Traditional Interpolation Research Articles

Fast Determination of Satellite-to-Moon Visibility Using an Adaptive Interpolation Method Based on Vertex Protection.

Fast determination of satellite visibility with respect to a target area is important for satellite navigation and positioning. In this paper, we propose an adaptive interpolation algorithm based on vertex protection to solve the satellite visibility period problem more accurately and quickly, where “vertex” refers to the local extremum point. The algorithm can avoid the error in the visibility period calculation caused by skimming the vertices when fitting the multi-hump visibility function under certain fitting accuracy requirements with the traditional adaptive interpolation method. The algorithm does not need to construct a cubic polynomial in each subinterval to determine whether the satellite is visible or not; it only constructs a cubic polynomial to solve the problem if the visibility function of that subinterval is judged to have a solution from the existence theorem of zero points, which can improve the computational efficiency. For the lunar navigation problem, a solution to satellite–Moon visibility calculations based on a vertex-protected adaptive interpolation is given, and the experimental results show that the computation time of the algorithm can be reduced by approximately 98% compared with the brute force method and by approximately 30% compared with the traditional adaptive interpolation algorithm.

Comparing machine learning and interpolation methods for loop-level calculations

The need to approximate functions is ubiquitous in science, either due to empirical constraints or high computational cost of accessing the function. In high-energy physics, the precise computation of the scattering cross-section of a process requires the evaluation of computationally intensive integrals. A wide variety of methods in machine learning have been used to tackle this problem, but often the motivation of using one method over another is lacking. Comparing these methods is typically highly dependent on the problem at hand, so we specify to the case where we can evaluate the function a large number of times, after which quick and accurate evaluation can take place. We consider four interpolation and three machine learning techniques and compare their performance on three toy functions, the four-point scalar Passarino-Veltman D_0D0 function, and the two-loop self-energy master integral M. We find that in low dimensions (d = 3), traditional interpolation techniques like the Radial Basis Function perform very well, but in higher dimensions (d=5, 6, 9) we find that multi-layer perceptrons (a.k.a neural networks) do not suffer as much from the curse of dimensionality and provide the fastest and most accurate predictions.

FC-ZSM: Spatiotemporal Downscaling of Rain Radar Data Using a Feature Constrained Zooming Slow-Mo Network

This work studies the application of deep learning methods in the spatiotemporal downscaling of meteorological elements. Aiming at solving the problems of the single network structure, single input data feature type, and single fusion mode in the existing downscaling problem’s deep learning methods, a Feature Constrained Zooming Slow-Mo network is proposed. In this method, a feature fuser based on the deformable convolution is added to fully fuse dynamic and static data. Tested on the public rain radar dataset, we found that the benchmark network without feature fusion is better than the mainstream U-Net series networks and traditional interpolation methods in various performance indexes. After fully integrating various data features, the performance can be further improved.

Efficient Vector Interpolation Method Based on Lebedev Quadrature for MLFMA

In this letter, an efficient vector interpolation method based on Lebedev quadrature to accelerate the matrix-vector multiplications in far-field regions for the multilevel fast multipole algorithm (MLFMA) is presented. This approach avoids the singularity on sphere poles in the traditional interpolation method based on Gaussian quadrature and maintains the same accuracy without increasing computational costs. As a consequence, both memory consumption and processing time can be reduced considerably, providing a viable alternative to solve large-scale electromagnetic scattering problems using MLFMA.

Local wavefield refinement using Fourier interpolation and boundary extrapolation for finite-element method based on domain reduction method

The domain reduction method based on the finite-element method (FEM) is promising for multiscale seismic wave simulations for local complex structures and rough topography. However, a transition region is required to refine the wavefields from coarse to fine grids, which may lead to strong artifacts. Traditional wavefield interpolation methods can only handle a small upsampling ratio due to their low accuracy. Here, we propose a high accuracy upsampling method using Fourier interpolation and boundary extrapolation. It requires that the wavefield in the transition region is evenly sampled, which may slightly reduce the flexibility of FEMs. Fortunately, this constraint only exists in two layers of nodes, in which the coarse and fine grids are collocated. To further apply our interpolation method to the wavefield upsampling on the nonuniform grid, we adopt cubic interpolation within the local region of interest, which is adequate in accuracy for regularizing the wavefield on the fine nonuniform grid. For a topographic surface, we perform wavefield extrapolation on the ground surface to avoid abnormal amplitude variations below and beyond the surface, which can greatly reduce potential artifacts caused by the Fourier interpolation. Numerical experiments find that our method is superior to traditional interpolation methods in accuracy, especially for large upsampling ratios. Its relative error is less than 2% even for a 40-time upsampling; in contrast, the relative error of linear and cubic interpolation is up to 90% and 41% in the same situation, respectively. We further verify the feasibility of our method for 3D heterogeneous models with rough topography, multilayer heterogeneity, and random perturbations of background models. The proposed method yields a significant speeding of the multiscale seismic simulation using the FEM for 3D models with complex local structures and topographies while being highly accurate.

Reconstructing Occluded Elevation Information in Terrain Maps With Self-Supervised Learning

Accurate and complete terrain maps enhance the awareness of autonomous robots and enable safe and optimal path planning. Rocks and topography often create occlusions and lead to missing elevation information in the Digital Elevation Map (DEM). Currently, these occluded areas are either fully avoided during motion planning or the missing values in the elevation map are filled-in using traditional interpolation, diffusion or patch-matching techniques. These methods cannot leverage the high-level terrain characteristics and the geometric constraints of line of sight we humans use intuitively to predict occluded areas. We introduce a self-supervised learning approach capable of training on real-world data without a need for ground-truth information to reconstruct the occluded areas in the DEMs. We accomplish this by adding artificial occlusion to the incomplete elevation maps constructed on a real robot by performing ray casting. We first evaluate a supervised learning approach on synthetic data for which we have the full ground-truth available and subsequently move to several real-world datasets. These real-world datasets were recorded during exploration of both structured and unstructured terrain with a legged robot, and additionally in a planetary scenario on Lunar analogue terrain. We state a significant improvement compared to the baseline methods both on synthetic terrain and for the real-world datasets. Our neural network is able to run in real-time on both CPU and GPU with suitable sampling rates for autonomous ground robots. We motivate the applicability of reconstructing occlusion in elevation maps with preliminary motion planning experiments.

Voids Filling of DEM with Multiattention Generative Adversarial Network Model

The digital elevation model (DEM) acquired through photogrammetry or LiDAR usually exposes voids due to phenomena such as instrumentation artifact, ground occlusion, etc. For this reason, this paper proposes a multiattention generative adversarial network model to fill the voids. In this model, a multiscale feature fusion generation network is proposed to initially fill the voids, and then a multiattention filling network is proposed to recover the detailed features of the terrain surrounding the void area, and the channel-spatial cropping attention mechanism module is proposed as an enhancement of the network. Spectral normalization is added to each convolution layer in the discriminator network. Finally, the training of the model by a combined loss function, including reconstruction loss and adversarial loss, is optimized. Three groups of experiments with four different types of terrains, hillsides, valleys, ridges and hills, are conducted for validation of the proposed model. The experimental results show that (1) the structural similarity surrounding terrestrial voids in the three types of terrains (i.e., hillside, valley, and ridge) can reach 80–90%, which implies that the DEM accuracy can be improved by at least 10% relative to the traditional interpolation methods (i.e., Kriging, IDW, and Spline), and can reach 57.4%, while other deep learning models (i.e., CE, GL and CR) only reach 43.2%, 17.1% and 11.4% in the hilly areas, respectively. Therefore, it can be concluded that the structural similarity surrounding the terrestrial voids filled using the model proposed in this paper can reach 60–90% upon the types of terrain, such as hillside, valley, ridge, and hill.

A novel interpolation method to predict soil heavy metals based on a genetic algorithm and neural network model

To improve the prediction accuracy of soil heavy metals (HMs) by spatial interpolation, a novel interpolation method based on genetic algorithm and neural network model (GANN model), which integrates soil properties and environmental factors, was proposed to predict the soil HM content. Eleven soil HMs (Cu, Pb, Zn, Cd, Ni, Cr, Hg, As, Co, V and Mn) were predicted using the GANN model. The results showed that the model had a good prediction performance with correlation coefficients (R2) varying from 0.7901 to 0.9776. Compared with other traditional interpolation methods, including inverse distance weighting (IDW), ordinary kriging (OK), universal kriging (UK), and spline with barriers interpolation (SBI) methods, the GANN model had a relatively lower root mean square error value, ranging from 0.0497 to 77.43, suggesting that the GANN model might be a more accurate spatial interpolation method and the soil properties together with the environmental geographical factors played key roles in prediction of soil HMs.

Super-Resolution Reconstruction of Brain MR Images Using Pseudo-3D Convolutional Network

The medical image super-resolution (SR) reconstruction algorithm based on deep learning with standard 3D convolution has too many network parameters. This leads to high computational complexity and low network training efficiency. To address these problems, a lightweight densely-connected residual 3D-CNN (P3DSRNet) combining dense residual connection with pseudo-3D convolution is proposed. Firstly, the dense residual block is used to widen the channel of the convolution layer. Hence, more feature information is transmitted to the activation function, so that the low-layer image features are spread to the higher layers to improve medical image super-resolution. Then, the pseudo-3D separable convolution strategy is employed to train the network, where the standard 3D convolution kernel is separated into multiple convolution kernels. The network is trained stage by stage, so network training converges faster. It effectively solved the problem that the number of parameters increase sharply with the added network training difficulty due to the widened dimension of standard 3D convolution. The experimental results show that the medical images reconstructed by the P3DSRNet model have clearer texture details and better visual effects, compared with those by the traditional interpolation and LRTV super-resolution algorithms. The P3DSRNet model has fewer network parameters, compared with the SRCNN3D and ReCNN super-resolution algorithms. In addition, the SR image PSNRs increase by 1.88 dB, 0.30 dB, and the SSIMs increase by 0.009 6, 0.001 1, respectively, compared with SRCNN3D and ReCNN. The P3DSRNet not only reduces the number of parameters and computational complexity, but also improves the super-resolution performances of medical images.

An Efficient Modeling of Air Gap and Nonlinear Analysis of Magnetic Equivalent Circuit for Large Turbogenerators Under No-Load Condition

Fast and accurate modeling of large turbogenerators is of great importance for optimal design and commercial value. Therefore, a 2-D nonlinear magnetic equivalent circuit (MEC) model considering saturation and rotor motion is proposed in this article. When the node-based MEC adopts relaxation iteration for nonlinear calculation, it is not easy to converge by using traditional interpolation function and piecewise fitting of the core <i>B&#x2013;H</i> or <inline-formula> <tex-math notation="LaTeX">$u_{r} (B)$ </tex-math></inline-formula> curve. The main contribution of this article is to find that using continuous fitting function is of great significance for the convergence of nonlinear iteration. At the same time, a simple and effective MEC of air gap is also provided. The flux density of air gap and stator tooth obtained by the proposed method is in good agreement with results of the finite element. No-load characteristics were also verified by the finite element and experiment. The calculation time of a cycle takes about 700 s by the finite element, and however, MEC only takes about 2 s.

Comparison of DEM Super-Resolution Methods Based on Interpolation and Neural Networks.

High-resolution digital elevation models (DEMs) play a critical role in geospatial databases, which can be applied to many terrain-related studies such as facility siting, hydrological analysis, and urban design. However, due to the limitation of precision of equipment, there are big gaps to collect high-resolution DEM data. A practical idea is to recover high-resolution DEMs from easily obtained low-resolution DEMs, and this process is termed DEM super-resolution (SR). However, traditional DEM SR methods (e.g., bicubic interpolation) tend to over-smooth high-frequency regions on account of the operation of averaging local variations. With the recent development of machine learning, image SR methods have made great progress. Nevertheless, due to the complexity of terrain characters (e.g., peak and valley) and the huge difference between elevation field and image RGB (Red, Green, and Blue) value field, there are few works that apply image SR methods to the task of DEM SR. Therefore, this paper investigates the question of whether the state-of-the-art image SR methods are appropriate for DEM SR. More specifically, the traditional interpolation method and three excellent SR methods based on neural networks are chosen for comparison. Experimental results suggest that SRGAN (Super-Resolution with Generative Adversarial Network) presents the best performance on accuracy evaluation over a series of DEM SR experiments.

Using the Concept of Fuzzy Logic and Controller System in Interpolation and Functions Approximation

The main aim of this contribution is to present an alternative approach for interpolation and function approximation from a given data. Instead of the traditional interpolation methods we consider and propose a numerical procedure for interpolation using the concept of fuzzy logic and membership functions. The method can be used for interpolating data resulting from physical experiments, engineering, medicine, applied sciences etc. Fuzzification will be applied to the given data according to Mamdani technique and membership functions will be chosen to satisfy the interpolation mathematical condition. The defuzzification process will be implemented to get the crisp values of the interpolation. The procedure will be implemented on the mathematical code MATLAB and its Simulink fuzzy logic features. Finally the applicability and efficiency of the procedure is illustrated by numerical examples.

Enhancing digital rock image resolution with a GAN constrained by prior and perceptual information

In digital rock physics, pore distribution and microstructure of rocks affect the flow properties and elastic characteristic of rocks. It is difficult to accurately characterize these parameters in low-resolution images due to rock heterogeneity, and improving with instrument is costly. Traditional interpolation method to enhance the image resolution only enriches the low frequency information of the image without focusing on the boundary which is rich in high frequency information, and conventional deep-learning methods cannot perform a satisfying result in different-level instrument noise. To address these issues, a generative adversarial network of an image segmentation network as discriminator constrained by perspective information and prior information (SCPGAN) is proposed to improve images resolution by enhancing medium-high frequency information of images and improving network anti-noise capacity. The perceptual information is extracted by VGG19 to enrich boundary and texture information and the porosity is built by discriminator as prior information to guide generator to improve noise immunity. Traditional interpolation and CNN are used to verify that perceptual information can be augmented with medium-high frequency information, and GAN-based models are used to verify that prior information can improve network performance. The result shows the network with perceptual information can significantly improve images resolution and outperform the traditional interpolation on structural similarity index (SSIM), peak signal-to-noise ratio (PSNR), and multiple-point connectivity (MPC), while GAN-based model with prior information shows an excellent anti-noise capacity, especially high-level noise, and has similar physical properties to the high-resolution model in the permeability simulation.

Application of Indicator Kriging to hydraulic head data to test alternative conceptual models for spring source aquifers

Hydraulic head distributions can inform spring source-water characterisation by determining whether aquifers meet the thresholds required to sustain spring flow. Assessing hydraulic head data can be challenging in areas where data are sparsely distributed and subject to variable measurement uncertainty. Geostatistical methods can be used to estimate hydraulic head values at unmeasured locations with quantitative uncertainty estimates. While these methods have been applied extensively for hydraulic head estimation in management contexts, no studies have used these approaches for spring source-water conceptual model testing. In this study, an investigation into the hydraulic head distribution was conducted through the application of Ordinary Indicator Co-Kriging. Interpolated hydraulic head estimates were used to quantitatively assess the plausibility of source-aquifer conceptual models for the Doongmabulla Springs Complex (DSC), Queensland, Australia. The results offer insights into the likelihood of alternative source aquifers having adequate head to support flow to eight springs within the DSC. Probabilities of adequate head to support the springs ranged from 0.03 to 0.12 for the Permian Formations, compared to <0.01 to 0.49 for the Triassic Formations. Analyses indicated that the Triassic Formations are more likely to have adequate hydraulic head to support spring flow. However, significant uncertainty exists in the conceptual model assessment due to hydraulic head measurement scarcity, particularly in the vicinity of the springs. These findings have important implications given that the Permian Formations will be dewatered by the operation of the nearby Carmichael coal mine. The techniques employed here can inform conceptual model uncertainties arising from the interpretation of sparsely distributed hydraulic head datasets, a major benefit over traditional interpolation methods.

An Enhanced Double-Filter Deep Residual Neural Network for Generating Super Resolution DEMs

High-resolution DEMs are important spatial data, and are used in a wide range of analyses and applications. However, the high cost to obtain high-resolution DEM data over a large area through sensors with higher precision poses a challenge for many geographic analysis applications. Inspired by the convolution neural network (CNN) excellent performance in super-resolution (SR) image analysis, this paper investigates the use of deep residual neural networks and low-resolution DEMs to generate high-resolution DEMs. An enhanced double-filter deep residual neural network (EDEM-SR) method is proposed, which uses filters with different receptive field sizes to fuse and extract features and reconstruct a more realistic high-resolution DEM. The results were compared with those generated with the bicubic, bilinear, and EDSR methods. The numerical accuracy and terrain feature preserving effects of the EDEM-SR method can generate reconstructed DEMs that better match the original DEMs, show lower MAE and RMSE, and improve the accuracy of the terrain parameters. MAE is reduced by about 30 to 50% compared with traditional interpolation methods. The results show how the EDEM-SR method can generate high-resolution DEMs using low-resolution DEMs.

RSPCN: Super-Resolution of Digital Elevation Model Based on Recursive Sub-Pixel Convolutional Neural Networks

The digital elevation model (DEM) is known as one kind of the most significant fundamental geographical data models. The theory, method and application of DEM are hot research issues in geography, especially in geomorphology, hydrology, soil and other related fields. In this paper, we improve the efficient sub-pixel convolutional neural networks (ESPCN) and propose recursive sub-pixel convolutional neural networks (RSPCN) to generate higher-resolution DEMs (HRDEMs) from low-resolution DEMs (LRDEMs). Firstly, the structure of RSPCN is described in detail based on recursion theory. This paper explores the effects of different training datasets, with the self-adaptive learning rate Adam algorithm optimizing the model. Furthermore, the adding-“zero” boundary method is introduced into the RSPCN algorithm as a data preprocessing method, which improves the RSPCN method’s accuracy and convergence. Extensive experiments are conducted to train the method till optimality. Finally, comparisons are made with other traditional interpolation methods, such as bicubic, nearest-neighbor and bilinear methods. The results show that our method has obvious improvements in both accuracy and robustness and further illustrate the feasibility of deep learning methods in the DEM data processing area.

Data-driven super-resolution reconstruction of supersonic flow field by convolutional neural networks

The pursuit of high-resolution flow fields is meaningful for the development of hypersonic technology. Flow field super-resolution (SR) based on deep learning is a novel and effective method to provide HR flow fields in a scramjet isolator. Single-path and multiple-path network models based on convolutional neural networks (CNNs) have been developed to augment the spatial resolution of the experimental supersonic flow field. The single-path model uses a simple convolutional layer and fully connected layer serial architecture, and the multiple-path model increases the branch path by adding pooling layers to achieve a fusion structure architecture. Ground experiments of flow in a supersonic isolator at various working conditions are conducted to establish an experimental dataset. The trained single-path and multiple-path CNNs are compared with the traditional interpolation method on the flow field SR reconstruction accuracy. The results demonstrated that single-path CNNs have certain learning ability, but the SR accuracy is not satisfactory; multiple-path CNNs significantly improve the accuracy of flow field SR, and the multiple-path CNN with one branch path achieves the best SR performance.

De-aliased seismic data interpolation using conditional Wasserstein generative adversarial networks

When sampling at offset is too coarse during seismic acquisition, spatial aliasing will appear, affecting the accuracy of subsequent processing. The receiver spacing can be reduced by interpolating one or more traces between every two traces to remove the spatial aliasing. And the seismic data with spatial aliasing can be seen as regular missing data. Deep learning is an efficient method for seismic data interpolation. We propose to interpolate the regular missing seismic data to remove the spatial aliasing by using conditional generative adversarial networks (cGAN). Wasserstein distance, which can avoid gradient vanishing and mode collapse, is used in training cGAN (cWGAN) to improve the quality of the interpolated data. One velocity model is designed to simulate the training dataset. Test results on different seismic datasets show that the cWGAN with Wasserstein distance is an accurate way for de-aliased seismic data interpolation. Unlike the traditional interpolation methods, cWGAN can avoid the assumptions of low-rank, sparsity, or linearity of seismic data. Besides, once the neural network is trained, we do not need to test different parameters for the best interpolation result, which will improve efficiency.

An effective interpolation strategy for mitigating the day boundary discontinuities of precise GNSS orbit products

A precise Global Navigation Satellite System (GNSS) satellite orbit is an essential prerequisite for precise point positioning (PPP). Due to the daily orbit discontinuities (DODs) between adjacent daily orbit products provided by the International GNSS Service, the interpolation accuracy at the epochs near the day boundaries cannot be as high as expected and can significantly degrade the positioning accuracy. This is especially for the emerging Beidou and Galileo satellites with larger DODs. In this study, a new interpolation strategy was proposed to mitigate the DOD effect by estimating the zero- to second-order biases between the orbits of two adjacent days. The results show that the proposed interpolation strategy outperforms the traditional interpolation strategies. The 3D orbit interpolation error for the last 10 min on each day is reduced from almost a few centimeters or even meters to millimeters, an improvement of approximately 86–99% for all satellites. PPP validation also provides concrete evidence of this improvement, as the DOD-induced satellite phase residuals are reduced significantly. Thus, the new interpolation strategy mitigates the DOD effect and helps multi-GNSS users obtain the highest interpolation accuracy at the day boundaries, which can be comparable to that at the non-day boundaries.

Gaussian Radial Basis Function interpolation in vertical deformation analysis

In many deformation analyses, the partial derivatives at the interpolated scattered data points are required. In this paper, the Gaussian Radial Basis Functions (GRBF) is proposed for the interpolation and differentiation of the scattered data in the vertical deformation analysis. For the optimal selection of the shape parameter, which is crucial in the GRBF interpolation, two methods are used: the Power Gaussian Radial Basis Functions (PGRBF) and Leave One Out Cross Validation (LOOCV) (LGRBF). We compared the PGRBF and LGRBF to the traditional interpolation methods such as the Finite Element Method (FEM), polynomials, Moving Least Squares (MLS), and the usual GRBF in both the simulated and actual Interferometric Synthetic Aperture Radar (InSAR) data. The estimated results showed that the surface interpolation accuracy was greatly improved by LGRBF and PGRBF methods in comparison withFEM, polynomial, and MLS methods. Finally, LGRBF and PGRBF interpolation methods are used to compute invariant vertical deformation parameters, i.e., changes in Gaussian and mean Curvatures in the Groningen area in the North of Netherlands.