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A traditional grid model for soil sampling may suffer from poor efficiency and low accuracy. With a nonferrous metal processing plant as the study area, a three-dimensional kriging interpolation model was built based on this plant's preliminary investigation data for arsenic (As), and a detailed survey sampling programme was proposed. The sampling density at the pollution interval of the surface soil was estimated by the coefficient of variation method, and the sampling depth was determined by the pollution interval of the vertical prediction results. The results showed that the encrypted soil sampling distribution optimisation method obtains greater pointing accuracy with fewer points. The sampling accuracy was 87.62% after optimising the depth of pointing. Moreover, this approach could save 66.13% of the sampling costs and 56.93% of the testing costs compared to a full deployment programme. This study provides a new and cost-effective method for predicting the extent of contamination exceedance at a site and provides valuable information to guide post-remediation strategies for contaminated sites.

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Intense industrial activities and complex hydrogeological conditions at contaminated sites make accurate three-dimensional (3D) mapping challenging. The cause is the non-stationarity in the variance of soil pollutants in geographical space (G-space), making the stationary hypothesis required by the Kriging method unsatisfactory. To handle the variance non-stationarity, a Variance-Octree-Kriging (VOK) method was proposed. VOK is a spatial deformation method that constructs a stationary deformation space (D-space) by stretching and shrinking the G-spaces with low and high spatial correlation, respectively. VOK method consists of 3D stratification in G-space, space scaling and transformation, and ordinary Kriging (OK) in D-space. 3D stratification uses variance octree (VOT) to generate a set of anchor points in the G-space. The spatial scaling and transformation use the virtual force algorithm (VFA) and thin-plate spline to evenly distribute the anchor points and obtain the D-space, where the OK is implemented. The method was applied to predict the distribution of soil Benzo(a)pyrene (BaP) at a contaminated site in North China Plain. The results show that the interpolation accuracy of VOK was 9% higher than that of OK. The VOK method also changed the spatial structure from anisotropic to isotropic. The root mean squared error (RMSE) of fill, silt and clay layers decreased by 4.67%, 11.39%, and 20.46%, respectively. This method is applicable to the 3D interpolation of pollutants at contaminated sites, with the advantages of high interpolation accuracy and the ability to handle the non-stationarity in variance.

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Breast cancer is one of the life-threatening cancers occurring in women. In recent years, from the surveys provided by various medical organizations, it has become clear that the mortality rate of females is increasing owing to the late detection of breast cancer. Therefore, an automated algorithm is needed to identify the early occurrence of microcalcification, which would assist radiologists and physicians in reducing the false predictions via image processing techniques. In this work, we propose a new algorithm to detect the pattern of a microcalcification by calculating its physical characteristics. The considered physical characteristics are the reflection coefficient and mass density of the binned digital mammogram image. The calculation of physical characteristics doubly confirms the presence of malignant microcalcification. Subsequently, by interpolating the physical characteristics via thresholding and mapping techniques, a three-dimensional (3D) projection of the region of interest (RoI) is obtained in terms of the distance in millimeter. The size of a microcalcification is determined using this 3D-projected view. This algorithm is verified with 100 abnormal mammogram images showing microcalcification and 10 normal mammogram images. In addition to the size calculation, the proposed algorithm acts as a good classifier that is used to classify the considered input image as normal or abnormal with the help of only two physical characteristics. This proposed algorithm exhibits a classification accuracy of 99%.

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Standard 3D interpolation polynomials often suffer from numerical errors of the calculated field and lack of node points in the 3D solution. We introduce a novel method for accurate and smooth interpolation of arbitrary electromagnetic fields in the vicinity of the optical axis valid up to 90% of the bore radius. Our method combines Fourier analysis and Gaussian wavelet interpolation and provides the axial multipole field functions and their derivatives analytically. The results are accurate and noiseless, usually up to the 5th derivative. This is very advantageous for further applications, such as accurate particle tracing, and evaluation of aberration coefficients and other optical properties. The proposed method also enables studying the strength and orientation of all multipole field components. To illustrate the capabilities of the proposed algorithm, we present three examples: a magnetic lens with a hole in the polepiece, a saturated magnetic lens with an elliptic polepiece, and an electrostatic 8-electrode multipole.

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Medical image three-dimensional (3D) interpolation is an important means to improve the image effect in 3D reconstruction. In image processing, the time-frequency domain transform is an efficient method. In this article, several time-frequency domain transform methods are applied and compared in 3D interpolation. And a Sobel edge detection and 3D matching interpolation method based on wavelet transform is proposed. We combine wavelet transform, traditional matching interpolation methods, and Sobel edge detection together in our algorithm. What is more, the characteristics of wavelet transform and Sobel operator are used. They deal with the sub-images of wavelet decomposition separately. Sobel edge detection 3D matching interpolation method is used in low-frequency sub-images under the circumstances of ensuring high frequency undistorted. Through wavelet reconstruction, it can get the target interpolation image. In this article, we make 3D interpolation of the real computed tomography (CT) images. Compared with other interpolation methods, our proposed method is verified to be effective and superior.

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OBJECTIVE: In this paper we introduce a new interpolation method to use for scalp potential interpolation. The predictive value of this new interpolation technique (the multiquadric method) is compared to commonly used interpolation techniques like nearest-neighbour averaging and spherical splines. METHODS: The method of comparison is cross-validation, where the data of one or two electrodes is predicted by the rest of the data. The difference between the predicted and the measured data is used to determine two error measures. One is the maximal error in one interpolation technique and the other is the mean square error. The methods are tested on data stemming from 30 channel EEG of 10 healthy volunteers. RESULTS: The multiquadric interpolation methods performed best regarding both error measures and have been easier to calculate than spherical splines. CONCLUSION: Multiquadrics are a good alternative to commonly used EEG reconstruction methods. SIGNIFICANCE: Multiquadrics have been widely used in reconstruction on sphere-like surfaces, but until now, the advantages have not been investigated in EEG reconstruction.

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