniques for the simultaneous estimation of sofosbuvir (SOF) and ledipasvir (LED) in their synthetic mixtures and tablet dosage form. The applied chemometric approaches were continuous wavelet transform (CWT) and least squares support vector machine (LS-SVM). Characterization of AuNPs and AuNPs in combination with the drug was performed by UV–vis spectrophotometer, transmission electron microscopy (TEM), dynamic light scattering (DLS), and Fourier transform infrared (FTIR) spectroscopy. In the CWT method, the zero amplitudes were determined at 427 nm with Daubechies wavelet family for SOF (zero crossing point of LED) and 440 nm with Symlet wavelet family for LED (zero crossing point of SOF) over the concentration range of 7.5–90.0 μg/L and 40.0–100.0 μg/L with coefficients of determination (R2) of 0.9974 and 0.9907 for SOF and LED, respectively. The limit of detection (LOD) and limit of quantification (LOQ) of this method were found to be 7.92, 9.96 μg/L and 12.02, 30.2 μg/L for SOF and LED, respectively. In the LS-SVM model, the mean percentage recovery of SOF and LED in synthetic mixtures was 98.29 % and 99.25 % with root mean square error of 2.392 and 1.034, which were obtained by the optimization of regularization parameter (γ) and width of the function (σ) based on the cross-validation method. The proposed methods were also applied for the determination concentration of SOF and LED in the combined dosage form, recoveries were higher than 95 %, and relative standard deviation (RSD) values were lower than 0.4 %. The achieved results were statistically compared with those obtained from the high-performance liquid chromatography (HPLC) technique for the concurrent estimation of components through one-way analysis of variance (ANOVA), and no significant difference was found between the suggested approaches and the reference one. According to these results, simplicity, high speed, lack of time-consuming process, and cost savings are considerable benefits of colorimetry along with chemometrics methods compared to other ways.

Fluid-poroviscoelastic structure interaction problem with nonlinear geometric coupling

We investigate weak solutions to a fluid-structure interaction (FSI) problem between the flow of an incompressible, viscous fluid modeled by the Navier-Stokes equations, and a poroviscoelastic medium modeled by the Biot equations. These systems are coupled nonlinearly across an interface with mass and elastic energy, modeled by a reticular plate equation, which is transparent to fluid flow. We provide a constructive proof of the existence of a weak solution to a regularized problem. Next, a weak-classical consistency result is obtained, showing that the weak solution to the regularized problem converges, as the regularization parameter approaches zero, to a classical solution to the original problem, when such a classical solution exists. While the assumptions in the first step only require the Biot medium to be poroelastic, the second step requires additional regularity, namely, that the Biot medium is poroviscoelastic. This is the first weak solution existence result for an FSI problem with nonlinear coupling involving a Biot model for poro(visco)elastic media.

The Modified Ambiguity Function Approach with regularization for instantaneous precise GNSS positioning

Abstract The Modified Ambiguity Function Approach (MAFA) implicitly conducts the search procedure of carrier phase GNSS integer ambiguity resolution (IAR) in the coordinate domain using the integer least squares (ILS) principle, i.e. MAFA-ILS. One of the still open scientific problems is an accurate definition of the search region, especially in the context of instantaneous IAR. In doing so, the float solution results, which encompass float position (FP) and its variance-covariance (VC) matrix, must be improved as these are necessary for defining the search region. For this reason, the ambiguity parameters are separately regularized, and then the baseline parameters are conditioned on regularized float ambiguities. The conditional-regularized estimation is thus designed, obtaining the regularized FP (RFP) and its VC-matrix. This solution is promising because its accuracy is enhanced in the sense of mean squared error (MSE) thanks to the improved precision at the cost of regularized bias. The optimal regularization parameter (RP) values obtained for ambiguity parameters balance the contributions of improved precision and bias in the regularized float baseline solution’s MSE. Therefore, the regularized search region is defined accurately in the coordinate domain to contain such approximate coordinates that more frequently give the correct ILS solution. It also contains fewer MAFA-ILS candidates, improving the search procedure’s numerical efficiency. The regularized ILS estimator performs well with the presence of bias, increasing the probability of correct IAR in the coordinate domain.

Multi-Response Bridge Regularization Parameter Selection via Multivariate Generalized Information Criterion

This paper proposes a multivariate form of generalized information criterion (MGIC) for the multivariate response bridge regression (multi-bridge) model. Also, we prove the identifiability of the multi-bridge as a prerequisite for model selection. We introduce the general form of MGIC for regularization parameter selection in the multi-bridge model. We assess the performance of MGIC variants from three viewpoints: consistency of the obtained models, analysis of high-dimensional data, and comparison to other criteria. Based on the numerical study, we reach better performance for MGIC in comparison to other common criteria (cross-validation and GCV) using simulated and real datasets.

Identifying Community-Bridge Network Structures via Bayesian Learning With Mixed Sparsity Mode.

Identifying structures of complex networks based on time series of nodal data is of considerable interest and significance in many fields of science and engineering. This article presents a sparse Bayesian learning (SBL) method for identifying structures of community-bridge networks, where nodes are grouped to form communities connected via bridges. Using the structural information of such networks with unknown nodal dynamics and community formations, network structure identification is tackled similar to sparse signal reconstruction with mixed sparsity mode. The proposed method is theoretically proved to be convergent. Its superiority to mainstream baselines is demonstrated via extensive experiments without the need for manual adjustment of regularization parameters.

A cone-beam optical CT based on a convergent light source – Characterization and optimization

PurposeEmploying a Fresnel lens and a point-like light source to create a convergent light beam for the camera effectively minimizes stray light and enhances image quality in optical computed tomography (OCT), benefiting 3D dosimetry applications. This study outlines the development of an economical cone-beam optical computed scanner for 3D dosimetry. MethodsOptical performance was assessed by calculating modulation transfer function (MTF) with pattern charts. Stray light was evaluated by imaging a cylinder flask and a square grid with 5 mm diameter holes to determine the stray-to-primary ratio. Reconstruction quality was determined using SIRT-TV and compared with spectrophotometry attenuation coefficients, with the best regularization parameter (λ = 0.01) chosen based on contrast-to-noise ratio (CNR). Dosimetry performance was assessed by determining percentage dose depth (PDD) for a 6MV beam with a 5 × 5 cm2 field using FXO-f gel dosimeter, compared with ionization chamber data. ResultsMTF evaluation yielded ≥ 50 % agreement with pattern charts. Stray-to-primary ratio was less than 0.1 or 10 % of the total signal. Reconstruction showed low noise and artifacts, with optimal CNR at λ = 0.01. Attenuation coefficients from optical CT aligned with spectrometer measurements within 1.2 %. PDD calculated with FXO-f gel dosimeter closely matched ionization chamber data (<1.2 % difference), achieving a dose resolution of 0.1 Gy. ConclusionThe built and optimization the de optical-CT based on a convergent beam is read to perform the 3D quality assurance in clinical applications.

Estimating the first and second derivatives of discrete audio data

A new method for estimating the first and second derivatives of discrete audio signals intended to achieve higher computational precision in analyzing the performance and characteristics of digital audio systems is presented. The method could find numerous applications in modeling nonlinear audio circuit systems, e.g., for audio synthesis and creating audio effects, music recognition and classification, time-frequency analysis based on nonstationary audio signal decomposition, audio steganalysis and digital audio authentication or audio feature extraction methods. The proposed algorithm employs the ordinary 7 point-stencil central-difference formulas with improvements that minimize the round-off and truncation errors. This is achieved by treating the step size of numerical differentiation as a regularization parameter, which acts as a decision threshold in all calculations. This approach requires shifting discrete audio data by fractions of the initial sample rate, which was obtained by fractional delay FIR filters designed with modified 11-term cosine-sum windows for interpolation and shifting of audio signals. The maximum relative error in estimating first and second derivatives of discrete audio signals are respectively in order of 10-13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-13}$$\\end{document} and 10-10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-10}$$\\end{document} over the entire audio band, which is close to double-precision floating-point accuracy for the first and better than single-precision floating-point accuracy for the second derivative estimation. Numerical testing showed that this performance of the proposed method is not influenced by the type of signal being differentiated (either stationary or nonstationary), and provides better results than other known differentiation methods, in the audio band up to 21 kHz.

Impact force identification for composite structures using adaptive wavelet-regularised deconvolution

Impact force identification (IFI) through deconvolution methods from measured structural responses poses a challenge due to the ill-posed nature of the inversion problem. Regularisation techniques, such as Tikhonov, sparse, and wavelet regularisation, offer potential solutions to mitigate the ill-posedness. However, determining suitable regularisation parameters is time-consuming. This study presents an adaptive wavelet-regularised time-domain deconvolution method for efficient IFI, based on wavelet transform and multi-resolution analysis. By analysing impact sensor signals using wavelets, adaptive impact windows covering the entire impact duration are generated, reducing signal length for deconvolution. Multi-resolution analysis of sensor signals enables identification of wavelet bases for the multi-resolution representation of impact force history. Regularisation is achieved by filtering out insignificant wavelet bases based on their energy contributions. Validation is performed through experiments involving small-mass hammer and large-mass drop tower impacts, comparing against various deconvolution methods. Results demonstrate the superior computational efficiency and comparable accuracy of the proposed adaptive method in IFI across different time windows. Notably, accurate force deconvolution for large-mass impacts confirms the effectiveness of the deconvolution methods for IFI, particularly when the structure undergoes significant local deformation.

Deconvolution of high-resolution depth profiling data with sputtering induced roughness for reconstruction of nano-layer structure

In this paper, a deconvolution method is proposed to obtain the original nano-layer structure directly from measured high-resolution depth profiling data with sputtering induced roughness. This method combines the Mixing-Roughness-Information (MRI) depth resolution function and the Total Variation (TV)-Tikhonov regularization. The regularization parameter of α that influences strongly the error and stability of the deconvolution result is optimized based on the L-curve criterion by the simulated annealing algorithm. The simulation results show that this method can be used to effectively obtain the original nano-layer structure even if the depth profiling data contains noise and/or sputtering induced roughness. Subsequently, as an example, the original multilayer structure of 4 × Si(15 nm)/Al (15 nm) is obtained directly from measured AES depth profiling data and the obtained roughness values accordingly at the depths of the middle of the first Al sublayer and of the last Al sublayer agree well with the ones measured by AFM.

Convergent Plug-and-Play with Proximal Denoiser and Unconstrained Regularization Parameter

Convergent Plug-and-Play with Proximal Denoiser and Unconstrained Regularization Parameter

A nonconvex sparse recovery method for DOA estimation based on the trimmed lasso

Sparse direction-of-arrival (DOA) estimation methods can be formulated as a group-sparse optimization problem. Meanwhile, sparse recovery methods based on nonconvex penalty terms have been a hot topic in recent years due to their several appealing properties. Herein, this paper studies a new nonconvex regularized approach called the trimmed lasso for DOA estimation. We define the penalty term of the trimmed lasso in the multiple measurement vector model by ℓ2,1-norm. First, we use the smooth approximation function to change the nonconvex objective function to the convex weighted problem. Next, we derive sparse recovery guarantees based on the extended Restricted Isometry Property and regularization parameter for the trimmed lasso in the multiple measurement vector problem. Our proposed method can control the desired level of sparsity of estimators exactly and give a more precise solution to the DOA estimation problem. Numerical simulations show that our proposed method overperforms traditional approaches, which is more close to the Cramer-Rao bound.

Identification of unknown sources in time-space fractional parabolic equation

This study considers the issue for recognizing unknown source within a time-space fractional parabolic equation. This particular issue is characterized by severe ill-posedness, where the solution does not depend continuously on the data. To tackle this issue, the wavelet dual least squares method is extended to handle ill-posedness of the issue under priori rule. Additionally, a posterior wavelet regularization parameter selection rule is introduced to address the Cauchy problem. Furthermore, error estimates between the exact solution and its approximation are established using both a priori and a posteriori methodologies. Numerical examples are given to validate the effectiveness and stability of the proposed method.

Wave impedance inversion and interpretation of Ground Penetrating Radar (GPR) data for Amery Ice Shelf in East Antarctica

The polar ice sheet is vital for the global climate system, influencing the Antarctic ice sheet's mass balance, sea level rise, and Earth's surface energy. Accurate measurement of its thickness and internal structure is imperative for comprehending glacier evolution and climate change. Ground Penetrating Radar (GPR) is a high-resolution and non-invasive exploration instrument that is extensively used for glacier detection, but only limited geometric information can be identified in the GPR profile, making it difficult to capture the quantitative distribution of physical parameters. To image the fine dielectric parameters of GPR data acquired from the Amery Ice Shelf in East Antarctica in 2003, we propose a multi-trace GPR impedance inversion approach. This method utilizes the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm for GPR data, coupled with weighted L2-norm total-variation multiplicative regularization (MR) to quantitatively estimate the dielectric parameters in the interior of the ice sheet. This scheme adaptively adapts regularization parameters, enhances vertical resolution, and suppresses noise. Additionally, considering lateral correlation, we integrate directional differences to enhance lateral continuity. After validating with complex test data, we apply the method to Amery Ice Shelf GPR data, quantitatively imaging the ice sheet's geometric and dielectric parameters. The inversion results reveal ice thickness, internal features, and the interface between freshwater ice and refrozen sea ice. This allowed us to determine the ablation and refreezing zone boundary at the bottom of ice shelf, providing insights into melting/freezing mechanisms, ice shelf stability, and simulating ice shelf interior dynamics.

SAR target recognition through adaptive kernel sparse representation model based on local contrast perception

Sparse representation-based methods have shown promising prospects in synthetic aperture radar (SAR) target recognition due to their robustness under complex application conditions. However, these methods are still susceptible to the feature representation of SAR images. In this paper, we propose a new SAR target recognition method using an adaptive kernel sparse representation model based on local contrast perception (LCP). The LCP method combines a specially designed random projection matrix with two-dimensional filtering to capture extensive intensity contrasts between local regions in SAR images. A response map reconstruction technique shows that LCP can obtain discriminative properties between target and background regions and improve feature representation. The LCP features are then transformed into the kernel representation to improve linear separability by defining a reproducing kernel Hilbert space (RKHS) and using a nonlinear kernel function. The kernel representation is utilized to construct a new kernel sparse representation model for classification. Furthermore, neighborhood analysis (NA) is proposed to establish the relationship between the parameter and feature distribution, with an adaptive regularization parameter selection strategy to mitigate the parameter sensitivity. Experiments conducted on the moving and stationary target acquisition and recognition dataset demonstrate the superiority and robustness of the proposed method under different application conditions.

On a generalization of the Cahn-Hilliard type equation with logarithmic nonlinearities for formation of islands

Abstract In this paper, main objective is to demonstrate the existence of solutions for an equation resembling the Cahn-Hilliard model, featuring a proliferation term and a logarithmic nonlinear term. This equation has been conceptualized within the context of interactions in liquid-gas systems, particularly in the context of island formation. The primary challenge lies in the departure from the original Cahn-Hilliard equation, as we no longer maintain conservation of the spatial average mean of the order parameter. This departure introduces the complexity in establishing uniform estimates for the solutions of the approximated problems concerning the regularization parameter, as it may potentially result in finite-time blow-up.

Convex optimization via inertial algorithms with vanishing Tikhonov regularization: fast convergence to the minimum norm solution

In a Hilbertian framework, for the minimization of a general convex differentiable function f, we introduce new inertial dynamics and algorithms that generate trajectories and iterates that converge fastly towards the minimizer of f with minimum norm. Our study is based on the non-autonomous version of the Polyak heavy ball method, which, at time t, is associated with the strongly convex function obtained by adding to f a Tikhonov regularization term with vanishing coefficient ε(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon (t)$$\\end{document}. In this dynamic, the damping coefficient is proportional to the square root of the Tikhonov regularization parameter ε(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon (t)$$\\end{document}. By adjusting the speed of convergence of ε(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon (t)$$\\end{document} towards zero, we will obtain both rapid convergence towards the infimal value of f, and the strong convergence of the trajectories towards the element of minimum norm of the set of minimizers of f. In particular, we obtain an improved version of the dynamic of Su-Boyd-Candès for the accelerated gradient method of Nesterov. This study naturally leads to corresponding first-order algorithms obtained by temporal discretization. In the case of a proper lower semicontinuous and convex function f, we study the proximal algorithms in detail, and show that they benefit from similar properties.

Inference for possibly misspecified generalized linear models with nonpolynomial-dimensional nuisance parameters

Summary It is routine practice in statistical modelling to first select variables and then make inference for the selected model as in stepwise regression. Such inference is made upon the assumption that the selected model is true. However, without this assumption, one would not know the validity of the inference. Similar problems also exist in high-dimensional regression with regularization. To address these problems, we propose a dimension-reduced generalized likelihood ratio test for generalized linear models with nonpolynomial dimensionality, based on quasilikelihood estimation that allows for misspecification of the conditional variance. The test has nearly oracle performance when using the correct amount of shrinkage and has robust performance against the choice of regularization parameter across a large range. We further develop an adaptive data-driven dimension-reduced generalized likelihood ratio test and prove that, with probability going to one, it is an oracle generalized likelihood ratio test. However, in ultrahigh-dimensional models the penalized estimation may produce spuriously important variables that deteriorate the performance of the test. To tackle this problem, we introduce a cross-fitted dimension-reduced generalized likelihood ratio test, which is not only free of spurious effects, but robust against the choice of regularization parameter. We establish limiting distributions of the proposed tests. Their advantages are highlighted via theoretical and empirical comparisons to some competitive tests. An application to breast cancer data illustrates the use of our proposed methodology.