Existing Interpolation Methods Research Articles

A Seabed Terrain Feature Extraction Transformer for the Super-Resolution of the Digital Bathymetric Model

The acquisition of high-resolution (HR) digital bathymetric models (DBMs) is crucial for oceanic research activities. However, obtaining HR DBM data is challenging, which has led to the use of super-resolution (SR) methods to improve the DBM’s resolution, as, unfortunately, existing interpolation methods for DBMs suffer from low precision, which limits their practicality. To address this issue, we propose a seabed terrain feature extraction transform model that combines the seabed terrain feature extraction module with the efficient transform module, focusing on the terrain characteristics of DBMs. By taking advantage of these two modules, we improved the efficient extraction of seabed terrain features both locally and globally, and as a result, we obtained a highly accurate SR reconstruction of DBM data within the study area, including the Mariana Trench in the Pacific Ocean and the adjacent sea. A comparative analysis with bicubic interpolation, SRCNN, SRGAN, and SRResNet shows that the proposed method decreases the root mean square error (RMSE) by 16%, 10%, 13%, and 12%, respectively. These experimental results confirm the high accuracy of the proposed method in terms of reconstructing HR DBMs.

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Function (RBF) interpolation with Singular Value Decomposition (SVD) to preserve the positivity of the determinant of the deformation gradient tensor. The method involves decomposing the evaluations of the tensor at the quadrature nodes of the source mesh into rotation matrices and diagonal matrices of singular values; computing the RBF interpolation of the quaternion representation of rotation matrices and the singular value logarithms; reassembling the deformation gradient tensors at quadrature nodes of the destination mesh, to be used in the assembly of the electrophysiology model equations. The proposed method overcomes limitations of existing interpolation methods, including nested intergrid interpolation and RBF interpolation of the displacement field, that may lead to the loss of physical meaningfulness of the mathematical formulation and then to solver failures at the algebraic level, due to negative determinant values. Furthermore, the proposed method enables the transfer of solution variables between finite element spaces of different degrees and shapes and without stringent conformity requirements between different meshes, thus enhancing the flexibility and accuracy of electromechanical simulations. We show numerical results confirming that the proposed method enables the transfer of the deformation gradient tensor, allowing to successfully run simulations in cases where existing methods fail. This work provides an efficient and robust method for the intergrid transfer of the deformation gradient tensor, thus enabling independent tailoring of mesh discretizations to the particular characteristics of the individual physical components concurring to the of the multiphysics model.

Optimization technique for increasing resolution in computed tomography imaging

Starting from the importance of conforming to biological reality in medicine, in this paper we propose an optimization technique for increasing resolution of computed tomography (CT) images acquired using various existing scanners. Considering a three-dimensional Hounsfield Units (HU) array, together with the corresponding spatial metadata of interest (pixel sizes and slice thickness), the procedure is based on halving each voxel along the directions of the device's Cartesian frame of reference and find those values which are both satisfying the X-Rays attenuation coefficient average requirement and minimizing the HU distance to classical interpolation points. The discussed method was tested by implementing a C# .Net 6, cross-platform library containing two algorithm flavors that could be independently applied: “Z” for doubling the number of slices, and “XY” for doubling the resolution of individual slices. This design allows also chaining (e.g. one could apply the “Z,XY,Z” sequence in order to reduce four times slice thickness). In the context of existing unavoidable limitations, the first results are suggesting the “CT compatible” interpolation technique could provide a reasonable approximation of reality. However, the main advantage comes from satisfying mass conservation, which is of high importance in medical diagnosis and treatment.•The Hounsfield Units scale is defined as a linear transformation of the X-Rays attenuation coefficients. Thus, splitting a computed tomography voxel into two congruent volumes must satisfy the HU average requirement (the initial value must equal the average of the two output HU values).•Existing interpolation methods (linear, spline, etc.) are not compatible with the computed tomography HU average requirement. This could also result in mass estimate anomalies with significant impact in medical diagnosis.•The proposed “CT compatible” interpolation method is based on finding those values which are both satisfying the X-Rays attenuation coefficient average requirement and minimizing the Hounsfield Units distance to classical interpolation points.

A Multi-Attention Tensor Completion Network for Spatiotemporal Traffic Data Imputation

The widespread deployment of road sensors in the Internet of Things (IoT) allows for fine-grained data integration, which is a fundamental demand for data-driven applications. Sensing data with inevitable missing and substantial anomalies are unavoidable, due to unstable network communication, faulty sensors, etc. Recent tensor completion studies have demonstrated the superiority of deep learning in imputation tasks by precisely capturing the intricate spatiotemporal dependencies/correlations. However, ignoring the significance of initial interpolation in these methods results in unstable performance, especially for complicated missing scenarios across large-scale data. Additionally, the existing interpolation methods utilize recursive signal propagation along spatiotemporal dimensions, which produce noise accumulation where the dependencies are uncorrelated. In this study, we design a multiattention tensor completion network (MATCN) for modeling multidimensional representation in the presence of missing entries. MATCN sparsely sampled historical fragments and utilized a gated diffusion convolution layer to generate the initial schemes, which mitigate the exposure bias existing in previous traffic imputation models. In addition, we develop a spatial signal propagation module and a temporal self-attention module as the basic stack block of deep networks, which executes representation aggregation and dynamic dependencies extraction at the spatiotemporal level. This architecture empowers MATCN with progressive completion capacities for complex data missing scenarios. Numerical experiments on four real-world traffic data sets with various missing scenarios demonstrate the superiority of MATCN over multiple state-of-the-art imputation baselines.

Pixelwise Dynamic Convolution Neural Network for LiDAR Depth Data Interpolation

A light detecting and ranging (LiDAR) system is an important means that takes an omni-directional view to collect precise surrounding 3D information in high sampling frequency. However, due to the architecture of a LiDAR sensor, LiDAR data typically contains much less information in the vertical direction compared to the horizontal direction. In addition, LiDAR data are often defected during measurement. There have been previous researches about LiDAR data interpolation using a high-resolution reference image. However, they suffer from the calibration error due to vibration or shock during operation and do not consider defected data. Here, we propose a reference-free interpolation method with considering the defected LiDAR data using a two-step network architecture. Our proposed method is designed first to exploit the rich information in the horizontal direction of the LiDAR data to restore the defected data and then increase the vertical resolution of LiDAR data. Since the proposed interpolation method is a reference-free approach, it if free from the calibration issue. We confirm that our proposed method shows better performance than existing interpolation methods and is effective as a pre-processing function in other applications. For example, our proposed method can improve the performance of the human segmentation. We also propose a pixelwise dynamic convolution layer as a component of the proposed interpolation method. The proposed dynamic convolution layer adaptively processes each pixel with variable kernels, while existing dynamic layers only use fixed kernels. Experimental results show that the proposed dynamic layer is more effective than existing dynamic layers for LiDAR data interpolation.

Centered Multi-Task Generative Adversarial Network for Small Object Detection.

Despite the breakthroughs in accuracy and efficiency of object detection using deep neural networks, the performance of small object detection is far from satisfactory. Gaze estimation has developed significantly due to the development of visual sensors. Combining object detection with gaze estimation can significantly improve the performance of small object detection. This paper presents a centered multi-task generative adversarial network (CMTGAN), which combines small object detection and gaze estimation. To achieve this, we propose a generative adversarial network (GAN) capable of image super-resolution and two-stage small object detection. We exploit a generator in CMTGAN for image super-resolution and a discriminator for object detection. We introduce an artificial texture loss into the generator to retain the original feature of small objects. We also use a centered mask in the generator to make the network focus on the central part of images where small objects are more likely to appear in our method. We propose a discriminator with detection loss for two-stage small object detection, which can be adapted to other GANs for object detection. Compared with existing interpolation methods, the super-resolution images generated by CMTGAN are more explicit and contain more information. Experiments show that our method exhibits a better detection performance than mainstream methods.

A Modified Spatiotemporal Mixed-Effects Model for Interpolating Missing Values in Spatiotemporal Observation Data Series

Missing values in data series is a common problem in many research and applications. Most of existing interpolation methods are based on spatial or temporal interpolation, without considering the spatiotemporal correlation of observation data, resulting in poor interpolation effect. In this paper, a Modified Spatiotemporal Mixed-Effects (MSTME) model for interpolation of spatiotemporal data series is proposed. Experiments with simulated data and real SCIGN data are performed to assess the validity of the proposed model in comparison with Kriged Kalman Filter (KKF) model and Spatiotemporal Mixed-Effects (STME) model. The average improvements of simulated data and SCIGN data for observed stations are around 46% and 19% over the KKF model and 62% and 21% over the STME model, and those for unobserved stations are around 23% and 34% over the KKF model and 41% and 16% over the STME model, respectively, indicating that the proposed MSTME model can achieve better accuracy for interpolating missing values.

A GRID-Based Spatial Interpolation Method as a Tool Supporting Real Estate Market Analyses

The spatial distribution of prices is closely linked with the urban real estate market. Property prices are one of the key indicators of economic activity because they influence economic decisions. Decision-makers and consumers often need information about the spatial distribution of prices, but spatial-temporal analyses of the real estate market are based on the prices quoted in different locations across years (epochs). Due to this idiosyncrasy, the resulting datasets are dispersed (different across years) and difficult to compare. For this reason, the existing interpolation methods are not always effective in analyses of the real estate market. A different approach to interpolating real estate prices that supports the generation of continuous interpolated surfaces while maintaining the values of measurement points is thus needed. This paper proposes a method for replacing dispersed spatial data with a regular GRID structure. The GRID structure covers the measured object with a regular network of nodes, which supports uniform interpolation at every point of the analyzed space and a comparison of interpolation models in successive epochs (years). The proposed method was tested on a selected object. The results indicate that the GRID structure can be used in analyses of highly complex real estate markets where input data are incomplete, irregular and dispersed.

A Novel Interpolation-SVT Approach for Recovering Missing Low-Rank Air Quality Data

With increasing public demands for timely and accurate air pollution reporting, more air quality monitoring stations have been deployed by the governments in urban metropolises to increase the coverage of urban air pollution monitoring. However, due to systematic or accidental failures, some air pollution measurements obtained from these stations are found to have missing values, which will adversely affect the accuracy of any follow-up air pollution analyses and the quality of environmental decision-makings. In this study, the mathematical property of air quality measurements is investigated to recover the missing air pollution values. A new algorithm, which matches meteorology data with air pollution data from different locations, to reconstruct the data matrix and recover missing entries, is proposed. Next, a Low Rank Matrix Completion problem is used to reconstruct the missing values, by transforming the data recovery problem to a sub-gradient primal-dual problem, based on the duality theory, with Singular Value Thresholding (SVT) employed to develop sub-optimal solutions. Next, an Interpolation-SVT (ISVT) approach is adopted to handle the sparsity of observed measurements. Comprehensive case studies are conducted to evaluate the performance of the proposed methods. The simulation results have demonstrated that the proposed SVT and ISVT methods can effectively recover the missing air pollution data and outperform existing interpolation methods and data imputation techniques. The proposed study can improve air pollution estimation and prediction whenever the low-rank data types that are used as proxies for air pollution estimation contain a lot of missing values and require data recovery.

The Chebyshev method for the implied volatility

The implied volatility is a crucial element in any financial toolbox, since it is used to both quote and hedge options as well as for model calibration. In contrast to the Black–Scholes formula, its inverse, the implied volatility is not explicitly avail- able, and numerical approximation is required. In this paper, we propose a bivariate interpolation of the implied volatility surface based on Chebyshev polynomials. This yields a closed-form approximation of the implied volatility, which is easy to implement and to maintain. We prove a subexponential error decay. This allows us to obtain an accuracy close to machine precision with polynomials of a low degree. We compare the performance of our chosen method in terms of runtime and accuracy with the most common reference methods. In contrast to existing interpolation methods, our method is able to compute the implied volatility for all relevant option data. We use numerical experiments to confirm this results in a considerable increase in efficiency, especially for large data sets.

A generalized simple implicit interpolation scheme in CFD for non-conforming meshes

The non-conforming meshes are widely used in numerical simulations to solve complex flow problems and the key is to perform accurate and efficient interpolation between subdomains. This paper presents a generalized and simple implicit interpolation scheme at algebraic level for the coupling of non-conforming meshes in computational fluid dynamics (CFD). The final equations for most of numerical methods are always of an algebraic form and that is where the interpolation process is conducted. The substitution of dependent nodes with a linear combination of those in neighboring subdomains is imposed in algebraic equations to ensure continuity of variables. A simple reconstruction of the system matrix and right hand side is then executed which implements the reaction of the variable constraint of dependent nodes on replacing ones and maintains the properties of algebraic system. In other words, the proposed interpolation scheme can be regarded as a Dirichlet/Neumann condition performed on algebraic system implicitly. Compared with existing interpolation methods for non-conforming meshes, the new method escapes from the restraints of the type of problem, the form of grids, the discretization scheme and the solver. It also has advantages in simplicity and efficiency. Several benchmark problems were carried out to illustrate the accuracy of the proposed method.

An Efficient Machine-Learning Approach for PDF Tabulation in Turbulent Combustion Closure

ABSTRACT Probability density function (PDF) based turbulent combustion modeling is limited by the need to store multi-dimensional PDF tables that can take up large amounts of memory. A significant saving in storage can be achieved by using various machine-learning techniques that represent the thermo-chemical quantities of a PDF table using mathematical functions. These functions can be computationally more expensive than the existing interpolation methods used for thermo-chemical quantities. More importantly, the training time can amount to a considerable portion of the simulation time. In this work, we address these issues by introducing an adaptive training algorithm that relies on multi-layer perception (MLP) neural networks for regression and self-organizing maps (SOMs) for clustering data to tabulate using different networks. The algorithm is designed to address both the multi-dimensionality of the PDF table as well as the computational efficiency of the proposed algorithm. SOM clustering divides the PDF table into several parts based on similarities in data. Each cluster of data is trained using an MLP algorithm on simple network architectures to generate ‘local’ functions for thermo-chemical quantities. The algorithm is validated for the so-called DLR-A turbulent jet diffusion flame using both RANS and LES simulations and the results of the PDF tabulation are compared to the standard linear interpolation method. The comparison yields a very good agreement between the two tabulation techniques and establishes the MLP-SOM approach as a viable method for PDF tabulation.

Simultaneous interpolation and denoising based on a modified thresholding method

Seismic interpolation can provide complete data for some multichannel processing techniques such as time lapse imaging and wave equation migration. However, field seismic data often contains random noise and noisy data interpolation is a challenging task. A traditional method applies interpolation and denoising separately, but this needs two workflows. Simultaneous interpolation and denoising combines interpolation and denoising in one workflow and can also get acceptable results. Most existing interpolation methods can only recover missing traces but fail to attenuate noise in sampled traces. In this study, a novel thresholding strategy is proposed to remove the noise in the sampled traces and meanwhile recover missing traces during interpolation. For each iteration, the residual is multiplied by a weighting factor and then added to the iterative solution, after which the sum in the transformed domain is calculated using the thresholding operation to update the iterative solution. To ensure that the interpolation and denoising results are robust, the exponential method was chosen to reduce the threshold values in small quantities. The curvelet transform was used as sparse representation and three interpolation methods were chosen as benchmarks. Three numerical tests results proved the effectiveness of the proposed method on removing noise in the sampled traces when the minimum threshold values are correctly chosen.

Onboard satellite visibility prediction using metamodeling based framework

Satellite autonomous systems are employed to address complex space applications through onboard data processing and mission planning. To take advantage of onboard autonomous systems, rapid onboard satellite visibility predictions are necessary for certain decision-making missions, including Earth observation resource allocation and satellite data transmission. We consider this visibility prediction process as a roots-finding problem for a multiple hump function, and design a metamodeling-based framework with a self-adaptive interpolation method. Metamodels are developed as surrogates for visibility prediction functions to reduce expensive computational costs. Our proposed framework has a broad range of applications for all orbital types and orbit propagators. We conduct the experiments using different metamodeling techniques, radial basis functions, Kriging, and support vector regression based upon real China's satellites. Numerical simulations indicate that the proposed framework outperforms existing interpolation methods, efficiently reducing the onboard computational cost.

Response simulating interpolation methods for expanding experimental data based on numerical shape functions

An important issue in the existing interpolation methods is that their estimation accuracy usually cannot satisfy the analytical demand to expand experimental data, especially in the case of a few sample points, due to the essential deficiency of physical significance. To address the issue, this study presents an innovative category of interpolation methods which integrates the interpolation with the simulated response characteristics of experimental model. And two specific ones are proposed: the ordinary response simulating method (ORS) and the derivative response simulating method (DRS). ORS takes numerical shape functions simulated by a mechanical model as weighting functions based on general interpolation formula. DRS introduces the simulated model response as a priori estimate of response field, leading to the improvement of interpolation accuracy. Moreover, the two methods are verified through a quasi-real model considering randomness of both load and model defect as well as nonlinearities of material and geometry. It shows that DRS is usually more precise while ORS is more universal as the utilization of model information to different degrees. In sum, both demonstrate their excellent estimation performance and broad development prospects as a new category of interpolation methods.

Deep-Neural-Network-Based Sinogram Synthesis for Sparse-View CT Image Reconstruction

Recently, a number of approaches to low-dose computed tomography (CT) have been developed and deployed in commercialized CT scanners. Tube current reduction is perhaps the most actively explored technology with advanced image reconstruction algorithms. Sparse data sampling is another viable option to the low-dose CT, and sparse-view CT has been particularly of interest among the researchers in CT community. Since analytic image reconstruction algorithms would lead to severe image artifacts, various iterative algorithms have been developed for reconstructing images from sparsely view-sampled projection data. However, iterative algorithms take much longer computation time than the analytic algorithms, and images are usually prone to different types of image artifacts that heavily depend on the reconstruction parameters. Interpolation methods have also been utilized to fill the missing data in the sinogram of sparse-view CT thus providing synthetically full data for analytic image reconstruction. In this work, we introduce a deep-neural-network-enabled sinogram synthesis method for sparse-view CT, and show its outperformance to the existing interpolation methods and also to the iterative image reconstruction approach.

Effective coal seam surface modeling with an improved anisotropy-based, multiscale interpolation method

A reliable coal seam model is highly significant for mining design and resource assessment. However, due to the anisotropic nature of geological attributes, accurately modeling the surface using existing interpolation methods is difficult. Here, we propose a new method for coal seam surface modeling. First, we introduce a multiscale interpolation method using compactly supported radial basis functions (CSRBFs) and improve the modeling accuracy by anisotropy calculations using the raw mine data set. Then a fault modeling method is provided to simulate faults intersecting with coal seams. This method consists of three main parts: (1) anisotropy calculation to alleviate the effects of global anisotropy; (2) rapid coal seam surface modeling of large amounts of nonuniform data through an anisotropic multiscale CSRBF method and then visualization and organization of the surface into a triangulated irregular network (TIN); and (3) local reconstruction of the coal seam surface according to the faults. A prototype system was developed based on this method to build a coal seam model from the collected multisource coal seam data. A comparison with three existing interpolation methods shows that this method is feasible and time efficient and achieves higher accuracy than previous methods. We anticipate that the method can provide a reference for advances in digital and smart mines as well as 3D geological modeling.

Image enhancement for computed tomography using directional interpolation for sparsely-sampled sinogram

This paper presents an image enhancement for computed tomography (CT) using a directional sparsely-sampled sinogram interpolation. In CT scanning, radiation exposure to human tissues needs to be minimized. Naturally reducing radiation dose has been discussed in various approaches. Among them, a sparsely-sampled sinogram is an effective approach to minimize radiation dose itself in CT scanning. However, less radiation in CT scanning provide a poor image quality since reconstructed images suffer from the streak artifact due to lack of X-ray views. To reduce the streak artifact, an efficient sinogram interpolation method needs to be studied. In this paper, to enhance image quality, we propose a novel sinogram interpolation based on directional information. To do this, a directional interpolation from deinterlacing is introduced and applied to sinogram interpolation efficiently. To evaluate the proposed method, experiments with a simulated phantom and clinical CT images are carried out. The results indicate that the proposed sinogram interpolation method outperforms the existing interpolation methods in terms of image quality.

Radon-domain interferometric interpolation for reconstruction of the near-offset gap in marine seismic data

In towed marine seismic data acquisition, a gap between the source and the nearest recording channel is typical. Therefore, extrapolation of the missing near-offset traces is often required to avoid unwanted effects in subsequent data processing steps. However, most existing interpolation methods perform poorly when extrapolating traces. Interferometric interpolation methods are one particular method that have been developed for filling in trace gaps in shot gathers. Interferometry-type interpolation methods differ from conventional interpolation methods as they utilize information from several adjacent shot records to fill in the missing traces. In this study, we aim to improve upon the results generated by conventional time-space domain interferometric interpolation by performing interferometric interpolation in the Radon domain, in order to overcome the effects of irregular data sampling and limited source-receiver aperture. We apply both time-space and Radon-domain interferometric interpolation methods to the Sigsbee2B synthetic dataset and a real towed marine dataset from the Baltic Sea with the primary aim to improve the image of the seabed through extrapolation into the near-offset gap. Radon-domain interferometric interpolation performs better at interpolating the missing near-offset traces than conventional interferometric interpolation when applied to data with irregular geometry and limited source-receiver aperture. We also compare the interferometric interpolated results with those obtained using solely Radon transform (RT) based interpolation and show that interferometry–type interpolation performs better than solely RT-based interpolation when extrapolating the missing near-offset traces. After data processing, we show that the image of the seabed is improved by performing interferometry-type interpolation, especially when Radon-domain interferometric interpolation is applied.

Spatial Copula Model for Imputing Traffic Flow Data from Remote Microwave Sensors.

Issues of missing data have become increasingly serious with the rapid increase in usage of traffic sensors. Analyses of the Beijing ring expressway have showed that up to 50% of microwave sensors pose missing values. The imputation of missing traffic data must be urgently solved although a precise solution that cannot be easily achieved due to the significant number of missing portions. In this study, copula-based models are proposed for the spatial interpolation of traffic flow from remote traffic microwave sensors. Most existing interpolation methods only rely on covariance functions to depict spatial correlation and are unsuitable for coping with anomalies due to Gaussian consumption. Copula theory overcomes this issue and provides a connection between the correlation function and the marginal distribution function of traffic flow. To validate copula-based models, a comparison with three kriging methods is conducted. Results indicate that copula-based models outperform kriging methods, especially on roads with irregular traffic patterns. Copula-based models demonstrate significant potential to impute missing data in large-scale transportation networks.