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Sometimes observations in statistical analysis are not independent and typically are correlated with their spatial locations. In spatial statistics there are some methods to interpolate this kind of data. In this paper some of interpolators for spatial data will be studied. Then they will be evaluated and compared by means of mean square errors criteria. Finally it will be shown that kriging acts better than other methods such as spline, inverse distance, for interpolation of spatial data.

In this paper we consider multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have concentric spheres. Indeed, we consider the problem in three variables when it is not correct.

Image zooming is one of the important issues of image processing that maintains the quality and structure of image. Zooming an image necessitates placing the extra pixels in the image data. Moreover, adding the data to the image must be consistent with the texture in the image in order to prevent artificial blocks. In this study, the required pixels are estimated using barycentric rational interpolation. The proposed method is a non-linear one which can preserve the edges and reduces the blur and block artifacts on the zoomed image. Numerical results are presented using PSNR and SSIM fidelity measures and they are compared to some other methods. The average PSNR of the original image and image zooming was 33. 08 which can prove that image zooming is very similar to the original image. The experimental results reveal that the proposed method has a better performance compared to other methods and can provide good image quality.