Interpolation Framework Research Articles

A data integration framework for spatial interpolation of temperature observations using climate model data.

Meteorological station measurements are an important source of information for understanding the weather and its association with risk, and are vital in quantifying climate change. However, such data tend to lack spatial coverage and are often plagued with flaws such as erroneous outliers and missing values. Alternative meteorological data exist in the form of climate model output that have better spatial coverage, at the expense of bias. We propose a probabilistic framework to integrate temperature measurements with climate model (reanalysis) data, in a way that allows for biases and erroneous outliers, while enabling prediction at any spatial resolution. The approach is Bayesian which facilitates uncertainty quantification and simulation based inference, as illustrated by application to two countries from the Middle East and North Africa region, an important climate change hotspot. We demonstrate the use of the model in: identifying outliers, imputing missing values, non-linear bias correction, downscaling and aggregation to any given spatial configuration.

A Self-Adaptive Antialiasing Framework for Seismic Data Interpolation

Seismic interpolation is a widely adopted method to improve the resolution of seismic images. During the interpolation of regularly downsampled seismic data, the aliasing problem highly deteriorates the quality of the interpolation results. Nowadays, deep learning has shown great potential in extracting features from data and achieved significant improvement compared with traditional interpolation methods. However, only a few of them have addressed the aliasing problem. In this paper, we propose a novel self-adaptive anti-aliasing framework for seismic data interpolation. We theoretically analyze the aliasing problem in the frequency domain and adopt the shear transform to turn the severely aliased data into less aliased data. Moreover, a closed-loop framework is proposed to automatically evaluate the interpolation results and select the optimal parameter of the shear transform. The experimental results demonstrate that the proposed method can significantly improve the interpolation quality and suppress the aliasing problem.

Dynamic Frame Interpolation in Wavelet Domain.

Video frame interpolation is an important low-level vision task, which can increase frame rate for more fluent visual experience. Existing methods have achieved great success by employing advanced motion models and synthesis networks. However, the spatial redundancy when synthesizing the target frame has not been fully explored, that can result in lots of inefficient computation. On the other hand, the computation compression degree in frame interpolation is highly dependent on both texture distribution and scene motion, which demands to understand the spatial-temporal information of each input frame pair for a better compression degree selection. In this work, we propose a novel two-stage frame interpolation framework termed WaveletVFI to address above problems. It first estimates intermediate optical flow with a lightweight motion perception network, and then a wavelet synthesis network uses flow aligned context features to predict multi-scale wavelet coefficients with sparse convolution for efficient target frame reconstruction, where the sparse valid masks that control computation in each scale are determined by a crucial threshold ratio. Instead of setting a fixed value like previous methods, we find that embedding a classifier in the motion perception network to learn a dynamic threshold for each sample can achieve more computation reduction with almost no loss of accuracy. On the common high resolution and animation frame interpolation benchmarks, proposed WaveletVFI can reduce computation up to 40% while maintaining similar accuracy, making it perform more efficiently against other state-of-the-arts.

Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives

This study extends the functional interpolation framework, introduced by the Theory of Functional Connections, initially introduced for functions, derivatives, integrals, components, and any linear combination of them, to constraints made of shear-type and/or mixed derivatives. The main motivation comes from differential equations, often appearing in fluid dynamics and structures/materials problems that are subject to shear-type and/or mixed boundary derivatives constraints. This is performed by replacing these boundary constraints with equivalent constraints, obtained using indefinite integrals. In addition, this study also shows how to validate the constraints’ consistency when the problem involves the unknown constants of integrations generated by indefinite integrations.

Fast convex set projection with deep prior for seismic interpolation

Reconstruction of missing traces from seismic data is traditionally handled by physical methods with good interpretability. Popular deep learning methods provide promising end-to-end solutions, however requiring a large amount of labeled data. Currently, there is a trend to fuse physical and deep learning methods to take advantage of both. In this paper, we propose to incorporate the convolutional neural network denoising model for image restoration (IRCNN) into the physical fast convex set projection (FPOCS) framework for seismic data interpolation. IRCNN is an off-the-shelf denoising model that has been pre-trained with abundant natural images. We fine-tune it with a few thousands of synthetic and field seismic patches. Consequently, the new algorithm, which will be called IRCNN-FPOCS, has three advantages: (1) supports high-performance seismic interpolation with deep priors; (2) is interpretable; and 3) alleviates the problem of insufficient training data for the seismic field. Experiments are conducted on regularly and irregularly subsampled synthetic and field data in comparison with the Monte Carlo data-driven tight framework (DDTF) and the convex set projection method with CNN prior (CNN-POCS). Results show that our method is superior to the counterparts in terms of (1) visual effects and quantitative evaluation indicators; and (2) generalization ability to seismic data with different sampling ratios.

Automatic stochastic 3D clay fraction model from tTEM survey and borehole data

In most urbanized and agricultural areas of central Europe, the shallow underground is constituted of Quaternary deposits which are often the most extensively used layers (water pumping, shallow geothermic, material excavation). All these deposits are often complexly intertwined, leading to high spatial variability and high complexity. Geophysical data can be a fast and reliable source of information about the underground. Still, the integration of these data can be time-consuming, it lacks realistic interpolation in a full 3D space, and the final uncertainty is often not represented. In this study, we propose a new methodology to combine boreholes and geophysical data with uncertainty in an automatic framework. A spatially varying translator function that predicts the clay fraction from resistivity is inverted using boreholes description as control points. It is combined with a 3D stochastic interpolation framework based on a Multiple Points Statistics algorithm and Gaussian Random Function. This novel workflow allows incorporating robustly the data and their uncertainty and requires less user intervention than the already existing workflows. The methodology is illustrated for ground-based towed transient electromagnetic data (tTEM) and borehole data from the upper Aare valley, Switzerland. In this location, a 3D realistic high spatial resolution model of clay fraction was obtained over the whole valley. The very dense data set allowed to demonstrate the quality of the predicted values and their corresponding uncertainties using cross-validation.

Bridging Gaps in the Climate Observation Network: A Physics‐Based Nonlinear Dynamical Interpolation of Lagrangian Ice Floe Measurements via Data‐Driven Stochastic Models

AbstractModeling and understanding sea ice dynamics in marginal ice zones rely on measurements of sea ice. Lagrangian observations of ice floes provide insight into the dynamics of sea ice, the ocean, and the atmosphere. However, optical satellite images are susceptible to atmospheric noise, leading to gaps in the retrieved time series of floe positions. This paper presents an efficient and statistically accurate nonlinear dynamical interpolation framework for recovering missing floe observations. It exploits a balanced physics‐based and data‐driven construction to address the challenges posed by the high‐dimensional and nonlinear nature of the coupled atmosphere‐ice‐ocean system, where effective reduced‐order stochastic models, nonlinear data assimilation, and simultaneous parameter estimation are systematically integrated. The new method succeeds in recovering the locations, curvatures, angular displacements, and the associated strong non‐Gaussian distributions of the missing floes in the Beaufort Sea. It also accurately estimates floe thickness and recovers the unobserved underlying ocean field with an appropriate uncertainty quantification, advancing our understanding of Arctic climate.

STDIN: Spatio-temporal distilled interpolation for electron microscope images

Recently, flow-based approaches have shown considerable success in interpolating video images. However, in contrast to video images, electron microscope (EM) images are further complex due to noise and severe deformation between consecutive sections. Consequently, conventional flow-based interpolation algorithms, which assume a single offset per position, are not able to robustly model the movement of such complicated data. To address the aforementioned problems, this study propose a novel EM image interpolation framework that accommodates a range of offsets per location and further distills the intermediate features. First, a spatio-temporal ensemble (STE) interpolation module for capturing the missing middle features is presented. The STE is subdivided into two modules: temporal interpolation and residual spatial-correlated block (RSCB). The former predicts the intermediate features in two directions with several offsets at each location. Moreover, the RSCB uses the correlation coefficients for aggregated sampling. Thus, even if intermediate features are severely deformed, the STE effectively improves their accuracy. Second, a stackable feedback distillation block (SFDB) is introduced, which enhances the quality of intermediate features by distilling them from the input, and interpolated images, using a feedback mechanism. Extensive experiments demonstrate that the proposed method presents a superior performance compared with previous studies, both quantitatively and qualitatively.

Non-smooth interpolation of graph signals

We consider the problem of signal interpolation on graphs, i.e. recovering one or multiple graph signal values from incomplete measurements. We propose a review of the graph signal interpolation methods, which enlightens the restrictive underlying hypothesis of signal smoothness over the graph. We formulate a new interpolation framework based on a locality criterion designed to handle non-smooth signals, and provide corresponding specific solutions. We validate the proposed methods on synthetic and real-world interpolation problems, and analyse the stability of our methods regarding the interpolation problem main parameters.

Estimation of Scottish Pluvial Flooding Expected Annual Damages Using Interpolation Techniques

Flood modelling and mapping, underpinned by hydraulic modelling, are typically used to define flood hazard and allow a quantification of risk and associated Expected Annual Damages (EAD). At a regional or national scale, such modelling is often a lengthy process, which does not allow changes in risk resulting from new science such as revised rainfall frequency estimates or climate projections to be readily quantified by policy makers. A framework of interpolation and extrapolation methods has been developed in the R language via practical application to the city of Perth in central Scotland. These methods allow existing flood mapping, design rainfall estimates and property receptor datasets combined with revised design rainfall estimates to be used to rapidly assess the consequences of change in risk and EAD. The results are evaluated against detailed hydraulic modelling and are shown to provide a good approximation of changes in flood depth and EAD for properties previously modelled as at risk of flooding, particularly residential properties, with lower confidence for non-residential properties. In the Scottish context, the methods are considered to be robust for regional and national scale application and would allow policy makers with a means to rapidly determine the consequence of changes in design rainfall estimates without the immediate requirement to undertake complex hydraulic modelling.

Spectrum-sine interpolation framework for DTI processing.

Diffusion tensor imaging (DTI) data interpolation is important for DTI processing, which could affect the precision and computational complexity in the process of denoising, filtering, regularization, and DTI registration and fiber tracking. In this paper, we propose a novel DTI interpolation framework named with spectrum-sine (SS) focusing on tensor orientation variation in DTI processing. Compared with the state-of-the-art DTI interpolation method using Euler angles or quaternion to represent the orientation of DTI tensors, this method does not need to convert eigenvectors into Euler angles or quaternions, but interpolates each tensor's unit eigenvector directly. The prominent merit of this tensor interpolation method lies in tensor orientation information preservation, which is different from the existing DTI tensor interpolation methods that interpolating tensor's orientation information in a scalar way. The experimental results from both synthetic and real human brain DTI data demonstrated the proposed SS interpolation scheme not only maintains the advantages of Log-Euclidean and Riemannian interpolation frameworks, such as preserving the tensor's symmetric positive definiteness and the monotonic determinant variation, but also preserve the tensor's anisotropy property which was proposed in the spectral quaternion (SQ) method.

Homography-guided stereo matching for wide-baseline image interpolation

Image interpolation has a wide range of applications such as frame rate-up conversion and free viewpoint TV. Despite significant progresses, it remains an open challenge especially for image pairs with large displacements. In this paper, we first propose a novel optimization algorithm for motion estimation, which combines the advantages of both global optimization and a local parametric transformation model. We perform optimization over dynamic label sets, which are modified after each iteration using the prior of piecewise consistency to avoid local minima. Then we apply it to an image interpolation framework including occlusion handling and intermediate image interpolation. We validate the performance of our algorithm experimentally, and show that our approach achieves state-of-the-art performance.

Spatio‐Temporal Analysis of Hypoxia in the Central Basin of Lake Erie of North America

AbstractWe develop a spatio‐temporal geostatistical interpolation framework to estimate hypoxia extent (dissolved oxygen [DO] concentrations below 2 mg/L) with data from a network of DO loggers. The framework uses empirical orthogonal functions and Bayesian kriging to identify the spatially varying temporal pattern and estimate the distribution of hypoxia, including estimation uncertainty. A prototype web application is also developed in R. The framework is applied to analyze spatio‐temporal dynamics of DO in the central basin of Lake Erie in North America using data sampled from a logger network placed on the lake bottom during the summers of 2014, 2015, and 2016. Cross‐validation results demonstrate that the framework is capable of capturing the dynamic nature of bottom hypoxia over offshore areas, but nearshore areas have poor interpolation performance due to the impacts of complex physical processes such as seiche events. The findings showed that in the central basin, hypoxia started to emerge in early August of 2014, while in 2015 and 2016 hypoxia began in July. The peak hypoxia extent occurred in late September 2014, mid‐August 2015, and early September 2016. The prediction error of the overall spatial extent of hypoxia was as large as 25% of the interpolation area based on current logger deployment. Based on the cross‐validation and interpolation error, we suggest placing more loggers in nearshore areas to reduce prediction error near the margins of the hypoxic zone.

Rainfall estimates from opportunistic sensors in Germany across spatio-temporal scales

Study region: The study region is Germany and two sub-regions in Germany, i.e. the state of Rhineland-Palatinate and the city of Reutlingen.Study focus: Opportunistic rainfall sensors, namely personal weather stations and commercial microwave links, together with rain gauge data from the German Weather Service, were used in different combinations to derive rainfall maps with a geostatistical interpolation framework for Germany. This kriging type framework considered the uncertainty of opportunistic sensors and the line structure of commercial microwave links. The resulting rainfall maps were compared to two gauge-adjusted radar products and evaluated to three reference gauge datasets in the respective study regions on both daily and hourly basis.New Hydrological Insights for the Region: The interpolated rainfall products from opportunistic sensors provided good agreement to the reference rain gauges. The dataset combinations including information from the opportunistic sensors performed best. The addition of rain gauges from the German Weather Service did not consistently lead to an improvement of the interpolated rainfall maps. On the country-wide, daily scale the interpolated rainfall maps performed well, but the gauge-adjusted radar products were closer to the reference. For the regional and local scale in Rhineland-Palatinate and Reutlingen with an hourly resolution, the interpolated rainfall maps outperformed the interpolated product from DWD rain gauges and showed a similar agreement to the reference as the radar products.

Structure-preserving interpolation for model reduction of parametric bilinear systems

In this paper, we present a projection-based interpolation framework for structure-preserving model order reduction of parametric bilinear dynamical systems. We introduce a general setting, covering a broad variety of different structures for parametric bilinear systems, and then provide conditions on projection spaces for the interpolation of structured subsystem transfer functions such that the system structure and parameter dependencies are preserved in the reduced-order model. Two benchmark examples with different parameter dependencies are used to demonstrate the theoretical analysis.

Dealiased seismic data interpolation using a deep-learning-based prediction-error filter

Deep-learning (DL) technology has emerged as a new approach for seismic data interpolation. DL-based methods can automatically learn the mapping between regularly subsampled and complete data from a large training data set. Subsequently, the trained network can be used to directly interpolate new data. Therefore, compared with traditional methods, DL-based methods reduce the manual workload and render the interpolation process efficient and automatic by avoiding the selection of hyperparameters. However, two limitations of DL-based approaches exist. First, the generalization performance of the neural network is inadequate when processing new data with a different structure compared to the training data. Second, the interpretation of the trained networks is very difficult. To overcome these limitations, we have combined the deep neural network and classic prediction-error filter (PEF) methods, proposing a novel seismic data dealiased interpolation framework called prediction-error filters network (PEFNet). The PEFNet designs convolutional neural networks to learn the relationship between the subsampled data and the PEFs. Thus, the filters estimated by the trained network are used for the recovery of missing traces. The learning of filters enables the network to better extract the local dip of seismic data and has a good generalization ability. In addition, PEFNet has the same interpretability as traditional PEF-based methods. The applicability and the effectiveness of our method are demonstrated here by synthetic and field data examples.

A Numerical Framework for Elastic Surface Matching, Comparison, and Interpolation

Surface comparison and matching is a challenging problem in computer vision. While reparametrization-invariant Sobolev metrics provide meaningful elastic distances and point correspondences via the geodesic boundary value problem, solving this problem numerically tends to be difficult. Square root normal fields (SRNF) considerably simplify the computation of certain elastic distances between parametrized surfaces. Yet they leave open the issue of finding optimal reparametrizations, which induce elastic distances between unparametrized surfaces. This issue has concentrated much effort in recent years and led to the development of several numerical frameworks. In this paper, we take an alternative approach which bypasses the direct estimation of reparametrizations: we relax the geodesic boundary constraint using an auxiliary parametrization-blind varifold fidelity metric. This reformulation has several notable benefits. By avoiding altogether the need for reparametrizations, it provides the flexibility to deal with simplicial meshes of arbitrary topologies and sampling patterns. Moreover, the problem lends itself to a coarse-to-fine multi-resolution implementation, which makes the algorithm scalable to large meshes. Furthermore, this approach extends readily to higher-order feature maps such as square root curvature fields and is also able to include surface textures in the matching problem. We demonstrate these advantages on several examples, synthetic and real.

Comparison of vector and matrix format tangential interpolation for FDNE

Vector format tangential interpolation (VFTI) framework for deriving controllable and observable descriptor state space model using Loewner matrix pencil from the transfer matrix data has been recently proposed for VLSI circuits. It uses data sampled directionally i.e. two columns or two rows of the transfer matrix, called tangential interpolation data. In VFTI the information contained in the frequency samples is not fully utilized and the accuracy gets affected with large number of samples. Matrix format tangential interpolation (MFTI) has been proposed as an enhancement to VFTI in the literature which uses the entire transfer matrix so that all the information contained in the samples is fully utilized. This paper investigates the applicability of MFTI for state space modeling of power system FDNEs and proposes a novel MATLAB® based implementation for Loewner matrix construction. Properties of MFTI such as convergence speed, accuracy, stability and passivity are compared with vector fitting (VF) and VFTI. Impact of number of samples is also studied.

Direct Video Frame Interpolation With Multiple Latent Encoders

We present a simple but effective video interpolation framework that can be applied to various types of videos including conventional videos and 360° videos. Our main idea is to predict the latent feature of an intermediate frame, through the latent feature encoders between encoder and decoder networks, without explicitly computing optical flow or depth maps. The latent feature encoders take latent features of input images and then predict the latent feature of a target image, i . e . an intermediate frame. Afterward, the decoder network reconstructs the target image from the latent feature. The proposed framework consists of fully convolutional networks, and it is therefore end-to-end trainable from scratch without requiring additional information except for consecutive frames. We experimentally verify the superiority of proposed method by comparing it to state-of-the-art methods with various types of datasets. Moreover, an ablation study is carried out to analyze the key components of the proposed method. Our proposed method performs interpolation in latent domain, it is advantageous to apply various video interpolation ( e . g . NIR and depth videos) without limiting the type of input data.

A Missing Type-Aware Adaptive Interpolation Framework for Sensor Data

Data missing problems often occur on the Internet-of-Things domains. This article proposes a missing type-aware interpolation framework (IMA) for data loss problems in city-wide environmental monitoring systems that contain many scattered stations. To interpolate data as accurately as possible, IMA considers three aspects of information, i.e., spatiotemporal, all attributes of one measurement, and all values and accordingly develop three methods to estimate the missing data. First, we develop an improved multiviewer method, which uses the spatiotemporal correlation of data from neighbor stations to estimate random missing values. Second, we propose a new multi-eXtreme Gradient Boosting (multi-XGBoost) method that uses the values of the co-occurring and correlated correct attributes to predict the value of the missing attribute. Third, we take advantage of matrix factorization to estimate the missing parts if the data of the interpolation matrix are not all missing. To avoid the influence of uncorrelated data, IMA calculates Pearson's correlation coefficient between data of each station and uses those data from its top k highest correlation neighbors to form an interpolation matrix. Furthermore, due to the complexity of missing cases, IMA uses confidence levels in each of the three data prediction methods. For example, if the multiviewer method fails, IMA weights all valid results with confidence levels. We conduct our experiments on two real-world datasets from air quality monitoring stations in Beijing. Both datasets contain numerous missing measurements. Experimental results show that IMA outperforms other counterpart methods in interpolating the missing measurements, in terms of accuracy and effectiveness. Compared with the most related method, IMA improves the interpolation accuracy from 0.818 to 0.849 in a small dataset and from 0.214 to 0.759 in a large one.