Interpolation-based Method Research Articles

Dimethyl sulfide (DMS) climatologies, fluxes, and trends – Part 1: Differences between seawater DMS estimations

Abstract. Dimethyl sulfide (DMS) is a naturally emitted trace gas that can affect the Earth's radiative budget by changing cloud albedo. Most atmospheric models that represent aerosol processes depend on regional or global distributions of seawater DMS concentrations and sea–air flux parameterizations to estimate its emissions. In this study, we analyse the differences between three estimations of seawater DMS, one of which is an observation-based interpolation method following Hulswar et al. (2022) (hereafter referred to as H22) and two of which are proxy-based parameterization methods following Galí et al. (2018) (hereafter referred to as G18) and Wang et al. (2020a) (hereafter referred to as W20). The interpolation-based method depends on the distribution of observations and the methods used to fill data between observations, while the parameterization-based methods rely on establishing a relationship between DMS and environmental parameters such as chlorophyll a, mixed-layer depth, nutrients, sea surface temperature, etc., which can then be used to predict DMS concentrations. On average, the interpolation-based methods show higher DMS values compared to the parameterization-based methods. Even though the interpolation method shows higher values than the parameterization-based methods, it fails to capture mesoscale variability. The regression-based parameterization method (G18) shows the lowest values compared to other estimations, especially in the Southern Ocean, which is the high-DMS region in austral summer. The parameterization-based methods suggest positive long-term trends in seawater DMS (3.82±0.79 % per decade for G18 and 2.13±0.32 % per decade for W20). Since large differences, often more than 100 %, are observed between the different estimations of seawater DMS, the derived sea–air fluxes and, hence, the impact of DMS on the radiative budget are sensitive to the estimate used.

Heavy metal in radiation therapy: A simple method to differentiate hip prosthesis materials.

In recent years, the number of hip replacement patients receiving radiation therapy has steadily increased. In parallel, strategies have been developed to reduce metal artifacts in computed tomography (CT) images and improve the accuracy of dose calculation algorithms. However, in certain situations, knowledge of the type of prosthesis material is required to accurately determine the dose distribution. This study aims to identify physical materials in hip prostheses to correctly assign them in the treatment planning system and improve dose calculation accuracy. We first verified the validity of the extended CT mass density calibration curve measured on titanium (Ti) and stainless steel (SS) metal inserts of two different diameters. Then using dedicated reference objects of various circular diameters, we developed a method based on interpolation functions to differentiate between Ti and SS material groups. Forty data sets from 18 patients were used to validate our method on two different reconstruction kernels: a standard Br44f and the electron DirectDensity (Sd40f) kernels from Siemens. Hounsfield units (HU) of Ti and SS inserts were found to vary widely depending on insert diameter, CT spectrum, and reconstruction kernels due to cupping artifacts. The largest HU difference (-79%) was obtained for SS at 70kV with Br44f when the diameter increased from 8 to 30mm. Therefore, under these conditions, the extended CT-density calibration curve is not recommended for heavy metal density determination. Using our interpolation-based method, we achieved excellent detection (100%) and material differentiation (100%) results for stems in both reconstruction kernels. At CT energies between 110 and 140kV, the detection and material differentiation rates were 93.3% and 92.9% for the heads and 93.3% and 92.9% for the acetabular cups, respectively, with the Br44f. Similarly, the use of Sd40f resulted in detection and differentiation rates of 94.7% and 100% for the heads and 100% and 95.0% for the acetabular cups, respectively. This method makes it possible to differentiate between hip prosthesis materials and correctly assign them to the Ti or SS group without prior knowledge of the prosthesis type, regardless of the reconstruction kernels. In combination with the Acuros XB (Varian) or Monte Carlo dose algorithms, excellent dosimetric accuracy can be achieved even in the vicinity of hip prostheses. By performing basic measurements, the method can be adapted to other CT units and reconstruction kernels, replacing the use of an extended CT-density calibration curve.

Interpolation-Based Contrastive Learning for Few-Label Semi-Supervised Learning.

Semi-supervised learning (SSL) has long been proved to be an effective technique to construct powerful models with limited labels. In the existing literature, consistency regularization-based methods, which force the perturbed samples to have similar predictions with the original ones have attracted much attention for their promising accuracy. However, we observe that the performance of such methods decreases drastically when the labels get extremely limited, e.g., 2 or 3 labels for each category. Our empirical study finds that the main problem lies with the drift of semantic information in the procedure of data augmentation. The problem can be alleviated when enough supervision is provided. However, when little guidance is available, the incorrect regularization would mislead the network and undermine the performance of the algorithm. To tackle the problem, we: 1) propose an interpolation-based method to construct more reliable positive sample pairs and 2) design a novel contrastive loss to guide the embedding of the learned network to change linearly between samples so as to improve the discriminative capability of the network by enlarging the margin decision boundaries. Since no destructive regularization is introduced, the performance of our proposed algorithm is largely improved. Specifically, the proposed algorithm outperforms the second best algorithm (Comatch) with 5.3% by achieving 88.73% classification accuracy when only two labels are available for each class on the CIFAR-10 dataset. Moreover, we further prove the generality of the proposed method by improving the performance of the existing state-of-the-art algorithms considerably with our proposed strategy. The corresponding code is available at https://github.com/xihongyang1999/ICL_SSL.

Vision-HD: road change detection and registration using images and high-definition maps

High-definition (HD) maps are becoming increasingly important for autonomous vehicles and advanced driver assistance systems (ADAS), as they provide detailed and accurate information about the road environment. Vision localization using HD maps can improve accuracy, but maps can become outdated. Image perception can be useful for HD map change detection. However, achieving robust and high-precision alignment between images and HD maps is challenging in varying environmental conditions. In addition, evaluating alignment in the absence of ground truth data is inconvenient. This article proposes a trajectory interpolation-based method for reconstructing lane markings from images to detect road changes when compared with the HD grid map. Images and HD maps are registered using a distance transform and cross-entropy-based optimization. The article also proposes a metric based on intersection over union for evaluating alignment accuracy. Experiments were conducted using a third-party-collected campus dataset and the Argoverse2 open-source dataset to demonstrate the effectiveness of the proposed methods in detecting road changes and achieving high-precision image and HD map fusion.

Compaction Quality Control and Assurance of Silt Subgrade Using Roller-Integrated Compaction Monitoring Technology

Abstract The compaction quality is critical to the stability and durability of highway subgrades. Currently, there is a clear lack of research on the specific application effects of roller-integrated compaction monitoring (RICM) technology and RICM measurement values for silty soil, which are difficult to compact and have unique material properties. In addition, practical applications have shown that existing assessment methods based on geostatistical methods have many shortcomings that need to be addressed urgently. In this study, RICM technology was combined with a real-time kinematic Beidou positioning system to monitor the compaction of subgrades filled with two types of silt. First, field experiments were conducted, and the correlations between the RICM measurements, compaction parameters, and in situ measurements were analyzed. The compaction control value (CCV) was then selected by comparing with E to achieve a more reliable monitoring and assessment. Subsequently, different types of quality regression models were established to find a model that considers the advantages of accuracy and convenience, which was then used to estimate the compaction quality. Subsequently, a CCV- and Green spline interpolation-based method was proposed to calculate both the CCV and compaction quality and draw color-coded maps at any location. A case study demonstrated that CCV are highly correlated with the compaction parameters and the compactness and can serve as a reliable index for monitoring compaction quality owing to its strong stability and low dispersion. Taking moisture content into account can make the regression model more statistically significant and improve the correlation. The proposed assessment method effectively solves the problems of the existing method. A rapid and continuous assessment covering 100 % of the work area can be achieved using the proposed method to provide timely identification of quality defect areas and feedback improvement, thus realizing effective quality control and quality assurance of highway subgrades.

A robust and precise centroid positioning method for the weak beacon spot in long-distance inter-satellite optical wireless communications.

The centroid estimation of the beacon spot is crucial to the pointing, acquisition, and tracking subsystem in inter-satellite optical wireless communication (IsOWC), especially for the received very weak beacon caused by a long link distance. In this work, we propose an accurate centroid positioning method to calculate the centroid of such a weak beacon with a low peak signal-to-noise ratio. The proposed method is based on the idea that uses the normalized amplitude of the gray gradient to enhance the weights near the center of the beacon spot. Both comparative numerical simulation and experimental verification are implemented, which demonstrate the effectiveness and feasibility of the proposed method. Compared to the gray centroid method, interpolation-based method, Hough transform method, and Gaussian fitting method, the proposed method has stronger robustness and higher accuracy, which could be helpful to applications in IsOWC as well as beacon-based pointing and tracking systems.

A robust interpolation-based method for forensic soil provenancing: A Bayesian likelihood ratio approach

Soil is a complex and spatially variable material that has a demonstrated potential as a useful evidence class in forensic casework and intelligence operations. Here, the capability to spatially constrain police search areas and prioritise resources by triaging areas as low and high interest is advantageous. Conducted between 2017 and 2021, a forensically relevant topsoil survey (0–5 cm depth; 1 sample per 1 km2) was carried out over Canberra, Australia, aiming to document the distribution of chemical elements in an urban/suburban environment, and of acting as a testbed for investigating various aspects of forensic soil provenancing. Geochemical data from X-Ray Fluorescence (XRF; for total major oxides) and Inductively Coupled Plasma-Mass Spectrometry (ICP-MS; for trace elements) following a total digestion (HF + HNO3) of the fused XRF beads were obtained from the survey’s 685 topsoil samples (plus 138 additional quality control samples and six “Blind” simulated evidentiary samples). Using those “Blind” samples, we document a likelihood ratio approach where for each grid cell the analytical similarity between the grid cell and evidentiary sample is attributed from a measure of overlap between the two Cauchy distributions, including appropriate uncertainties. Unlike existing methods that base inclusion/exclusion on an arbitrary threshold (e.g., ± three standard deviations), our approach is free from strict binary or Boolean thresholds, providing an unconstrained gradual transition dictated by the analytical similarity. Using this provenancing model, we present and evaluate a new method for upscaling from a fine (25 m x 25 m) interpolated grid to a more appropriate coarser (500 m x 500 m) grid. In addition, an objective method using Random Match Probabilities for ranking individual variables to be used for provenancing prior to receiving evidentiary material was demonstrated. Our results show this collective procedure generates more consistent and robust provenance maps when applied to two different interpolation algorithms (e.g., inverse distance weighting, and natural neighbour), with different grid placements (e.g., grid shifts to the north or east) and by different theoretical users (e.g., different computer systems, or forensic geoscientists).

Bloch mode synthesis for band-structure computation of unit cell with non-matching boundaries

Bloch mode synthesis is an efficient method to calculate the band property of periodic structures, which involves the repeated solution of many eigenvalue problems on each wave vector around the Brillouin zone. It is based on projecting internal degrees of freedom (DOFs) of the unit cell to the modal domain and keeping the boundary DOFs in the physical domain. While this transformation greatly reduces the model order of the unit cell, it leaves the question of how to impose the Floquet-Bloch boundary conditions when the boundary nodes are non-matching. In this paper, an interpolation-based method is proposed to address the non-conformity problem, which consists of building a smooth function by interpolating the variables on the master boundary and determining the variables on the slave boundary by sampling that smooth function. This procedure creates an interpolation matrix to connect the master and slave variables, which can be integrated into the original Bloch mode synthesis formulation to absolve the incompatibility caused by non-matching boundaries. The accuracy of the proposed method is verified using one non-conforming unit cell example in the end.

Data-driven surrogate modelling of residual stresses in Laser Powder-Bed Fusion

ABSTRACT In order to enable the industrialization of additive manufacturing, it is necessary to develop process simulation models that can rapidly predict part quality. Although multi-physics simulations have shown success at predicting residual stress, distortion, microstructure and mechanical properties of additively manufactured parts, they are generally too computationally expensive to be directly used in applications, such as optimization, controls, or digital twinning. In this study, a critical evaluation is made of how data-driven surrogate models can be used to model the residual stress of parts fabricated by Laser Powder-Bed Fusion. Residual stress data is generated by using an inherent-strain based process simulation for two families of part geometries. Three different models using varying levels of sophistication are compared: a multilayer perceptron (MLP), a convolutional neural network (CNN) based on the U-Net architecture, and an interpolation-based method based on mapping geometries onto a reference. All three methods were found to be sufficient for part design, providing mechanical predictions for a CPU time below 0.2 s, representing a runtime speed-up of at least 3900 × . Neural network-based models are significantly more expensive to train compared to using interpolation. However, the generality of models based on the U-Net architecture is attractive for applications in optimization.

Detection and Reconstruction of Poor-Quality Channels in High-Density EMG Array Measurements

High-density electromyography (HD-EMG) arrays allow for the study of muscle activity in both time and space by recording electrical potentials produced by muscle contractions. HD-EMG array measurements are susceptible to noise and artifacts and frequently contain some poor-quality channels. This paper proposes an interpolation-based method for the detection and reconstruction of poor-quality channels in HD-EMG arrays. The proposed detection method identified artificially contaminated channels of HD-EMG for signal-to-noise ratio (SNR) levels 0 dB and lower with ≥99.9% precision and ≥97.6% recall. The interpolation-based detection method had the best overall performance compared with two other rule-based methods that used the root mean square (RMS) and normalized mutual information (NMI) to detect poor-quality channels in HD-EMG data. Unlike other detection methods, the interpolation-based method evaluated channel quality in a localized context in the HD-EMG array. For a single poor-quality channel with an SNR of 0 dB, the F1 scores for the interpolation-based, RMS, and NMI methods were 99.1%, 39.7%, and 75.9%, respectively. The interpolation-based method was also the most effective detection method for identifying poor channels in samples of real HD-EMG data. F1 scores for the detection of poor-quality channels in real data for the interpolation-based, RMS, and NMI methods were 96.4%, 64.5%, and 50.0%, respectively. Following the detection of poor-quality channels, 2D spline interpolation was used to successfully reconstruct these channels. Reconstruction of known target channels had a percent residual difference (PRD) of 15.5 ± 12.1%. The proposed interpolation-based method is an effective approach for the detection and reconstruction of poor-quality channels in HD-EMG.

Improving group velocity based estimates of arterial stiffness

Arterial stiffness is a predictor of cardiovascular diseases, the leading causes of death worldwide. Ultrasound-based methods that measure arterial wave propagation have promise for evaluating local stiffness in vivo. However, geometric properties of arteries cause dispersion, invalidating typical assumptions underlying the relationship between shear modulus G and group velocity cg, which clinical implementations of ultrasound shear wave elastography do not consider. Here, we examine the dependence of these estimates on geometry and evaluate alternative approaches. Wave motion in the proximal wall of an artery after application of focused acoustic radiation force is simulated with a semi-analytical finite element (SAFE) model, and cg is estimated using a time-to-peak algorithm to determine G with several methods. First, the value of G a clinical scanner would report is calculated assuming a bulk medium. Second, a pulse wave velocity (PWV)-based G estimate is calculated by taking cg = PWV and applying the Moens–Korteweg equation. Third, we develop an interpolation-based method to provide a corrected G estimate using data generated by the SAFE model. Simulation results show severe geometry-dependent bias with the bulk method, which is partially ameliorated with the PWV method and substantially improved with the interpolation approach. Results are validated using arterial phantoms.

All-Pass Filter Design Using Unimodular Interpolation

Many signal processing applications involve designing an all-pass filter with a desired phase response. Earlier methods have largely focused on approximating the desired response using an optimisation based approach, or by using numerical computations of the group delay at specific frequencies with Blaschke interpolation. The former method does not offer any guarantee to match the estimated phase response at given points, whereas the latter one matches the phases at the input points, but is sensitive to the numerical precision of the specified group delays. In this work, we present a unimodular interpolation-based method to obtain all-pass filter coefficients that match the desired phase response at the given points without the need for group delays at the interpolating points. Through detailed simulations, we show that the proposed method is more suited for obtaining all-pass filters that match the target phases when compared to earlier approaches.

Fully analytic shading model with specular reflections for polygon-based hologram

For polygon-based holograms, the efficiency of the fully analytical algorithm is outstanding compared with that of the spectral interpolation-based method. However, the full analytical algorithm is not beneficial for the rendering of objects, owing to the uniform amplitude of each triangle. In this paper, we propose a shading rendering method based on a fully analytical spectrum. We used the Blinn-Phong reflection model to simulate a scene with realistic lighting and render a glossy, smooth object surface without changing the number of polygons sampled. The proposed method develops approximate exponential functions to replace cumbersome diffuse and specular reflections, allowing us to derive fully analytical spectra. The computational results for several 3D objects show that the proposed method is highly efficient and presents realistic illumination effects owing to the analytical equations.

Neural Network-Based Channel Estimation and Detection in Spatial Modulation VLC Systems

We consider a spatial modulation aided indoor visible light communication system with user mobility and random receiver orientation. Two artificial neural networks (ANNs) are proposed which are able to predict the channel state information (CSI) with high accuracy and resolution. These architectures use estimated CSI at pilot instances obtained using least square or minimum mean square error estimation and predict CSI at intermediate locations. Moreover in ANN 2, predicted user position information is used to improve the performance. Numerical results show that the proposed ANNs deliver a better bit error rate compared to a benchmark spline interpolation-based method. Further, ANN 2 is shown to perform robustly in a high mobility scenario.

Dynamic long-term expansion planning of electric vehicle parking lots considering lost opportunity cost and energy saving

In this paper, a practical approach is presented to long-term expansion planning of electric vehicle (EV) parking lots which aims to maximize the parking lot operator’s profit. The optimal number, location, capacity, and time for construction or expansion of EV parking lots have also been determined. Moreover, a method based on drivers’ travel patterns is proposed to estimate the number of EVs referring to each area, in which the unscented transformation method (UTM) is used to calculate the annual growth rate of EVs. An innovative and real-time method for optimal charge and discharge scheduling of EVs is also provided, which can calculate the parking lots’ demand at different times. The most important advantages of this method are its independence from iterative-based optimization algorithms and from modeling some input parameters such as the initial state of charge (SOC) and the arrival time of EVs into the parking lot as uncertain parameters. Also, a Lagrange interpolation-based method is proposed to minimize the energy consumption required for EVs to reach a parking lot. In addition, in order to prevent the reduction of parking lot operator’s profit in case of non-fulfillment of the obligations of the EV owners, an approach based on paying the lost opportunity cost (LOC) is presented. Real-world data has been used for numerical studies. The results show that based on travel patterns and estimating the number of EVs available in each municipal district and using the proposed real-time scheduling method, parking lot’s demand can be calculated as the main prerequisite for parking lots expansion planning. Also, the proposed method for parking selection compared to two other methods will save energy by 26.6% and 8.33%, respectively. Moreover, the proposed approach increases the total parking lot operator’s profit by 4.23%.

Intraoperative Data-Based Haptic Feedback for Arthroscopic Partial Meniscectomy Punch Simulation

The use of intraoperative tool-tissue interaction data for arthroscopic digital twins has the potential to enhance haptic feedback in surgical simulations. This study demonstrates the implementation of an interpolation-based method, and a Kalman filter-based method using intraoperative interaction data to provide nonlinear haptic feedback in a partial meniscectomy punch simulation. These methods were demonstrated using a novel inexpensive haptic system for simulating an arthroscopic partial meniscectomy punch. Tool-tissue interaction data were collected from a cadaveric meniscus and used for the simulations. The software, computer-aided design models, and collected data are provided open-source on GitHub. The face validity of the methods was evaluated in user studies, including six experienced orthopedic surgeons, and five non-professionals. The findings showed that experienced surgeons could distinguish between a nonlinear interpolation-based force signal, and a linear-elastic ideally-plastic finite element-based reference signal in a partial meniscectomy punch simulation. Surgeons preferred the interpolation method as a haptic rendering strategy in this study. The Kalman filter method was not as effective as interpolation in recreating nonlinear haptic feedback for the tested parameters, but demonstrated coupling of haptic force signals from intraoperative data and an idealized finite element method in a partial meniscectomy punch simulation.

Performance Comparison Study of Several Interpolation Methods on Streak Metal Artifacts Reduction of CT Images

In the course of generating the CT images, the streak metal artifacts emerge from the reconstructed images, often degraded the quality of the images and blur the fringe information around the metal implant. Although a number of attempts had been reported, among them, our proposed interpolation-based method is the simplest and most efficient approaches. In this paper, three interpolation approaches are compared with subjective and objective criterion based on both simulation and clinical cases. Our results have shown an improvement from the original images. As for the comparison with NRMSD and MAD. For the execution time, the L-MAR possesses the shortest time with S-MAR time being the slowest among the interpolation-based methods. For NRMSD and MAD, the digits from small to large are P-MAR, S-MAR, L-MAR and original. This shows that among interpolation-based methods the image corrected by P-MAR approach is the closest to the ideal image, followed by S-MAR correction, L-MAR correction, and the gap between the original image and the ideal image is the largest.

Hybrid Method of ACA and Interpolation-based Algorithms for Analysis of Eddy Current Nondestructive Evaluations

ABSTRACT In this article, the hybridization of adaptive cross approximation (ACA) algorithm and interpolation-based separation of the kernel function is proposed to accelerate solving the matrix equations resulted in the boundary element method (BEM) for 3D arbitrary-shaped eddy current nondestructive evaluation problems. The hybrid method combines the advantages of both the ACA algorithm and the interpolation-based methods, and resolves the shortcoming of pure ACA method, when modeling the planar eddy current nondestructive evaluation problems, that it cannot compress the null entries the BEM generated when the testing and basis patches are co-planar. In the proposed method, the submatrices associated with the null entries are compressed by the interpolation-based method, while the others are compressed by the ACA algorithm. Several benchmarks are shown to demonstrate both the robustness and efficiency of the proposed fast and general solver.

Visibility Interpolation in Solar Hard X-Ray Imaging: Application to RHESSI and STIX

Abstract Space telescopes for solar hard X-ray imaging provide observations made of sampled Fourier components of the incoming photon flux. The aim of this study is to design an image reconstruction method relying on enhanced visibility interpolation in the Fourier domain. The interpolation-based method is applied to synthetic visibilities generated by means of the simulation software implemented within the framework of the Spectrometer/Telescope for Imaging X-rays (STIX) mission on board Solar Orbiter. An application to experimental visibilities observed by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is also considered. In order to interpolate these visibility data, we have utilized an approach based on Variably Scaled Kernels (VSKs), which are able to realize feature augmentation by exploiting prior information on the flaring source and which are used here, for the first time, in the context of inverse problems. When compared to an interpolation-based reconstruction algorithm previously introduced for RHESSI, VSKs offer significantly better performance, particularly in the case of STIX imaging, which is characterized by a notably sparse sampling of the Fourier domain. In the case of RHESSI data, this novel approach is particularly reliable when the flaring sources are either characterized by narrow, ribbon-like shapes or high-resolution detectors are utilized for observations. The use of VSKs for interpolating hard X-ray visibilities allows remarkable image reconstruction accuracy when the information on the flaring source is encoded by a small set of scattered Fourier data and when the visibility surface is affected by significant oscillations in the frequency domain.

Numerical Approximation of One- and Two-Dimensional Coupled Nonlinear Schrödinger Equation by Implementing Barycentric Lagrange Interpolation Polynomial DQM

In this paper, a new numerical method named Barycentric Lagrange interpolation-based differential quadrature method is implemented to get numerical solution of 1D and 2D coupled nonlinear Schrödinger equations. In the present study, spatial discretization is done with the aid of Barycentric Lagrange interpolation basis function. After that, a reduced system of ordinary differential equations is solved using strong stability, preserving the Runge-Kutta 43 method. In order to check the accuracy of the proposed scheme, we have used the formula ofL∞error norm. The matrix stability analysis method is implemented to test the proposed method’s stability, which confirms that the proposed scheme is unconditionally stable. The present scheme produces better results, and it is easy to implement to obtain numerical solutions of a class of partial differential equations.