Accurate Interpolation Method Research Articles

A comparison of interpolation methods to predict chill accumulation in a Mediterranean stone fruit production area (Región de Murcia, SE Spain)

One of the most important agroclimatic variables for stone fruit production is winter chill accumulation. To estimate chill accumulation in locations where climatic data is not recorded, spatial interpolation is necessary. In this study, we compare different interpolation methods for mean and Safe Winter Chill (SWC) in a Mediterranean stone fruit production area (Region of Murcia, SE Spain) using data from 49 climatic stations. To choose the most accurate interpolation method, as its choice may substantially influence the prediction accuracy, the predictive capability of several interpolation methods with different parameterizations (for a total number of 32 instances) was compared through out-of-bag bootstrap cross-validation, concluding that the best ones were Radial Basis Functions applied on the altitude-dependent regression residuals for mean winter chill and the altitude+latitude linear regression for SWC. The incorporation of altitude in the interpolation increased greatly the accuracy of the estimation. In fact, most of the chill accumulation spatial dependency was explained through altitude. The accuracy of the interpolation was not homogeneous across the study area. Chill accumulation in warmer coastal localities was overestimated by all the methods, possibly due to the proximity to the sea, highlighting the importance of microclimatic variables at higher-resolution spatial interpolations. Differences between methods were more notable in higher locations, where distance-only based methods underestimated chill accumulation and methods that consider altitude slightly overestimated it. This study demonstrates the importance of comparing the performance of multiple spatial interpolation methods before applying any for chill accumulation data.

Limited Sampling Spatial Interpolation Evaluation for 3D Radio Environment Mapping.

The increasing densification and diversification of modern and upcoming wireless networks have become an important motivation for the development of agile spectrum sharing. Radio environment maps (REMs) are a basic tool for spectrum utilisation characterisation and adaptive resource allocation, but they need to be estimated through accurate interpolation methods. This work evaluated the performance of two established algorithms for spatial three-dimensional (3D) data collected in two real-world scenarios: indoors, through a mechanical measuring system, and outdoors, through an unmanned aerial vehicle (UAV) for measurement collection. The investigation was undertaken for the complete dataset on two-dimensional (2D) planes of different altitudes and for a subset of limited samples (representing the regions of interest or RoIs), which were combined together to describe the spatial 3D environment. A minimum error of -9.5 dB was achieved for a sampling ratio of 21%. The methods' performance and the input data were analysed through the resulting Kriging error standard deviation (STD) and the STD of the distances between the measurement and the estimated points. Based on the results, several challenges for the interpolation performance and the analysis of the spatial RoIs are described. They facilitate the future development of 3D spectrum occupancy characterisation in indoor and UAV-based scenarios.

Neural network-based emulation of interstellar medium models

Context. The interpretation of observations of atomic and molecular tracers in the galactic and extragalactic interstellar medium (ISM) requires comparisons with state-of-the-art astrophysical models to infer some physical conditions. Usually, ISM models are too timeconsuming for such inference procedures, as they call for numerous model evaluations. As a result, they are often replaced by an interpolation of a grid of precomputed models. Aims. We propose a new general method to derive faster, lighter, and more accurate approximations of the model from a grid of precomputed models for use in inference procedures. Methods. These emulators are defined with artificial neural networks (ANNs) with adapted architectures and are fitted using regression strategies instead of interpolation methods. The specificities inherent in ISM models need to be addressed to design and train adequate ANNs. Indeed, such models often predict numerous observables (e.g., line intensities) from just a few input physical parameters and can yield outliers due to numerical instabilities or physical bistabilities and multistabilities. We propose applying five strategies to address these characteristics: (1) an outlier removal procedure; (2) a clustering method that yields homogeneous subsets of lines that are simpler to predict with different ANNs; (3) a dimension reduction technique that enables us to adequately size the network architecture; (4) the physical inputs are augmented with a polynomial transform to ease the learning of nonlinearities; and (5) a dense architecture to ease the learning of simpler relations between line intensities and physical parameters. Results. We compare the proposed ANNs with four standard classes of interpolation methods, nearest-neighbor, linear, spline, and radial basis function (RBF), to emulate a representative ISM numerical model known as the Meudon PDR code. Combinations of the proposed strategies produce networks that outperform all interpolation methods in terms of accuracy by a factor of 2 in terms of the average error (reaching 4.5% on the Meudon PDR code) and a factor of 3 for the worst-case errors (33%). These networks are also 1000 times faster than accurate interpolation methods and require ten to forty times less memory. Conclusions. This work will enable efficient inferences on wide-field multiline observations of the ISM.

Temporal and Spatial Analysis of Rainfall and Evapotranspiration in Erbil Plain and the Peripheral Areas

Since analysis of spatial events is region specific and cannot be generalized, local studies are of vital importance to identify the most accurate interpolation methods. Furthermore, the trend analysis of climatic parameters at different time scales is helpful for making a better climate change adaptation and mitigation plan to overcome water scarcity. Accordingly, the current study was proposed to detect trends in rainfall and evapotranspiration at monthly and annual time scales over the Erbil plain and the surrounding area using parametric and non-parametric tests. Moreover, four deterministic and five geostatistical methods were evaluated for searching the best interpolation method to generate a continuous surface for the indicated climatic variables. The results revealed that the majority of data sets are categorized useful class and serially independent. Furthermore, it was found both rainfall and potential evapotranspiration have a mix of upward and downward trends and most of them are insignificant at 5% level of significance. Further, the interpolation analysis indicated that local polynomial interpolation (LPI) method was proven to be best interpolator for generating continuous surfaces for rainfall and ETo over the area under study followed by the empirical Bayesian Kriging method.

4-dimensional local radial basis function interpolation of large, uniformly spaced datasets

Background and ObjectiveLarge, uniformly spaced, complex and time varying datasets derived from high resolution medical image velocimetry can provide a wealth of information regarding small-scale transient physiological flow phenomena and pulsation of anatomical boundaries. However, there remains a need for interpolation techniques to effectively reconstruct a fully 4-dimensional functional relationship from this data. This paper presents a preliminary evaluation of a 4-dimensional local radial basis function (RBF) algorithm as a means of addressing this problem for laminar flows. MethodsA 4D interpolation algorithm is proposed based on a Local Hermitian Interpolation (LHI) using a combination of multi-quadric RBF with a partition of unity scheme. The domain is divided into uniform sub-systems with size restricted to immediately neighbouring points. The validity of the algorithm is first established on a known 4D analytical dataset and a CFD based laminar flow phantom. Application is then demonstrated through characterisation of a large 4D laminar flow dataset obtained from magnetic resonance imaging (MRI) measurements of cerebrospinal fluid velocities in the brain. ResultsPerformance of the algorithm is compared to that of a quad-linear interpolation, demonstrating favourable improvement in accuracy. The technique is shown to be robust, computationally efficient and capable of refined interpolation in Euclidean space and time. Application to MR velocimetry data is shown to produce promising results for the 4D reconstruction of the transient flow field and movement of the fluid boundaries at spatial and temporal locations intermediate to the original data. ConclusionThis study has demonstrated feasibility of an accurate, stable and efficient 4-dimensional local RBF interpolation method for large, transient laminar flow velocimetry datasets. The proposed approach does not suffer from ill-conditioning or high computational cost due to domain decomposition into local stencils where the RBF is only ever applied to a limited number of points. This work offers a potential tool to assist medical diagnoses and drug delivery through better understanding of physiological flow fields such as cerebrospinal fluid. Further work will evaluate the technique on a wider range of flow fields and against CFD simulation.

An efficient and accurate interpolation method for parametric curve machining.

A subsection interpolation method based on the curve curvature threshold is proposed to resolve the incompatible problem of machining accuracy and machining efficiency in parametric curve machining. In the pre-interpolation stage, the curve curvature threshold is calculated based on geometric and kinematic constraints. The subsection interpolation key points and their nominal velocities are then determined from the curvature threshold points and the start and end points of the curve, and the arc length of each subsegment can be calculated based on the adaptive Simpson method. As a result, the S-type speed planning algorithm and the bidirectional speed scanning algorithm are used to update and realize the global speed curve to reduce the speed fluctuation. In the real-time interpolation stage, the curve interpolation parameters are calculated using the parametric modified second-order Runge–Kutta method, which could improve the interpolation accuracy significantly and also shorten the interpolation time. Finally, it is found using numerical cases that the proposed method can smooth the overall interpolation speed, reduce the speed fluctuation effectively and improve the real-time performance of the interpolation.

Mapping Soil Properties at a Regional Scale: Assessing Deterministic vs. Geostatistical Interpolation Methods at Different Soil Depths

To determine which interpolation technique is the most suitable for each case study is an essential task for a correct soil mapping, particularly in studies performed at a regional scale. So, our main goal was to identify the most accurate method for mapping 12 soil variables at three different depth intervals: 0–5, 5–10 and >10 cm. For doing that, we have compared nine interpolation methods (deterministic and geostatistical), drawing soil maps of the Spanish region of Extremadura (41,635 km2 in size) from more than 400 sampling sites in total (e.g., more than 500 for pH for the depth of 0–5 cm). We used the coefficient of determination (R2), the mean error (ME) and the root mean square error (RMSE) as statistical parameters to assess the accuracy of each interpolation method. The results indicated that the most accurate method varied depending on the property and depth of study. In soil properties such as clay, EBK (Empirical Bayesian Kriging) was the most accurate for 0–5 cm layer (R2 = 0.767 and RMSE = 3.318). However, for 5–10 cm in depth, it was the IDW (Inverse Distance Weighted) method with R2 and RMSE values of 0.689 and 5.131, respectively. In other properties such as pH, the CRS (Completely Regularized Spline) method was the best for 0–5 cm in depth (R2 = 0.834 and RMSE = 0.333), while EBK was the best for predicting values below 10 cm (R2 = 0.825 and RMSE = 0.399). According to our findings, we concluded that it is necessary to choose the most accurate interpolation method for a proper soil mapping.

A GIS-Based Hydrogeological Approach to the Assessment of the Groundwater Circulation in the Ischia Volcanic Island (Italy)

Assessing the variations in space and time of groundwater circulation in volcanic islands is of paramount importance to the description of the hydro-geo-thermal system and implementation of hydrogeological, geochemical, and volcanic monitoring systems. In fact, the reliable reconstruction of the groundwater potentiometric surface in such composite volcanic aquifer systems can enable the identification of the most advantageous strategies for both the sustainable use of groundwater resources and the management of volcanic risk. Geographical Information System (GIS) platforms can support the integration and analysis of many spatial and temporal variables derived from monitoring of active volcanoes and the elaboration of spatially continuous data. However, open issues still affect the reliability and general applicability of common spatial interpolation methods in the case of groundwater potentiometric surfaces. This is related to the assessment of the main stratigraphic and volcano-tectonic features affecting the hydraulic head changes. With regard to the dynamically very active Ischia Island (Italy), this study illustrates a GIS-based hydrogeological approach to identify the most accurate interpolation method for mapping the potentiometric surface in complex hydrogeological terrains. The proposed approach has been applied to the existing dataset (1977–2003) stored by Istituto Nazionale di Geofisica e Vulcanologia. Based on a careful geological and hydrogeological survey, a total of 267 wells, from 5 to 250 m in depth, were processed. The data pre-processing involved four meteorological time-series data (1922–1997) and six long records of piezometric water levels (1930–1994). As a result, knowledge of the delineation of rather homogeneous stratigraphic and volcano-tectonic structures at the basin-scale has improved. Thus, new, more reliable potentiometric surfaces of the four main geothermal areas closest to the coast were produced during both dry and wet seasons. The reliability of the processed potentiometric surface was then validated by comparing the spatially continuous data with complementary field data. These findings point toward an optimal interpolation approach for representing the seasonal and areal distribution of main hydrogeological parameters in complex aquifer systems. Finally, insights into variations of hydrological behavior at an active volcanic area will foster an understanding of possible involvement of fresh and thermal waters in triggering phreatic explosions.

Spatial analysis of the particulate matter (PM10) an assessment of air pollution in the region of Madrid (Spain): spatial interpolation comparisons and results

ABSTRACT This paper reports a comparison of different spatial and statistical models to predict the concentrations of the particulate matter (PM10), measured by the environmental stations of the Community of Madrid (Spain). Three methods were compared: Inverse Distance Weighting (IDW), Ordinary Kriging (OK) and Empirical Bayesian Kriging (EBK). The most accurate spatial interpolation method was the EBK. An interpolation map obtained by applying the EBK geostatistical method is presented to identify the areas with the highest pollution of PM10.]

Assessing the use of ERA5-Land reanalysis and spatial interpolation methods for retrieving precipitation estimates at basin scale

Precipitation data availability plays a crucial role in many climatic, hydrological and agricultural-related applications. In this study, the use of alternative data sources (i.e. interpolation methods and ERA5-Land reanalysis data) was combined for improving the spatially distributed precipitation estimates at the Simeto river basin, located in Eastern Sicily (Italy). A total of 51 rain gauges were used to generate a monthly precipitation dataset for the reference period 2002–2019. Among the 6 tested interpolation methods, Natural Neighbour was the method that predicted precipitation the best at monthly level with a Distance between Indices of Simulation and Observation (DISO) of 0.51. Radial Basis Functions and Inverse Distance Weighting provided the highest precipitation accuracies, respectively, for winter and autumn (with DISO values of 0.44 and 0.50, respectively), and for spring and summer seasons (with DISO values of 0.50 and 0.63, respectively). Underestimations on the ERA5-Land precipitation estimates were observed when compared to the most accurate interpolation methods both at monthly (25%) and seasonal temporal scales (21% in winter and summer, 36% in autumn), with the exception for spring. The performance was significantly improved when the interpolation estimates were corrected with local observations (with RMSD values ranging from 35.29 mm to 26.46 mm at monthly scale, and from 23.33–55.34 mm to 23.15–37.88 mm at seasonal level). The spatial distribution of the estimation errors associated to precipitation obtained from ERA5-Land reanalysis revealed a significant positive correlation (p value <0.05) with the altitude variation in each ERA5-Land cell within the basin under study. These results confirm the good performance on the combined use of alternative precipitation data sources, while adjustments are required to reduce site-specific uncertainties due to local microclimatic conditions occurring at the basin scale.

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.

Картографирование магнитной восприимчивости почв г. Чайковский

The article presents the results of an assessment of the heterogeneity of the volumetric magnetic susceptibility of soils in the city of Chaikovsky, Perm Territory, based on the results of its spatial modeling. Determination of magnetic susceptibility makes it possible to estimate the concentration of technogenic magnetic particles in urban soils. Their sources in the atmosphere and soil cover of urbanized landscapes are emissions from vehicles, thermal power plants, and industrial enterprises. The non-stoichiometric technogenic magnetite-maghemite complex of minerals in urban soils has an abnormally high magnetic susceptibility and contains potentially dangerous chemical elements belonging to the heavy metals (HM) group in the composition of the crystal lattice of magnetic particles. Cartographic materials make it possible to assess the environmental risk for city residents, identify unfavorable areas and conduct a spatial analysis of the relationship between their location and pollution sources. The purpose of the research is spatial modeling of the magnetic susceptibility of soils in the city of Chaikovsky. The research area covers a section of the city with a total area of 22 km². Spatial modeling was carried out using geostatistical and deterministic methods based on 140 points. As a result of cross-validation, it was found that the most accurate interpolation method is “Ordinary Kriging” with the help of which the boundaries of the contaminated areas of the city of Chaikovsky are established. Within these boundaries, soil samples were taken, in which the content of nickel, copper, zinc, and lead was determined. According to the data obtained, areas with high magnetic susceptibility of soils have higher concentrations of heavy metals. To bring the research results to the administration and residents of the city, a Web GIS application has been developed, access to which is organized through the GitHub platform.

Simultaneous estimation of projector and camera poses for multiple oneshot scan using pixel-wise correspondences estimated by U-Nets and GCN

ABSTRACT Dense and accurate 3D shape acquisition of objects by active-stereo technique has been an important research topic and intensively researched. One of the promising fields for active-stereo techniques is medical applications, such as 3D endoscope systems. In such systems, since a sensor is dynamically moved during the operation, single-frame shape reconstruction, a.k.a. oneshot scan, is necessary. For oneshot scan, there are several open problems, such as low resolution because of spatial coding, and unstable correspondence estimation between the detected patterns and the projected pattern because of irregular reflection. In this paper, we propose a solution for those problems. To increase the resolution, an accurate and stable interpolation method based on deep neural networks (DNNs) is proposed. Since most patterns used for oneshot scan are periodic, pixel-wise phase estimation can be achieved by detecting repetition in the pattern. A graph convolutional network (GCN), which is a deep neural network for graphs, is used for the correspondence problem. In the experiment, pixel-wise shape reconstruction results, as well as robust correspondence estimation using DNNs and a GCN, are shown. In addition, the effectiveness of the techniques is confirmed by comparing the proposed method with existing methods.

An assessment of statistical interpolation methods suited for gridded rainfall datasets

AbstractAccurate spatial distribution information of rainfall is essential to rainfall‐induced hazard predictions and statistical interpolation methods may serve as a useful tool to produce a detailed distribution from coarse data sources. Although numerous comparison studies about different interpolation methods have been conducted on irregular rain‐gauge networks, there is a need to perform such work on the increasingly available gridded rainfall data. Carried out in the Emilia‐Romagna region (Italy) from 2008 to 2018, this study aims to examine accurate and appropriate interpolation methods to produce finer rainfall surface maps based on the 0.25° × 0.25° ERA5 gridded precipitation datasets. Five interpolation techniques, namely Thiessen polygons, Inverse Distance Weighting (IDW), Thin Plate Spline (TPS), Ordinary Kriging (OK) and ordinary Co‐Kriging (CoK), have been selected and compared at different time scales (annual, monthly and annual maximum daily precipitation). To assess the accuracy, the leave‐one‐out‐cross‐validation test was used by using the indexes of Bias, correlation coefficient, the Nash‐Sutcliffe Efficiency, Root Mean Square Error and the Kling‐Gupta Efficiency (KGE). Additionally, visual inspections are employed to evaluate the plausibility of the interpolated maps. Results show: (a) All five interpolation methods have certain capabilities to improve spatial resolution, but they fail on accuracy at the daily scale. The OK generally outperforms the other four methods, while TPS shows better performance through the visual inspection at the monthly scale; (b) Unlike in the case of the interpolation using conventional point‐based rain‐gauge data, the multivariate method CoK is inferior to the univariate ones and the p‐power of the IDW also differs and (c) Winter and spring results are better than those of summer and autumn. This study has provided useful guidance on choosing suitable rainfall interpolation methods for gridded datasets, which can be expanded in other regions and data sources to explore the generality of the conclusions.

Scattered data interpolation: Strictly positive definite radial basis/cardinal functions

Radial basis functions are a simple and accurate method for multivariate interpolation but the ill-conditioning situation due to their interpolation matrices, discourages an acceptable approximation for both large number of nodes or flat function interpolation. In current work, a new type of basis named well-conditioned RBFs (WRBFs) was created by adding the strictly positive definite Radial Basis Functions (SPD-RBFs) to cardinal functions, was introduced and applied for interpolation. To light up this manner, two classes of global cardinal functions were used for adding by SPD-RBFs. These cardinal functions are Shepard functions and Quasi-cardinal RBFs. Theoretical and numerical analyses prove that utilizing WRBFs has some advantages such as eliminating the ill-conditioning system which has arisen from the global positive definite RBFs interpolation, improving the convergence of pure cardinal functions interpolation and also working better than pure RBFs for small shape parameters.

Accurate interpolation methods for the annual simulation of solar central receiver systems using celestial coordinate system

Heliostat field layout optimization bases on simulations of the annual energy production. To reduce the computation time of the optimization process, one can try to reduce the number of simulation points of the annual domain, while keeping similar accuracy. For the temporal domain, there exist already different approaches as aggregation of days. To further reduce the number of needed simulation points, in this paper we decouple the power computation from the irradiation, such that we just regard the computation of the power plant efficiency. This time-dependent parameter is transformed into a celestial coordinate system where the solar angle-dependent efficiency will be approximated using suitable multi-dimensional interpolation methods.We distinguish between an accurate approximation of the received annual optical energy and the electrical energy of each moment of a year. These methods are demonstrated for the existing heliostat field layouts PS10 and Gemasolar in Seville, while using realistic weather conditions. With this new approach just around 40 simulation points suffice to reach an accuracy of 99.9% for the received power for smaller power plants as PS10, and for larger plants as Gemasolar. Compared to a state-of-the-art method, this investigation helps to accelerate the simulation by factor three.

Spatial variability of soil Cd content based on IDW and RBF in Fujiang River, Mianyang, China

Establishing the spatial distribution of soil properties in agro-ecosystems is critical to increasing the productivity of intensive tillage soils and reducing environmental pressure. Thus, a comprehensive understanding of soil’s heavy metal distribution characteristics is important for optimal management. The goal of this study was to determine the most accurate soil Cd interpolation method for the study area and analyze the variation and spatial distribution of Cd content with depth. In this work, we employed two common spatial interpolation methods—inverse distance weighting (IDW) and radial basis function (RBF)—in conjunction with a geographic information system (GIS) to interpolate sampling data of the heavy metal cadmium (Cd) throughout Santai County; a locale in the lower part of Fujiang River, Mianyang, in the northeast of Sichuan Province. The results of our investigation are as follows. (1) At depths of 0–50 cm, the Cd content decreased with depth while the coefficient of variation (Cv) increased with depth. The exponential model and the Gauss model adequately described the Cd content’s spatial autocorrelation and the determination coefficient (R2) varied within 0.747–0.962, indicating that the model had high precision. (2) With respect to the accuracy of the IDW and RBF methods, IDW was more accurate than the RBF in the 0–20 cm soil layer, yet the reverse was found in the 20–50 cm soil layer. (3) Three-dimensional spatial distribution maps—constructed using the RBF and IDW methods at different soil depths—showed that the RBF method provided a greater smoothing effect than the IDW method. The spatial variability of soil Cd content shows that: (1) the Cd content’s spatial autocorrelation was strong in the 0–50 cm soil layer. (2) The IDW method is suitable for areas that are greatly influenced by human or farming activities while the RBF method is appropriate for areas that are greatly influenced by internal soil factors. The RBF is superior for evaluating the spatial distribution of soil Cd content in this area.

Efficient Triangular Interpolation Methods: Error Analysis and Applications

The interpolation errors of bivariate Lagrange polynomial and triangular interpolations are studied for the plane waves. The maximum and root-mean-square (rms) errors on the right triangular, equilateral triangular, and rectangular (bivariate Lagrange polynomial) interpolations are analyzed. It is found that the maximum and rms errors are directly proportional to the ( p + 1)th power of kh for both 1-D and (2-D, bivariate) interpolations, where k is the wavenumber and h is the mesh size. The interpolation regions for the right triangular, equilateral triangular, and rectangular interpolations are selected based on the regions with smallest errors. The triangular and rectangular interpolations are applied to evaluate the 2-D singly periodic Green's function. The numerical results show that the equilateral triangular interpolation is the most accurate interpolation method, whereas the right triangular interpolation is the most efficient interpolation method.

Error Analysis of Higher Order Bivariate Lagrange and Triangular Interpolations in Electromagnetics

The interpolation errors of the higher order bivariate Lagrange polynomial interpolation based on the rectangular, right and equilateral triangular interpolations are measured by using the maximum and root-mean-square (RMS) errors. The error distributions of above three kinds of interpolations are analyzed to find the regions having the smallest interpolation error. Both analytical and numerical results show that the right triangular interpolation is the most efficient interpolation method. Although both the maximum and RMS errors of the right triangular interpolation are larger than that of the rectangular interpolation, the number of data points used in the triangular interpolation is up to 50% less than that used in the rectangular one. On the other hand, the equilateral triangular interpolation using the regions inside a big triangle as interpolation area is proved to be the most accurate interpolation method. The interpolation errors of the equilateral triangular are almost half of that of the rectangular interpolation. In addition, the right triangular, equilateral triangular and rectangular interpolations for the third and fourth orders are applied to accelerate the calculation of doubly periodic Green's function (PGF).

Effects of Interpolation on the Inverse Problem of Electrocardiography.

Electrocardiographic Imaging (ECGI) aims to reconstruct electrograms from the body surface potential measurements. Bad leads are usually excluded from the inverse problem solution. Alternatively, interpolation can be applied. This study explores how sensitive ECGI is to different bad-lead configurations and interpolation methods. Experimental data from a Langendorff-perfused pig heart suspended in a human-shaped torso-tank was used. Epicardial electrograms were acquired during 30 s (31 beats) of RV pacing using a 108-electrode array, simultaneously with torso potentials from 128 electrodes embedded in the tank surface. Six different bad lead cases were designed based on clinical experience. Inverse problem was solved by applying Tikhonov regularization i) using the complete data, ii) bad-leads-removed data, and iii) interpolated data, with 5 different methods. Our results showed that ECGI accuracy of an interpolation method highly depends on the location of the bad leads. If they are in the high-potential-gradient regions of the torso, a highly accurate interpolation method is needed to achieve an ECGI accuracy close to using complete data. If the BSP reconstruction of the interpolation method is poor in these regions, the reconstructed electrograms also have lower accuracy, suggesting that bad leads should be removed instead of interpolated. The inverse-forward method was found to be the best among all interpolation methods applied in this study in terms of both missing BSP lead reconstruction and ECGI accuracy, even for the bad leads located over the chest.